重回帰を本当はPythonで解きたいけど表計算で解けと言われたので.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 用いるデータ\n",
    "\n",
    "<a href=\"http://mh.rgr.jp/memo/mq0111.htm\" target=\"_blank\">分子性物質のデータ（融点・沸点）</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent\n",
       "0        HF         19.500              20.0       1.826567\n",
       "1       HCl        -84.900              36.5       1.108600\n",
       "2       HBr        -67.000              80.9       0.827100\n",
       "3        HI        -35.100             127.9       0.447700\n",
       "4       H2O        100.000              18.0       1.854600\n",
       "5       H2S        -60.700              34.1       0.978325\n",
       "6      H2Se        -42.000              81.0       0.627000\n",
       "7       NH3        -33.400              17.0       1.471772\n",
       "8       PH3        -87.000              34.0       0.573970\n",
       "9      AsH3        -55.000              77.9       0.217000\n",
       "10     SbH3        -17.100             124.8       0.116000\n",
       "11      CH4       -161.490              16.0       0.000000\n",
       "12     SiH4       -111.800              32.1       0.000000\n",
       "13     GeH4        -90.000              76.6       0.000000\n",
       "14     SnH4        -52.000             122.7       0.000000\n",
       "15       He       -268.934               4.0       0.000000\n",
       "16       Ne       -246.048              20.2       0.000000\n",
       "17       Ar       -185.700              39.9       0.000000\n",
       "18       Kr       -152.300              83.8       0.000000\n",
       "19       Xe       -108.100             131.3       0.000000"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = [['HF', 19.5, 20.0, 1.826567],\n",
    "        ['HCl', -84.9, 36.5, 1.1086],\n",
    "        ['HBr', -67.0, 80.9, 0.8271],\n",
    "        ['HI', -35.1, 127.9, 0.4477],\n",
    "        ['H2O', 100.0, 18.0, 1.8546],\n",
    "        ['H2S', -60.7, 34.1, 0.978325],\n",
    "        ['H2Se', -42, 81.0, 0.627],\n",
    "        ['NH3', -33.4, 17.0, 1.471772],\n",
    "        ['PH3', -87, 34.0, 0.57397],\n",
    "        ['AsH3', -55, 77.9, 0.217],\n",
    "        ['SbH3', -17.1, 124.8, 0.116],\n",
    "        ['CH4', -161.49, 16.0, 0],\n",
    "        ['SiH4', -111.8, 32.1, 0],\n",
    "        ['GeH4', -90, 76.6, 0],\n",
    "        ['SnH4', -52, 122.7, 0],\n",
    "        ['He', -268.934, 4.0, 0],\n",
    "        ['Ne', -246.048, 20.2, 0],\n",
    "        ['Ar', -185.7, 39.9, 0],\n",
    "        ['Kr', -152.3, 83.8, 0],\n",
    "        ['Xe', -108.1, 131.3, 0],\n",
    "       ]\n",
    "df = pd.DataFrame(data, columns = ['molecule', 'boiling point', 'molecular weight', 'dipole monent'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    {
     "data": {
      "text/plain": [
       "array([[  2.00000000e+01,   1.82656700e+00],\n",
       "       [  3.65000000e+01,   1.10860000e+00],\n",
       "       [  8.09000000e+01,   8.27100000e-01],\n",
       "       [  1.27900000e+02,   4.47700000e-01],\n",
       "       [  1.80000000e+01,   1.85460000e+00],\n",
       "       [  3.41000000e+01,   9.78325000e-01],\n",
       "       [  8.10000000e+01,   6.27000000e-01],\n",
       "       [  1.70000000e+01,   1.47177200e+00],\n",
       "       [  3.40000000e+01,   5.73970000e-01],\n",
       "       [  7.79000000e+01,   2.17000000e-01],\n",
       "       [  1.24800000e+02,   1.16000000e-01],\n",
       "       [  1.60000000e+01,   0.00000000e+00],\n",
       "       [  3.21000000e+01,   0.00000000e+00],\n",
       "       [  7.66000000e+01,   0.00000000e+00],\n",
       "       [  1.22700000e+02,   0.00000000e+00],\n",
       "       [  4.00000000e+00,   0.00000000e+00],\n",
       "       [  2.02000000e+01,   0.00000000e+00],\n",
       "       [  3.99000000e+01,   0.00000000e+00],\n",
       "       [  8.38000000e+01,   0.00000000e+00],\n",
       "       [  1.31300000e+02,   0.00000000e+00]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df.loc[:, ['molecular weight', 'dipole monent']].as_matrix()\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  19.5  ,  -84.9  ,  -67.   ,  -35.1  ,  100.   ,  -60.7  ,\n",
       "        -42.   ,  -33.4  ,  -87.   ,  -55.   ,  -17.1  , -161.49 ,\n",
       "       -111.8  ,  -90.   ,  -52.   , -268.934, -246.048, -185.7  ,\n",
       "       -152.3  , -108.1  ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = df['boiling point'].as_matrix()\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ZleRz7QK0+qtkV6jGxYFE8UX6Ww3sVElGZnYF8AFgD+AAd38wTm8hWu1zL6Kl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10631f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas.tools.plotting import *\n",
    "scatter_matrix(df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# まずは一番便利な scikit-learn から"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.17775083,  124.38195483])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 回帰係数\n",
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-218.85778226168119"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 切片\n",
    "lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = f(x) = w1x1 + w2x2 + t; (w1, w2, t) = (1.1777508314139944, 124.38195482549655, -218.8577822616812)\n"
     ]
    }
   ],
   "source": [
    "print(\"y = f(x) = w1x1 + w2x2 + t; (w1, w2, t) = ({0}, {1}, {2})\".format(lr.coef_[0], lr.coef_[1], lr.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.78084985722905187"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 決定係数\n",
    "lr.score(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 78.88336143])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([200, 0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-42.19515755,  23.29925571])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([[150, 0], [100, 1.0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 次は、ガチPythonで。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 平均値を求める関数\n",
    "def mean(list):\n",
    "    sum = 0\n",
    "    for x in list:\n",
    "        sum += x\n",
    "    return sum / len(list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分散を求める関数\n",
    "def variance(list):\n",
    "    ave = mean(list)\n",
    "    sum = 0\n",
    "    for x in list:\n",
    "        sum += (x - ave) ** 2\n",
    "    return sum / len(list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 標準偏差を求める関数\n",
    "import math\n",
    "def standard_deviation(list):\n",
    "    return math.sqrt(variance(list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 共分散 = 偏差積の平均\n",
    "def covariance(list1, list2): \n",
    "    mean1 = mean(list1)\n",
    "    mean2 = mean(list2)\n",
    "    sum = 0\n",
    "    for d1, d2 in zip(list1, list2):\n",
    "        sum += (d1 - mean1) * (d2 - mean2)\n",
    "    return sum / len(list1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 相関係数 = 共分散を list1, list2 の標準偏差で割ったもの\n",
    "def correlation(list1, list2):\n",
    "    return covariance(list1, list2) / (standard_deviation(list1) * standard_deviation(list2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a の影響を除いた、b と y の偏回帰係数 partial regression coefficient を求める関数\n",
    "def partial_regression(a, b, y):\n",
    "    rby = correlation(b, y)\n",
    "    ray = correlation(a, y)\n",
    "    rab = correlation(a, b)\n",
    "    return (rby - ray * rab) * standard_deviation(y) / ((1 - rab ** 2) * standard_deviation(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 定数 w1 = （x2 の影響を除いた、x1 と y の偏回帰係数）\n",
    "w1 = partial_regression(X[:, 1], X[:, 0], Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 定数 w2 = （x1 の影響を除いた、x2 と y の偏回帰係数）\n",
    "w2 = partial_regression(X[:, 0], X[:, 1], Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 定数 t　＝　yの平均　－　w1*x1の平均　－　w2*x2の平均\n",
    "t = mean(Y) - w1 * mean(X[:, 0]) - w2 * mean(X[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = f(x) = w1x1 + w2x2 + t; (w1, w2, t) = (1.1777508314139928, 124.38195482549644, -218.85778226168105)\n"
     ]
    }
   ],
   "source": [
    "# 回帰直線の式を表示\n",
    "print(\"y = f(x) = w1x1 + w2x2 + t; (w1, w2, t) = ({0}, {1}, {2})\".format(w1, w2, t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(X):\n",
    "    return w1 * X[:, 0] + w2 * X[:, 1] + t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.78084985722905187"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = 1. - sum((Y - f(X))**2) / sum((Y - mean(Y))**2)\n",
    "r2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# さて、表計算で解けと言われたので pandas で書いてみましょうか。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent\n",
       "0        HF         19.500              20.0       1.826567\n",
       "1       HCl        -84.900              36.5       1.108600\n",
       "2       HBr        -67.000              80.9       0.827100\n",
       "3        HI        -35.100             127.9       0.447700\n",
       "4       H2O        100.000              18.0       1.854600\n",
       "5       H2S        -60.700              34.1       0.978325\n",
       "6      H2Se        -42.000              81.0       0.627000\n",
       "7       NH3        -33.400              17.0       1.471772\n",
       "8       PH3        -87.000              34.0       0.573970\n",
       "9      AsH3        -55.000              77.9       0.217000\n",
       "10     SbH3        -17.100             124.8       0.116000\n",
       "11      CH4       -161.490              16.0       0.000000\n",
       "12     SiH4       -111.800              32.1       0.000000\n",
       "13     GeH4        -90.000              76.6       0.000000\n",
       "14     SnH4        -52.000             122.7       0.000000\n",
       "15       He       -268.934               4.0       0.000000\n",
       "16       Ne       -246.048              20.2       0.000000\n",
       "17       Ar       -185.700              39.9       0.000000\n",
       "18       Kr       -152.300              83.8       0.000000\n",
       "19       Xe       -108.100             131.3       0.000000"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import copy\n",
    "from IPython.display import display\n",
    "excel = copy.deepcopy(df)\n",
    "excel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  \n",
       "0   1.826567  \n",
       "1   1.108600  \n",
       "2   0.827100  \n",
       "3   0.447700  \n",
       "4   1.854600  \n",
       "5   0.978325  \n",
       "6   0.627000  \n",
       "7   1.471772  \n",
       "8   0.573970  \n",
       "9   0.217000  \n",
       "10  0.116000  \n",
       "11  0.000000  \n",
       "12  0.000000  \n",
       "13  0.000000  \n",
       "14  0.000000  \n",
       "15  0.000000  \n",
       "16  0.000000  \n",
       "17  0.000000  \n",
       "18  0.000000  \n",
       "19  0.000000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.9536</td>\n",
       "      <td>58.935</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            y      x1        x2\n",
       "mean -86.9536  58.935  0.502432"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['y'] = excel['boiling point']\n",
    "excel['x1'] = excel['molecular weight']\n",
    "excel['x2'] = excel['dipole monent']\n",
    "mean_y = mean(excel['y'])\n",
    "mean_x1 = mean(excel['x1'])\n",
    "mean_x2 = mean(excel['x2'])\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2]], columns=['y','x1', 'x2'], index=['mean']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  \n",
       "0   1.826567   106.4536      -38.935     1.324135  \n",
       "1   1.108600     2.0536      -22.435     0.606168  \n",
       "2   0.827100    19.9536       21.965     0.324668  \n",
       "3   0.447700    51.8536       68.965    -0.054732  \n",
       "4   1.854600   186.9536      -40.935     1.352168  \n",
       "5   0.978325    26.2536      -24.835     0.475893  \n",
       "6   0.627000    44.9536       22.065     0.124568  \n",
       "7   1.471772    53.5536      -41.935     0.969340  \n",
       "8   0.573970    -0.0464      -24.935     0.071538  \n",
       "9   0.217000    31.9536       18.965    -0.285432  \n",
       "10  0.116000    69.8536       65.865    -0.386432  \n",
       "11  0.000000   -74.5364      -42.935    -0.502432  \n",
       "12  0.000000   -24.8464      -26.835    -0.502432  \n",
       "13  0.000000    -3.0464       17.665    -0.502432  \n",
       "14  0.000000    34.9536       63.765    -0.502432  \n",
       "15  0.000000  -181.9804      -54.935    -0.502432  \n",
       "16  0.000000  -159.0944      -38.735    -0.502432  \n",
       "17  0.000000   -98.7464      -19.035    -0.502432  \n",
       "18  0.000000   -65.3464       24.865    -0.502432  \n",
       "19  0.000000   -21.1464       72.365    -0.502432  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.9536</td>\n",
       "      <td>58.935</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            y      x1        x2\n",
       "mean -86.9536  58.935  0.502432"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['y-mean(y)'] = [y - mean_y for y in excel['y']]\n",
    "excel['x1-mean(x1)'] = [x1 - mean_x1 for x1 in excel['x1']]\n",
    "excel['x2-mean(x2)'] = [x2 - mean_x2 for x2 in excel['x2']]\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2]], columns=['y','x1', 'x2'], index=['mean']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  \n",
       "0        1515.934225          1.753334  \n",
       "1         503.329225          0.367440  \n",
       "2         482.461225          0.105410  \n",
       "3        4756.171225          0.002996  \n",
       "4        1675.674225          1.828359  \n",
       "5         616.777225          0.226474  \n",
       "6         486.864225          0.015517  \n",
       "7        1758.544225          0.939621  \n",
       "8         621.754225          0.005118  \n",
       "9         359.671225          0.081471  \n",
       "10       4338.198225          0.149329  \n",
       "11       1843.414225          0.252438  \n",
       "12        720.117225          0.252438  \n",
       "13        312.052225          0.252438  \n",
       "14       4065.975225          0.252438  \n",
       "15       3017.854225          0.252438  \n",
       "16       1500.400225          0.252438  \n",
       "17        362.331225          0.252438  \n",
       "18        618.268225          0.252438  \n",
       "19       5236.693225          0.252438  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.9536</td>\n",
       "      <td>58.935</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            y      x1        x2\n",
       "mean -86.9536  58.935  0.502432"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(y-mean(y))**2'] = [sa ** 2 for sa in excel['y-mean(y)']]\n",
    "excel['(x1-mean(x1))**2'] = [sa ** 2 for sa in excel['x1-mean(x1)']]\n",
    "excel['(x2-mean(x2))**2'] = [sa ** 2 for sa in excel['x2-mean(x2)']]\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2]], columns=['y','x1', 'x2'], index=['mean']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  \n",
       "0        1515.934225          1.753334  \n",
       "1         503.329225          0.367440  \n",
       "2         482.461225          0.105410  \n",
       "3        4756.171225          0.002996  \n",
       "4        1675.674225          1.828359  \n",
       "5         616.777225          0.226474  \n",
       "6         486.864225          0.015517  \n",
       "7        1758.544225          0.939621  \n",
       "8         621.754225          0.005118  \n",
       "9         359.671225          0.081471  \n",
       "10       4338.198225          0.149329  \n",
       "11       1843.414225          0.252438  \n",
       "12        720.117225          0.252438  \n",
       "13        312.052225          0.252438  \n",
       "14       4065.975225          0.252438  \n",
       "15       3017.854225          0.252438  \n",
       "16       1500.400225          0.252438  \n",
       "17        362.331225          0.252438  \n",
       "18        618.268225          0.252438  \n",
       "19       5236.693225          0.252438  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "variance_y = mean(excel['(y-mean(y))**2'])\n",
    "variance_x1 = mean(excel['(x1-mean(x1))**2'])\n",
    "variance_x2 = mean(excel['(x2-mean(x2))**2'])\n",
    "sd_y = math.sqrt(variance_y)\n",
    "sd_x1 = math.sqrt(variance_x1)\n",
    "sd_x2 = math.sqrt(variance_x2)\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                             [variance_y, variance_x1, variance_x2], \n",
    "                             [sd_y, sd_x1, sd_x2]], \n",
    "                            columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))  \n",
       "0                  -4144.770916                   140.958970  \n",
       "1                    -46.072516                     1.244827  \n",
       "2                    438.280824                     6.478301  \n",
       "3                   3576.083524                    -2.838036  \n",
       "4                  -7652.945616                   252.792731  \n",
       "5                   -652.008156                    12.493912  \n",
       "6                    991.901184                     5.599794  \n",
       "7                  -2245.770216                    51.911663  \n",
       "8                      1.156984                    -0.003319  \n",
       "9                    606.000024                    -9.120570  \n",
       "10                  4600.907364                   -26.993645  \n",
       "11                  3200.220334                    37.449450  \n",
       "12                   666.753144                    12.483619  \n",
       "13                   -53.814656                     1.530608  \n",
       "14                  2228.816304                   -17.561797  \n",
       "15                  9997.093274                    91.432722  \n",
       "16                  6162.521584                    79.934070  \n",
       "17                  1879.637724                    49.613322  \n",
       "18                 -1624.838236                    32.832103  \n",
       "19                 -1530.259236                    10.624622  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(x1-mean(x1)) * (x2-mean(x2))'] = excel['x1-mean(x1)'] * excel['x2-mean(x2)']\n",
    "excel['(y-mean(y)) * (x1-mean(x1))'] = excel['y-mean(y)'] * excel['x1-mean(x1)']\n",
    "excel['(y-mean(y)) * (x2-mean(x2))'] = excel['y-mean(y)'] * excel['x2-mean(x2)']\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                             [variance_y, variance_x1, variance_x2], \n",
    "                             [sd_y, sd_x1, sd_x2]], \n",
    "                            columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))  \n",
       "0                  -4144.770916                   140.958970  \n",
       "1                    -46.072516                     1.244827  \n",
       "2                    438.280824                     6.478301  \n",
       "3                   3576.083524                    -2.838036  \n",
       "4                  -7652.945616                   252.792731  \n",
       "5                   -652.008156                    12.493912  \n",
       "6                    991.901184                     5.599794  \n",
       "7                  -2245.770216                    51.911663  \n",
       "8                      1.156984                    -0.003319  \n",
       "9                    606.000024                    -9.120570  \n",
       "10                  4600.907364                   -26.993645  \n",
       "11                  3200.220334                    37.449450  \n",
       "12                   666.753144                    12.483619  \n",
       "13                   -53.814656                     1.530608  \n",
       "14                  2228.816304                   -17.561797  \n",
       "15                  9997.093274                    91.432722  \n",
       "16                  6162.521584                    79.934070  \n",
       "17                  1879.637724                    49.613322  \n",
       "18                 -1624.838236                    32.832103  \n",
       "19                 -1530.259236                    10.624622  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1,x2</th>\n",
       "      <th>x1,y</th>\n",
       "      <th>x2,y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>-9.880045</td>\n",
       "      <td>819.944636</td>\n",
       "      <td>36.543167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>-0.380609</td>\n",
       "      <td>0.234005</td>\n",
       "      <td>0.698912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x1,x2        x1,y       x2,y\n",
       "covariance  -9.880045  819.944636  36.543167\n",
       "correlation -0.380609    0.234005   0.698912"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "covar_x1x2 = mean(excel['(x1-mean(x1)) * (x2-mean(x2))'])\n",
    "covar_x1y = mean(excel['(y-mean(y)) * (x1-mean(x1))'])\n",
    "covar_x2y = mean(excel['(y-mean(y)) * (x2-mean(x2))'])\n",
    "\n",
    "corr_x1x2 = covar_x1x2 / (sd_x1 * sd_x2)\n",
    "corr_x1y = covar_x1y / (sd_x1 * sd_y)\n",
    "corr_x2y = covar_x2y / (sd_x2 * sd_y)\n",
    "display(excel, pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                             [variance_y, variance_x1, variance_x2], \n",
    "                             [sd_y, sd_x1, sd_x2]], \n",
    "                            columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']),\n",
    "       pd.DataFrame([[covar_x1x2, covar_x1y, covar_x2y], [corr_x1x2, corr_x1y, corr_x2y]], \n",
    "                    index=['covariance', 'correlation'], columns=['x1,x2','x1,y', 'x2,y']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))  \n",
       "0                  -4144.770916                   140.958970  \n",
       "1                    -46.072516                     1.244827  \n",
       "2                    438.280824                     6.478301  \n",
       "3                   3576.083524                    -2.838036  \n",
       "4                  -7652.945616                   252.792731  \n",
       "5                   -652.008156                    12.493912  \n",
       "6                    991.901184                     5.599794  \n",
       "7                  -2245.770216                    51.911663  \n",
       "8                      1.156984                    -0.003319  \n",
       "9                    606.000024                    -9.120570  \n",
       "10                  4600.907364                   -26.993645  \n",
       "11                  3200.220334                    37.449450  \n",
       "12                   666.753144                    12.483619  \n",
       "13                   -53.814656                     1.530608  \n",
       "14                  2228.816304                   -17.561797  \n",
       "15                  9997.093274                    91.432722  \n",
       "16                  6162.521584                    79.934070  \n",
       "17                  1879.637724                    49.613322  \n",
       "18                 -1624.838236                    32.832103  \n",
       "19                 -1530.259236                    10.624622  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1,x2</th>\n",
       "      <th>x1,y</th>\n",
       "      <th>x2,y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>-9.880045</td>\n",
       "      <td>819.944636</td>\n",
       "      <td>36.543167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>-0.380609</td>\n",
       "      <td>0.234005</td>\n",
       "      <td>0.698912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x1,x2        x1,y       x2,y\n",
       "covariance  -9.880045  819.944636  36.543167\n",
       "correlation -0.380609    0.234005   0.698912"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>w1</th>\n",
       "      <th>w2</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = w1x1 + w2x2 + t</th>\n",
       "      <td>1.177751</td>\n",
       "      <td>124.381955</td>\n",
       "      <td>-218.857782</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  w1          w2           t\n",
       "y = f(x) = w1x1 + w2x2 + t  1.177751  124.381955 -218.857782"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w1 = (corr_x1y - corr_x2y * corr_x1x2) * sd_y / ((1 - corr_x1x2 ** 2) * sd_x1)\n",
    "w2 = (corr_x2y - corr_x1y * corr_x1x2) * sd_y / ((1 - corr_x1x2 ** 2) * sd_x2)\n",
    "t = mean_y - w1 * mean_x1 - w2 * mean_x2\n",
    "display(excel, \n",
    "        pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                      [variance_y, variance_x1, variance_x2], \n",
    "                      [sd_y, sd_x1, sd_x2]], \n",
    "                     columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([[covar_x1x2, covar_x1y, covar_x2y], [corr_x1x2, corr_x1y, corr_x2y]], \n",
    "                     index=['covariance', 'correlation'], columns=['x1,x2','x1,y', 'x2,y']),\n",
    "        pd.DataFrame([[w1, w2, t]], columns=[\"w1\", \"w2\", \"t\"], index=[\"y = f(x) = w1x1 + w2x2 + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x1, x2):\n",
    "    return w1 * x1 + w2 * x2 + t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "      <th>f(x1,x2)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "      <td>31.889208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "      <td>-37.980042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "      <td>-20.701425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "      <td>-12.537650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "      <td>33.020506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "      <td>-57.010503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "      <td>-45.472479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "      <td>-15.774140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "      <td>-107.422743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "      <td>-100.120108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "      <td>-57.446172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "      <td>-200.013769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "      <td>-181.051981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "      <td>-128.642069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "      <td>-74.347755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "      <td>-214.146779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "      <td>-195.067215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "      <td>-171.865524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "      <td>-120.162263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "      <td>-64.219098</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))    f(x1,x2)  \n",
       "0                  -4144.770916                   140.958970   31.889208  \n",
       "1                    -46.072516                     1.244827  -37.980042  \n",
       "2                    438.280824                     6.478301  -20.701425  \n",
       "3                   3576.083524                    -2.838036  -12.537650  \n",
       "4                  -7652.945616                   252.792731   33.020506  \n",
       "5                   -652.008156                    12.493912  -57.010503  \n",
       "6                    991.901184                     5.599794  -45.472479  \n",
       "7                  -2245.770216                    51.911663  -15.774140  \n",
       "8                      1.156984                    -0.003319 -107.422743  \n",
       "9                    606.000024                    -9.120570 -100.120108  \n",
       "10                  4600.907364                   -26.993645  -57.446172  \n",
       "11                  3200.220334                    37.449450 -200.013769  \n",
       "12                   666.753144                    12.483619 -181.051981  \n",
       "13                   -53.814656                     1.530608 -128.642069  \n",
       "14                  2228.816304                   -17.561797  -74.347755  \n",
       "15                  9997.093274                    91.432722 -214.146779  \n",
       "16                  6162.521584                    79.934070 -195.067215  \n",
       "17                  1879.637724                    49.613322 -171.865524  \n",
       "18                 -1624.838236                    32.832103 -120.162263  \n",
       "19                 -1530.259236                    10.624622  -64.219098  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1,x2</th>\n",
       "      <th>x1,y</th>\n",
       "      <th>x2,y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>-9.880045</td>\n",
       "      <td>819.944636</td>\n",
       "      <td>36.543167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>-0.380609</td>\n",
       "      <td>0.234005</td>\n",
       "      <td>0.698912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x1,x2        x1,y       x2,y\n",
       "covariance  -9.880045  819.944636  36.543167\n",
       "correlation -0.380609    0.234005   0.698912"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>w1</th>\n",
       "      <th>w2</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = w1x1 + w2x2 + t</th>\n",
       "      <td>1.177751</td>\n",
       "      <td>124.381955</td>\n",
       "      <td>-218.857782</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  w1          w2           t\n",
       "y = f(x) = w1x1 + w2x2 + t  1.177751  124.381955 -218.857782"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['f(x1,x2)'] = f(excel['x1'], excel['x2'])\n",
    "display(excel, \n",
    "        pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                      [variance_y, variance_x1, variance_x2], \n",
    "                      [sd_y, sd_x1, sd_x2]], \n",
    "                     columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([[covar_x1x2, covar_x1y, covar_x2y], [corr_x1x2, corr_x1y, corr_x2y]], \n",
    "                     index=['covariance', 'correlation'], columns=['x1,x2','x1,y', 'x2,y']),\n",
    "        pd.DataFrame([[w1, w2, t]], columns=[\"w1\", \"w2\", \"t\"], index=[\"y = f(x) = w1x1 + w2x2 + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "      <th>f(x1,x2)</th>\n",
       "      <th>(y-f(x1,x2))**2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "      <td>31.889208</td>\n",
       "      <td>153.492486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "      <td>-37.980042</td>\n",
       "      <td>2201.482478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "      <td>-20.701425</td>\n",
       "      <td>2143.558032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "      <td>-12.537650</td>\n",
       "      <td>509.059649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "      <td>33.020506</td>\n",
       "      <td>4486.252600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "      <td>-57.010503</td>\n",
       "      <td>13.612388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "      <td>-45.472479</td>\n",
       "      <td>12.058112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "      <td>-15.774140</td>\n",
       "      <td>310.670951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "      <td>-107.422743</td>\n",
       "      <td>417.088447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "      <td>-100.120108</td>\n",
       "      <td>2035.824173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "      <td>-57.446172</td>\n",
       "      <td>1627.813574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "      <td>-200.013769</td>\n",
       "      <td>1484.080775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "      <td>-181.051981</td>\n",
       "      <td>4795.836813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "      <td>-128.642069</td>\n",
       "      <td>1493.209464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "      <td>-74.347755</td>\n",
       "      <td>499.422165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "      <td>-214.146779</td>\n",
       "      <td>3001.639592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "      <td>-195.067215</td>\n",
       "      <td>2599.040392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "      <td>-171.865524</td>\n",
       "      <td>191.392724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "      <td>-120.162263</td>\n",
       "      <td>1032.834166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "      <td>-64.219098</td>\n",
       "      <td>1925.533552</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))    f(x1,x2)  \\\n",
       "0                  -4144.770916                   140.958970   31.889208   \n",
       "1                    -46.072516                     1.244827  -37.980042   \n",
       "2                    438.280824                     6.478301  -20.701425   \n",
       "3                   3576.083524                    -2.838036  -12.537650   \n",
       "4                  -7652.945616                   252.792731   33.020506   \n",
       "5                   -652.008156                    12.493912  -57.010503   \n",
       "6                    991.901184                     5.599794  -45.472479   \n",
       "7                  -2245.770216                    51.911663  -15.774140   \n",
       "8                      1.156984                    -0.003319 -107.422743   \n",
       "9                    606.000024                    -9.120570 -100.120108   \n",
       "10                  4600.907364                   -26.993645  -57.446172   \n",
       "11                  3200.220334                    37.449450 -200.013769   \n",
       "12                   666.753144                    12.483619 -181.051981   \n",
       "13                   -53.814656                     1.530608 -128.642069   \n",
       "14                  2228.816304                   -17.561797  -74.347755   \n",
       "15                  9997.093274                    91.432722 -214.146779   \n",
       "16                  6162.521584                    79.934070 -195.067215   \n",
       "17                  1879.637724                    49.613322 -171.865524   \n",
       "18                 -1624.838236                    32.832103 -120.162263   \n",
       "19                 -1530.259236                    10.624622  -64.219098   \n",
       "\n",
       "    (y-f(x1,x2))**2  \n",
       "0        153.492486  \n",
       "1       2201.482478  \n",
       "2       2143.558032  \n",
       "3        509.059649  \n",
       "4       4486.252600  \n",
       "5         13.612388  \n",
       "6         12.058112  \n",
       "7        310.670951  \n",
       "8        417.088447  \n",
       "9       2035.824173  \n",
       "10      1627.813574  \n",
       "11      1484.080775  \n",
       "12      4795.836813  \n",
       "13      1493.209464  \n",
       "14       499.422165  \n",
       "15      3001.639592  \n",
       "16      2599.040392  \n",
       "17       191.392724  \n",
       "18      1032.834166  \n",
       "19      1925.533552  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1,x2</th>\n",
       "      <th>x1,y</th>\n",
       "      <th>x2,y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>-9.880045</td>\n",
       "      <td>819.944636</td>\n",
       "      <td>36.543167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>-0.380609</td>\n",
       "      <td>0.234005</td>\n",
       "      <td>0.698912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x1,x2        x1,y       x2,y\n",
       "covariance  -9.880045  819.944636  36.543167\n",
       "correlation -0.380609    0.234005   0.698912"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>w1</th>\n",
       "      <th>w2</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = w1x1 + w2x2 + t</th>\n",
       "      <td>1.177751</td>\n",
       "      <td>124.381955</td>\n",
       "      <td>-218.857782</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  w1          w2           t\n",
       "y = f(x) = w1x1 + w2x2 + t  1.177751  124.381955 -218.857782"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(y-f(x1,x2))**2'] = (excel['y'] - excel['f(x1,x2)'])**2\n",
    "display(excel, \n",
    "        pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                      [variance_y, variance_x1, variance_x2], \n",
    "                      [sd_y, sd_x1, sd_x2]], \n",
    "                     columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([[covar_x1x2, covar_x1y, covar_x2y], [corr_x1x2, corr_x1y, corr_x2y]], \n",
    "                     index=['covariance', 'correlation'], columns=['x1,x2','x1,y', 'x2,y']),\n",
    "        pd.DataFrame([[w1, w2, t]], columns=[\"w1\", \"w2\", \"t\"], index=[\"y = f(x) = w1x1 + w2x2 + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>molecule</th>\n",
       "      <th>boiling point</th>\n",
       "      <th>molecular weight</th>\n",
       "      <th>dipole monent</th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>x1-mean(x1)</th>\n",
       "      <th>x2-mean(x2)</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(x1-mean(x1))**2</th>\n",
       "      <th>(x2-mean(x2))**2</th>\n",
       "      <th>(x1-mean(x1)) * (x2-mean(x2))</th>\n",
       "      <th>(y-mean(y)) * (x1-mean(x1))</th>\n",
       "      <th>(y-mean(y)) * (x2-mean(x2))</th>\n",
       "      <th>f(x1,x2)</th>\n",
       "      <th>(y-f(x1,x2))**2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>HF</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.826567</td>\n",
       "      <td>106.4536</td>\n",
       "      <td>-38.935</td>\n",
       "      <td>1.324135</td>\n",
       "      <td>11332.368953</td>\n",
       "      <td>1515.934225</td>\n",
       "      <td>1.753334</td>\n",
       "      <td>-51.555208</td>\n",
       "      <td>-4144.770916</td>\n",
       "      <td>140.958970</td>\n",
       "      <td>31.889208</td>\n",
       "      <td>153.492486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>1.108600</td>\n",
       "      <td>2.0536</td>\n",
       "      <td>-22.435</td>\n",
       "      <td>0.606168</td>\n",
       "      <td>4.217273</td>\n",
       "      <td>503.329225</td>\n",
       "      <td>0.367440</td>\n",
       "      <td>-13.599386</td>\n",
       "      <td>-46.072516</td>\n",
       "      <td>1.244827</td>\n",
       "      <td>-37.980042</td>\n",
       "      <td>2201.482478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>0.827100</td>\n",
       "      <td>19.9536</td>\n",
       "      <td>21.965</td>\n",
       "      <td>0.324668</td>\n",
       "      <td>398.146153</td>\n",
       "      <td>482.461225</td>\n",
       "      <td>0.105410</td>\n",
       "      <td>7.131339</td>\n",
       "      <td>438.280824</td>\n",
       "      <td>6.478301</td>\n",
       "      <td>-20.701425</td>\n",
       "      <td>2143.558032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>0.447700</td>\n",
       "      <td>51.8536</td>\n",
       "      <td>68.965</td>\n",
       "      <td>-0.054732</td>\n",
       "      <td>2688.795833</td>\n",
       "      <td>4756.171225</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>-3.774572</td>\n",
       "      <td>3576.083524</td>\n",
       "      <td>-2.838036</td>\n",
       "      <td>-12.537650</td>\n",
       "      <td>509.059649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1.854600</td>\n",
       "      <td>186.9536</td>\n",
       "      <td>-40.935</td>\n",
       "      <td>1.352168</td>\n",
       "      <td>34951.648553</td>\n",
       "      <td>1675.674225</td>\n",
       "      <td>1.828359</td>\n",
       "      <td>-55.351009</td>\n",
       "      <td>-7652.945616</td>\n",
       "      <td>252.792731</td>\n",
       "      <td>33.020506</td>\n",
       "      <td>4486.252600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>0.978325</td>\n",
       "      <td>26.2536</td>\n",
       "      <td>-24.835</td>\n",
       "      <td>0.475893</td>\n",
       "      <td>689.251513</td>\n",
       "      <td>616.777225</td>\n",
       "      <td>0.226474</td>\n",
       "      <td>-11.818810</td>\n",
       "      <td>-652.008156</td>\n",
       "      <td>12.493912</td>\n",
       "      <td>-57.010503</td>\n",
       "      <td>13.612388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0.627000</td>\n",
       "      <td>44.9536</td>\n",
       "      <td>22.065</td>\n",
       "      <td>0.124568</td>\n",
       "      <td>2020.826153</td>\n",
       "      <td>486.864225</td>\n",
       "      <td>0.015517</td>\n",
       "      <td>2.748600</td>\n",
       "      <td>991.901184</td>\n",
       "      <td>5.599794</td>\n",
       "      <td>-45.472479</td>\n",
       "      <td>12.058112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>1.471772</td>\n",
       "      <td>53.5536</td>\n",
       "      <td>-41.935</td>\n",
       "      <td>0.969340</td>\n",
       "      <td>2867.988073</td>\n",
       "      <td>1758.544225</td>\n",
       "      <td>0.939621</td>\n",
       "      <td>-40.649285</td>\n",
       "      <td>-2245.770216</td>\n",
       "      <td>51.911663</td>\n",
       "      <td>-15.774140</td>\n",
       "      <td>310.670951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>0.573970</td>\n",
       "      <td>-0.0464</td>\n",
       "      <td>-24.935</td>\n",
       "      <td>0.071538</td>\n",
       "      <td>0.002153</td>\n",
       "      <td>621.754225</td>\n",
       "      <td>0.005118</td>\n",
       "      <td>-1.783808</td>\n",
       "      <td>1.156984</td>\n",
       "      <td>-0.003319</td>\n",
       "      <td>-107.422743</td>\n",
       "      <td>417.088447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>0.217000</td>\n",
       "      <td>31.9536</td>\n",
       "      <td>18.965</td>\n",
       "      <td>-0.285432</td>\n",
       "      <td>1021.032553</td>\n",
       "      <td>359.671225</td>\n",
       "      <td>0.081471</td>\n",
       "      <td>-5.413212</td>\n",
       "      <td>606.000024</td>\n",
       "      <td>-9.120570</td>\n",
       "      <td>-100.120108</td>\n",
       "      <td>2035.824173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>0.116000</td>\n",
       "      <td>69.8536</td>\n",
       "      <td>65.865</td>\n",
       "      <td>-0.386432</td>\n",
       "      <td>4879.525433</td>\n",
       "      <td>4338.198225</td>\n",
       "      <td>0.149329</td>\n",
       "      <td>-25.452324</td>\n",
       "      <td>4600.907364</td>\n",
       "      <td>-26.993645</td>\n",
       "      <td>-57.446172</td>\n",
       "      <td>1627.813574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-74.5364</td>\n",
       "      <td>-42.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>5555.674925</td>\n",
       "      <td>1843.414225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>21.571905</td>\n",
       "      <td>3200.220334</td>\n",
       "      <td>37.449450</td>\n",
       "      <td>-200.013769</td>\n",
       "      <td>1484.080775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.8464</td>\n",
       "      <td>-26.835</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>617.343593</td>\n",
       "      <td>720.117225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>13.482755</td>\n",
       "      <td>666.753144</td>\n",
       "      <td>12.483619</td>\n",
       "      <td>-181.051981</td>\n",
       "      <td>4795.836813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.0464</td>\n",
       "      <td>17.665</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9.280553</td>\n",
       "      <td>312.052225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-8.875456</td>\n",
       "      <td>-53.814656</td>\n",
       "      <td>1.530608</td>\n",
       "      <td>-128.642069</td>\n",
       "      <td>1493.209464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34.9536</td>\n",
       "      <td>63.765</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>1221.754153</td>\n",
       "      <td>4065.975225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-32.037557</td>\n",
       "      <td>2228.816304</td>\n",
       "      <td>-17.561797</td>\n",
       "      <td>-74.347755</td>\n",
       "      <td>499.422165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-181.9804</td>\n",
       "      <td>-54.935</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>33116.865984</td>\n",
       "      <td>3017.854225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>27.601085</td>\n",
       "      <td>9997.093274</td>\n",
       "      <td>91.432722</td>\n",
       "      <td>-214.146779</td>\n",
       "      <td>3001.639592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-159.0944</td>\n",
       "      <td>-38.735</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>25311.028111</td>\n",
       "      <td>1500.400225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>19.461692</td>\n",
       "      <td>6162.521584</td>\n",
       "      <td>79.934070</td>\n",
       "      <td>-195.067215</td>\n",
       "      <td>2599.040392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-98.7464</td>\n",
       "      <td>-19.035</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>9750.851513</td>\n",
       "      <td>362.331225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>9.563787</td>\n",
       "      <td>1879.637724</td>\n",
       "      <td>49.613322</td>\n",
       "      <td>-171.865524</td>\n",
       "      <td>191.392724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-65.3464</td>\n",
       "      <td>24.865</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>4270.151993</td>\n",
       "      <td>618.268225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-12.492964</td>\n",
       "      <td>-1624.838236</td>\n",
       "      <td>32.832103</td>\n",
       "      <td>-120.162263</td>\n",
       "      <td>1032.834166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-21.1464</td>\n",
       "      <td>72.365</td>\n",
       "      <td>-0.502432</td>\n",
       "      <td>447.170233</td>\n",
       "      <td>5236.693225</td>\n",
       "      <td>0.252438</td>\n",
       "      <td>-36.358470</td>\n",
       "      <td>-1530.259236</td>\n",
       "      <td>10.624622</td>\n",
       "      <td>-64.219098</td>\n",
       "      <td>1925.533552</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight  dipole monent        y     x1  \\\n",
       "0        HF         19.500              20.0       1.826567   19.500   20.0   \n",
       "1       HCl        -84.900              36.5       1.108600  -84.900   36.5   \n",
       "2       HBr        -67.000              80.9       0.827100  -67.000   80.9   \n",
       "3        HI        -35.100             127.9       0.447700  -35.100  127.9   \n",
       "4       H2O        100.000              18.0       1.854600  100.000   18.0   \n",
       "5       H2S        -60.700              34.1       0.978325  -60.700   34.1   \n",
       "6      H2Se        -42.000              81.0       0.627000  -42.000   81.0   \n",
       "7       NH3        -33.400              17.0       1.471772  -33.400   17.0   \n",
       "8       PH3        -87.000              34.0       0.573970  -87.000   34.0   \n",
       "9      AsH3        -55.000              77.9       0.217000  -55.000   77.9   \n",
       "10     SbH3        -17.100             124.8       0.116000  -17.100  124.8   \n",
       "11      CH4       -161.490              16.0       0.000000 -161.490   16.0   \n",
       "12     SiH4       -111.800              32.1       0.000000 -111.800   32.1   \n",
       "13     GeH4        -90.000              76.6       0.000000  -90.000   76.6   \n",
       "14     SnH4        -52.000             122.7       0.000000  -52.000  122.7   \n",
       "15       He       -268.934               4.0       0.000000 -268.934    4.0   \n",
       "16       Ne       -246.048              20.2       0.000000 -246.048   20.2   \n",
       "17       Ar       -185.700              39.9       0.000000 -185.700   39.9   \n",
       "18       Kr       -152.300              83.8       0.000000 -152.300   83.8   \n",
       "19       Xe       -108.100             131.3       0.000000 -108.100  131.3   \n",
       "\n",
       "          x2  y-mean(y)  x1-mean(x1)  x2-mean(x2)  (y-mean(y))**2  \\\n",
       "0   1.826567   106.4536      -38.935     1.324135    11332.368953   \n",
       "1   1.108600     2.0536      -22.435     0.606168        4.217273   \n",
       "2   0.827100    19.9536       21.965     0.324668      398.146153   \n",
       "3   0.447700    51.8536       68.965    -0.054732     2688.795833   \n",
       "4   1.854600   186.9536      -40.935     1.352168    34951.648553   \n",
       "5   0.978325    26.2536      -24.835     0.475893      689.251513   \n",
       "6   0.627000    44.9536       22.065     0.124568     2020.826153   \n",
       "7   1.471772    53.5536      -41.935     0.969340     2867.988073   \n",
       "8   0.573970    -0.0464      -24.935     0.071538        0.002153   \n",
       "9   0.217000    31.9536       18.965    -0.285432     1021.032553   \n",
       "10  0.116000    69.8536       65.865    -0.386432     4879.525433   \n",
       "11  0.000000   -74.5364      -42.935    -0.502432     5555.674925   \n",
       "12  0.000000   -24.8464      -26.835    -0.502432      617.343593   \n",
       "13  0.000000    -3.0464       17.665    -0.502432        9.280553   \n",
       "14  0.000000    34.9536       63.765    -0.502432     1221.754153   \n",
       "15  0.000000  -181.9804      -54.935    -0.502432    33116.865984   \n",
       "16  0.000000  -159.0944      -38.735    -0.502432    25311.028111   \n",
       "17  0.000000   -98.7464      -19.035    -0.502432     9750.851513   \n",
       "18  0.000000   -65.3464       24.865    -0.502432     4270.151993   \n",
       "19  0.000000   -21.1464       72.365    -0.502432      447.170233   \n",
       "\n",
       "    (x1-mean(x1))**2  (x2-mean(x2))**2  (x1-mean(x1)) * (x2-mean(x2))  \\\n",
       "0        1515.934225          1.753334                     -51.555208   \n",
       "1         503.329225          0.367440                     -13.599386   \n",
       "2         482.461225          0.105410                       7.131339   \n",
       "3        4756.171225          0.002996                      -3.774572   \n",
       "4        1675.674225          1.828359                     -55.351009   \n",
       "5         616.777225          0.226474                     -11.818810   \n",
       "6         486.864225          0.015517                       2.748600   \n",
       "7        1758.544225          0.939621                     -40.649285   \n",
       "8         621.754225          0.005118                      -1.783808   \n",
       "9         359.671225          0.081471                      -5.413212   \n",
       "10       4338.198225          0.149329                     -25.452324   \n",
       "11       1843.414225          0.252438                      21.571905   \n",
       "12        720.117225          0.252438                      13.482755   \n",
       "13        312.052225          0.252438                      -8.875456   \n",
       "14       4065.975225          0.252438                     -32.037557   \n",
       "15       3017.854225          0.252438                      27.601085   \n",
       "16       1500.400225          0.252438                      19.461692   \n",
       "17        362.331225          0.252438                       9.563787   \n",
       "18        618.268225          0.252438                     -12.492964   \n",
       "19       5236.693225          0.252438                     -36.358470   \n",
       "\n",
       "    (y-mean(y)) * (x1-mean(x1))  (y-mean(y)) * (x2-mean(x2))    f(x1,x2)  \\\n",
       "0                  -4144.770916                   140.958970   31.889208   \n",
       "1                    -46.072516                     1.244827  -37.980042   \n",
       "2                    438.280824                     6.478301  -20.701425   \n",
       "3                   3576.083524                    -2.838036  -12.537650   \n",
       "4                  -7652.945616                   252.792731   33.020506   \n",
       "5                   -652.008156                    12.493912  -57.010503   \n",
       "6                    991.901184                     5.599794  -45.472479   \n",
       "7                  -2245.770216                    51.911663  -15.774140   \n",
       "8                      1.156984                    -0.003319 -107.422743   \n",
       "9                    606.000024                    -9.120570 -100.120108   \n",
       "10                  4600.907364                   -26.993645  -57.446172   \n",
       "11                  3200.220334                    37.449450 -200.013769   \n",
       "12                   666.753144                    12.483619 -181.051981   \n",
       "13                   -53.814656                     1.530608 -128.642069   \n",
       "14                  2228.816304                   -17.561797  -74.347755   \n",
       "15                  9997.093274                    91.432722 -214.146779   \n",
       "16                  6162.521584                    79.934070 -195.067215   \n",
       "17                  1879.637724                    49.613322 -171.865524   \n",
       "18                 -1624.838236                    32.832103 -120.162263   \n",
       "19                 -1530.259236                    10.624622  -64.219098   \n",
       "\n",
       "    (y-f(x1,x2))**2  \n",
       "0        153.492486  \n",
       "1       2201.482478  \n",
       "2       2143.558032  \n",
       "3        509.059649  \n",
       "4       4486.252600  \n",
       "5         13.612388  \n",
       "6         12.058112  \n",
       "7        310.670951  \n",
       "8        417.088447  \n",
       "9       2035.824173  \n",
       "10      1627.813574  \n",
       "11      1484.080775  \n",
       "12      4795.836813  \n",
       "13      1493.209464  \n",
       "14       499.422165  \n",
       "15      3001.639592  \n",
       "16      2599.040392  \n",
       "17       191.392724  \n",
       "18      1032.834166  \n",
       "19      1925.533552  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-86.953600</td>\n",
       "      <td>58.935000</td>\n",
       "      <td>0.502432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7057.696185</td>\n",
       "      <td>1739.624275</td>\n",
       "      <td>0.387350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>84.010096</td>\n",
       "      <td>41.708803</td>\n",
       "      <td>0.622375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y           x1        x2\n",
       "mean       -86.953600    58.935000  0.502432\n",
       "variance  7057.696185  1739.624275  0.387350\n",
       "sd          84.010096    41.708803  0.622375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1,x2</th>\n",
       "      <th>x1,y</th>\n",
       "      <th>x2,y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>-9.880045</td>\n",
       "      <td>819.944636</td>\n",
       "      <td>36.543167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>-0.380609</td>\n",
       "      <td>0.234005</td>\n",
       "      <td>0.698912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x1,x2        x1,y       x2,y\n",
       "covariance  -9.880045  819.944636  36.543167\n",
       "correlation -0.380609    0.234005   0.698912"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>w1</th>\n",
       "      <th>w2</th>\n",
       "      <th>t</th>\n",
       "      <th>r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = w1x1 + w2x2 + t</th>\n",
       "      <td>1.177751</td>\n",
       "      <td>124.381955</td>\n",
       "      <td>-218.857782</td>\n",
       "      <td>0.78085</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  w1          w2           t       r2\n",
       "y = f(x) = w1x1 + w2x2 + t  1.177751  124.381955 -218.857782  0.78085"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r2 = 1. - sum(excel['(y-f(x1,x2))**2']) / sum(excel['(y-mean(y))**2'])\n",
    "display(excel, \n",
    "        pd.DataFrame([[mean_y, mean_x1, mean_x2], \n",
    "                      [variance_y, variance_x1, variance_x2], \n",
    "                      [sd_y, sd_x1, sd_x2]], \n",
    "                     columns=['y','x1', 'x2'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([[covar_x1x2, covar_x1y, covar_x2y], [corr_x1x2, corr_x1y, corr_x2y]], \n",
    "                     index=['covariance', 'correlation'], columns=['x1,x2','x1,y', 'x2,y']),\n",
    "        pd.DataFrame([[w1, w2, t, r2]], columns=[\"w1\", \"w2\", \"t\", \"r2\"], index=[\"y = f(x) = w1x1 + w2x2 + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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