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

{
 "cells": [
  {
   "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": {
    "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",
       "    </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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight\n",
       "0        HF         19.500              20.0\n",
       "1       HCl        -84.900              36.5\n",
       "2       HBr        -67.000              80.9\n",
       "3        HI        -35.100             127.9\n",
       "4       H2O        100.000              18.0\n",
       "5       H2S        -60.700              34.1\n",
       "6      H2Se        -42.000              81.0\n",
       "7      H2Te         -1.800             129.6\n",
       "8       NH3        -33.400              17.0\n",
       "9       PH3        -87.000              34.0\n",
       "10     AsH3        -55.000              77.9\n",
       "11     SbH3        -17.100             124.8\n",
       "12      CH4       -161.490              16.0\n",
       "13     SiH4       -111.800              32.1\n",
       "14     GeH4        -90.000              76.6\n",
       "15     SnH4        -52.000             122.7\n",
       "16       He       -268.934               4.0\n",
       "17       Ne       -246.048              20.2\n",
       "18       Ar       -185.700              39.9\n",
       "19       Kr       -152.300              83.8\n",
       "20       Xe       -108.100             131.3"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = [['HF', 19.5, 20.0],\n",
    "        ['HCl', -84.9, 36.5],\n",
    "        ['HBr', -67.0, 80.9],\n",
    "        ['HI', -35.1, 127.9],\n",
    "        ['H2O', 100.0, 18.0],\n",
    "        ['H2S', -60.7, 34.1],\n",
    "        ['H2Se', -42, 81.0],\n",
    "        ['H2Te', -1.8, 129.6],\n",
    "        ['NH3', -33.4, 17.0],\n",
    "        ['PH3', -87, 34.0],\n",
    "        ['AsH3', -55, 77.9],\n",
    "        ['SbH3', -17.1, 124.8],\n",
    "        ['CH4', -161.49, 16.0],\n",
    "        ['SiH4', -111.8, 32.1],\n",
    "        ['GeH4', -90, 76.6],\n",
    "        ['SnH4', -52, 122.7],\n",
    "        ['He', -268.934, 4.0],\n",
    "        ['Ne', -246.048, 20.2],\n",
    "        ['Ar', -185.7, 39.9],\n",
    "        ['Kr', -152.3, 83.8],\n",
    "        ['Xe', -108.1, 131.3],\n",
    "       ]\n",
    "df = pd.DataFrame(data, columns = ['molecule', 'boiling point', 'molecular weight'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  20. ],\n",
       "       [  36.5],\n",
       "       [  80.9],\n",
       "       [ 127.9],\n",
       "       [  18. ],\n",
       "       [  34.1],\n",
       "       [  81. ],\n",
       "       [ 129.6],\n",
       "       [  17. ],\n",
       "       [  34. ],\n",
       "       [  77.9],\n",
       "       [ 124.8],\n",
       "       [  16. ],\n",
       "       [  32.1],\n",
       "       [  76.6],\n",
       "       [ 122.7],\n",
       "       [   4. ],\n",
       "       [  20.2],\n",
       "       [  39.9],\n",
       "       [  83.8],\n",
       "       [ 131.3]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df.loc[:, ['molecular weight']].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.   ,   -1.8  ,  -33.4  ,  -87.   ,  -55.   ,  -17.1  ,\n",
       "       -161.49 , -111.8  ,  -90.   ,  -52.   , -268.934, -246.048,\n",
       "       -185.7  , -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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mnTJzo9y8U2ZulFv0UKMsIiIiIhKEGmURERERkSDUKEtILFiwINIlxBxl5ka5eafM3Cg3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\n+VFu0SkzP8otOVQoS0FMnTo17i6kjjLzo9yiU2Z+lFt0ysyPcksOFcp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f87b4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "# 散布図\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X, Y, alpha=0.3)\n",
    "for name, x, y in zip(df.loc[:, ['molecule']].as_matrix(), X, Y):\n",
    "    plt.text(x, y, name[0], size=8)\n",
    "plt.xlabel('molecular weight')\n",
    "plt.ylabel('boiling point')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "logX = np.array([[math.log(x)] for x in X[:,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.99573227],\n",
       "       [ 3.59731226],\n",
       "       [ 4.39321382],\n",
       "       [ 4.85124871],\n",
       "       [ 2.89037176],\n",
       "       [ 3.52929738],\n",
       "       [ 4.39444915],\n",
       "       [ 4.86445278],\n",
       "       [ 2.83321334],\n",
       "       [ 3.52636052],\n",
       "       [ 4.35542595],\n",
       "       [ 4.82671246],\n",
       "       [ 2.77258872],\n",
       "       [ 3.46885603],\n",
       "       [ 4.33859708],\n",
       "       [ 4.80974235],\n",
       "       [ 1.38629436],\n",
       "       [ 3.0056826 ],\n",
       "       [ 3.68637632],\n",
       "       [ 4.42843301],\n",
       "       [ 4.87748478]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# まずは一番便利な scikit-learn から"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(logX, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 33.87205496])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 回帰係数\n",
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-211.66384118386563"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 切片\n",
    "lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = f(x) = wlogx + t; (w, t) = (33.872054963641745, -211.66384118386563)\n"
     ]
    }
   ],
   "source": [
    "print(\"y = f(x) = wlogx + t; (w, t) = ({0}, {1})\".format(lr.coef_[0], lr.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13487033631665779"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 決定係数R2\n",
    "lr.score(logX, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sX7+e7t27U1ZWRk5ODnl5eQwcOJDXXnuNSZMm8fvf/54xY8YAsGjRIkaPHs3GjRvp0qVL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\n57du3dpon7Vr17Jv3z5GjBgBwKxZs7j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ceumlzJkzh+9+97vp2YkMoGMtGOUWHUEK5a8B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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f8c7080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "# 散布図\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X, Y, alpha=0.3)\n",
    " \n",
    "# 回帰直線\n",
    "plt.title('Linear regression')\n",
    "plt.plot(sorted(X), sorted(lr.predict(logX)))\n",
    "for name, x, y in zip(df.loc[:, ['molecule']].as_matrix(), X, Y):\n",
    "    plt.text(x, y, name[0], size=8)\n",
    "plt.xlabel('molecular weight')\n",
    "plt.ylabel('boiling point')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 次は、ガチPythonで。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 15,
   "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": 16,
   "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": 17,
   "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": 18,
   "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": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の傾き＝相関係数＊（（yの標準偏差）／（xの標準偏差））\n",
    "def w_fit(xlist, ylist):\n",
    "    return correlation(xlist, ylist) * standard_deviation(ylist) / standard_deviation(xlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# y切片＝yの平均－（傾き＊xの平均）\n",
    "def t_fit(xlist, ylist):\n",
    "    return mean(ylist) - w_fit(xlist, ylist) * mean(xlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = f(x) = wlogx + t; (w, t) = ([ 33.87205496], [-211.66384118])\n"
     ]
    }
   ],
   "source": [
    "# 回帰直線の式を表示\n",
    "w = w_fit(logX, Y)\n",
    "t = t_fit(logX, Y)\n",
    "print(\"y = f(x) = wlogx + t; (w, t) = ({0}, {1})\".format(w, t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の式を関数として表現\n",
    "def f(x):\n",
    "    return w * x + t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 決定係数R2\n",
    "def r2(xlist, ylist):\n",
    "    wa1 = 0.\n",
    "    wa2 = 0.\n",
    "    for x, y in zip(xlist, ylist):\n",
    "        wa1 += (y - f(x))**2\n",
    "        wa2 += (y - mean(ylist))**2\n",
    "    return 1. - wa1 / wa2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.13487034])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2(logX, Y)"
   ]
  },
  {
   "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",
       "    </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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HCl</td>\n",
       "      <td>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HBr</td>\n",
       "      <td>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>HI</td>\n",
       "      <td>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H2O</td>\n",
       "      <td>100.000</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>H2S</td>\n",
       "      <td>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>H2Se</td>\n",
       "      <td>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight\n",
       "0        HF         19.500              20.0\n",
       "1       HCl        -84.900              36.5\n",
       "2       HBr        -67.000              80.9\n",
       "3        HI        -35.100             127.9\n",
       "4       H2O        100.000              18.0\n",
       "5       H2S        -60.700              34.1\n",
       "6      H2Se        -42.000              81.0\n",
       "7      H2Te         -1.800             129.6\n",
       "8       NH3        -33.400              17.0\n",
       "9       PH3        -87.000              34.0\n",
       "10     AsH3        -55.000              77.9\n",
       "11     SbH3        -17.100             124.8\n",
       "12      CH4       -161.490              16.0\n",
       "13     SiH4       -111.800              32.1\n",
       "14     GeH4        -90.000              76.6\n",
       "15     SnH4        -52.000             122.7\n",
       "16       He       -268.934               4.0\n",
       "17       Ne       -246.048              20.2\n",
       "18       Ar       -185.700              39.9\n",
       "19       Kr       -152.300              83.8\n",
       "20       Xe       -108.100             131.3"
      ]
     },
     "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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732\n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312\n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214\n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249\n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372\n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297\n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449\n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453\n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213\n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361\n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426\n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712\n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589\n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856\n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597\n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742\n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294\n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683\n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376\n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433\n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485"
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y    log(x)\n",
       "mean -82.898667  3.801516"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['y'] = excel['boiling point']\n",
    "excel['x'] = excel['molecular weight']\n",
    "excel['log(x)'] = [math.log(x) for x in excel['x']]\n",
    "mean_y = mean(excel['y'])\n",
    "mean_logx = mean(excel['log(x)'])\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx]], columns=['y','log(x)'], 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  \n",
       "0   102.398667            -0.805784  \n",
       "1    -2.001333            -0.204204  \n",
       "2    15.898667             0.591697  \n",
       "3    47.798667             1.049732  \n",
       "4   182.898667            -0.911145  \n",
       "5    22.198667            -0.272219  \n",
       "6    40.898667             0.592933  \n",
       "7    81.098667             1.062936  \n",
       "8    49.498667            -0.968303  \n",
       "9    -4.101333            -0.275156  \n",
       "10   27.898667             0.553909  \n",
       "11   65.798667             1.025196  \n",
       "12  -78.591333            -1.028928  \n",
       "13  -28.901333            -0.332660  \n",
       "14   -7.101333             0.537081  \n",
       "15   30.898667             1.008226  \n",
       "16 -186.035333            -2.415222  \n",
       "17 -163.149333            -0.795834  \n",
       "18 -102.801333            -0.115140  \n",
       "19  -69.401333             0.626917  \n",
       "20  -25.201333             1.075968  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y    log(x)\n",
       "mean -82.898667  3.801516"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['y-mean(y)'] = [y - mean_y for y in excel['y']]\n",
    "excel['log(x)-mean(log(x))'] = [logx - mean_logx for logx in excel['log(x)']]\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx]], columns=['y','log(x)'], 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \n",
       "0   102.398667            -0.805784    10485.486935                  0.649288  \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699  \n",
       "2    15.898667             0.591697      252.767602                  0.350106  \n",
       "3    47.798667             1.049732     2284.712535                  1.101938  \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185  \n",
       "5    22.198667            -0.272219      492.780802                  0.074103  \n",
       "6    40.898667             0.592933     1672.700935                  0.351569  \n",
       "7    81.098667             1.062936     6576.993735                  1.129834  \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611  \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711  \n",
       "10   27.898667             0.553909      778.335602                  0.306816  \n",
       "11   65.798667             1.025196     4329.464535                  1.051027  \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692  \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663  \n",
       "14   -7.101333             0.537081       50.428935                  0.288456  \n",
       "15   30.898667             1.008226      954.727602                  1.016519  \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298  \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352  \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257  \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024  \n",
       "20  -25.201333             1.075968      635.107202                  1.157708  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              y    log(x)\n",
       "mean -82.898667  3.801516"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(y-mean(y))**2'] = [sa ** 2 for sa in excel['y-mean(y)']]\n",
    "excel['(log(x)-mean(log(x)))**2'] = [sa ** 2 for sa in excel['log(x)-mean(log(x))']]\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx]], columns=['y','log(x)'], 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \n",
       "0   102.398667            -0.805784    10485.486935                  0.649288  \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699  \n",
       "2    15.898667             0.591697      252.767602                  0.350106  \n",
       "3    47.798667             1.049732     2284.712535                  1.101938  \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185  \n",
       "5    22.198667            -0.272219      492.780802                  0.074103  \n",
       "6    40.898667             0.592933     1672.700935                  0.351569  \n",
       "7    81.098667             1.062936     6576.993735                  1.129834  \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611  \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711  \n",
       "10   27.898667             0.553909      778.335602                  0.306816  \n",
       "11   65.798667             1.025196     4329.464535                  1.051027  \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692  \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663  \n",
       "14   -7.101333             0.537081       50.428935                  0.288456  \n",
       "15   30.898667             1.008226      954.727602                  1.016519  \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298  \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352  \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257  \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024  \n",
       "20  -25.201333             1.075968      635.107202                  1.157708  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "variance_y = mean(excel['(y-mean(y))**2'])\n",
    "variance_logx = mean(excel['(log(x)-mean(log(x)))**2'])\n",
    "sd_y = math.sqrt(variance_y)\n",
    "sd_logx = math.sqrt(variance_logx)\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))  \n",
       "0                            -82.511226  \n",
       "1                              0.408681  \n",
       "2                              9.407199  \n",
       "3                             50.175802  \n",
       "4                           -166.647151  \n",
       "5                             -6.042901  \n",
       "6                             24.250157  \n",
       "7                             86.202719  \n",
       "8                            -47.929713  \n",
       "9                              1.128506  \n",
       "10                            15.453336  \n",
       "11                            67.456530  \n",
       "12                            80.864803  \n",
       "13                             9.614330  \n",
       "14                            -3.813988  \n",
       "15                            31.152836  \n",
       "16                           449.316648  \n",
       "17                           129.839763  \n",
       "18                            11.836560  \n",
       "19                           -43.508844  \n",
       "20                           -27.115836  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(y-mean(y)) * (log(x)-mean(log(x)))'] = excel['y-mean(y)'] * excel['log(x)-mean(log(x))']\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))  \n",
       "0                            -82.511226  \n",
       "1                              0.408681  \n",
       "2                              9.407199  \n",
       "3                             50.175802  \n",
       "4                           -166.647151  \n",
       "5                             -6.042901  \n",
       "6                             24.250157  \n",
       "7                             86.202719  \n",
       "8                            -47.929713  \n",
       "9                              1.128506  \n",
       "10                            15.453336  \n",
       "11                            67.456530  \n",
       "12                            80.864803  \n",
       "13                             9.614330  \n",
       "14                            -3.813988  \n",
       "15                            31.152836  \n",
       "16                           449.316648  \n",
       "17                           129.839763  \n",
       "18                            11.836560  \n",
       "19                           -43.508844  \n",
       "20                           -27.115836  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "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>log(x),y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>28.073248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>0.367247</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              log(x),y\n",
       "covariance   28.073248\n",
       "correlation   0.367247"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "covar_logxy = mean(excel['(y-mean(y)) * (log(x)-mean(log(x)))'])\n",
    "corr_logxy = covar_logxy / (sd_logx * sd_y)\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], index=['mean', 'variance', 'sd']),\n",
    "       pd.DataFrame([covar_logxy, corr_logxy], index=['covariance', 'correlation'], columns=['log(x),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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))  \n",
       "0                            -82.511226  \n",
       "1                              0.408681  \n",
       "2                              9.407199  \n",
       "3                             50.175802  \n",
       "4                           -166.647151  \n",
       "5                             -6.042901  \n",
       "6                             24.250157  \n",
       "7                             86.202719  \n",
       "8                            -47.929713  \n",
       "9                              1.128506  \n",
       "10                            15.453336  \n",
       "11                            67.456530  \n",
       "12                            80.864803  \n",
       "13                             9.614330  \n",
       "14                            -3.813988  \n",
       "15                            31.152836  \n",
       "16                           449.316648  \n",
       "17                           129.839763  \n",
       "18                            11.836560  \n",
       "19                           -43.508844  \n",
       "20                           -27.115836  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
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     "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>log(x),y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>28.073248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>0.367247</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              log(x),y\n",
       "covariance   28.073248\n",
       "correlation   0.367247"
      ]
     },
     "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>w</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = wlog(x) + t</th>\n",
       "      <td>33.872055</td>\n",
       "      <td>-211.663841</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                w           t\n",
       "y = f(x) = wlog(x) + t  33.872055 -211.663841"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = corr_logxy * sd_y / sd_logx\n",
    "t = mean_y - w * mean_logx\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y', 'log(x)'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([covar_logxy, corr_logxy], index=['covariance', 'correlation'], columns=['log(x),y']),\n",
    "        pd.DataFrame([[w, t]], columns=[\"w\", \"t\"], index=[\"y = f(x) = wlog(x) + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 回帰直線の式を関数として表現\n",
    "def f(x):\n",
    "    return w * x + 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</th>\n",
       "      <th>f(x)</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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</td>\n",
       "      <td>-110.192233</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</td>\n",
       "      <td>-89.815483</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</td>\n",
       "      <td>-62.856661</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</td>\n",
       "      <td>-47.342078</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</td>\n",
       "      <td>-113.761010</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</td>\n",
       "      <td>-92.119286</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "      <td>-62.814818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "      <td>-46.894829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "      <td>-115.697083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "      <td>-92.218764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "      <td>-64.136614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "      <td>-48.173172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "      <td>-117.750564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "      <td>-94.166559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "      <td>-64.706643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "      <td>-48.747984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "      <td>-164.707202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "      <td>-109.855195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "      <td>-86.798700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "      <td>-61.663715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "      <td>-46.453409</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))        f(x)  \n",
       "0                            -82.511226 -110.192233  \n",
       "1                              0.408681  -89.815483  \n",
       "2                              9.407199  -62.856661  \n",
       "3                             50.175802  -47.342078  \n",
       "4                           -166.647151 -113.761010  \n",
       "5                             -6.042901  -92.119286  \n",
       "6                             24.250157  -62.814818  \n",
       "7                             86.202719  -46.894829  \n",
       "8                            -47.929713 -115.697083  \n",
       "9                              1.128506  -92.218764  \n",
       "10                            15.453336  -64.136614  \n",
       "11                            67.456530  -48.173172  \n",
       "12                            80.864803 -117.750564  \n",
       "13                             9.614330  -94.166559  \n",
       "14                            -3.813988  -64.706643  \n",
       "15                            31.152836  -48.747984  \n",
       "16                           449.316648 -164.707202  \n",
       "17                           129.839763 -109.855195  \n",
       "18                            11.836560  -86.798700  \n",
       "19                           -43.508844  -61.663715  \n",
       "20                           -27.115836  -46.453409  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "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>log(x),y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>28.073248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>0.367247</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              log(x),y\n",
       "covariance   28.073248\n",
       "correlation   0.367247"
      ]
     },
     "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>w</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = wlog(x) + t</th>\n",
       "      <td>33.872055</td>\n",
       "      <td>-211.663841</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                w           t\n",
       "y = f(x) = wlog(x) + t  33.872055 -211.663841"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['f(x)'] = f(excel['log(x)'])\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([covar_logxy, corr_logxy], index=['covariance', 'correlation'], columns=['log(x),y']),\n",
    "        pd.DataFrame([[w, t]], columns=[\"w\", \"t\"], index=[\"y = f(x) = wlog(x) + 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</th>\n",
       "      <th>f(x)</th>\n",
       "      <th>(y-f(x))**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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</td>\n",
       "      <td>-110.192233</td>\n",
       "      <td>16820.075290</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</td>\n",
       "      <td>-89.815483</td>\n",
       "      <td>24.161969</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</td>\n",
       "      <td>-62.856661</td>\n",
       "      <td>17.167258</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</td>\n",
       "      <td>-47.342078</td>\n",
       "      <td>149.868481</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</td>\n",
       "      <td>-113.761010</td>\n",
       "      <td>45693.769454</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</td>\n",
       "      <td>-92.119286</td>\n",
       "      <td>987.171545</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "      <td>-62.814818</td>\n",
       "      <td>433.256643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "      <td>-46.894829</td>\n",
       "      <td>2033.543613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "      <td>-115.697083</td>\n",
       "      <td>6772.809882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "      <td>-92.218764</td>\n",
       "      <td>27.235494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "      <td>-64.136614</td>\n",
       "      <td>83.477714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "      <td>-48.173172</td>\n",
       "      <td>965.541992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "      <td>-117.750564</td>\n",
       "      <td>1913.138297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "      <td>-94.166559</td>\n",
       "      <td>310.938239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "      <td>-64.706643</td>\n",
       "      <td>639.753932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "      <td>-48.747984</td>\n",
       "      <td>10.575609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "      <td>-164.707202</td>\n",
       "      <td>10863.225340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "      <td>-109.855195</td>\n",
       "      <td>18548.480187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "      <td>-86.798700</td>\n",
       "      <td>9781.467196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "      <td>-61.663715</td>\n",
       "      <td>8214.936167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "      <td>-46.453409</td>\n",
       "      <td>3800.302233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))        f(x)   (y-f(x))**2  \n",
       "0                            -82.511226 -110.192233  16820.075290  \n",
       "1                              0.408681  -89.815483     24.161969  \n",
       "2                              9.407199  -62.856661     17.167258  \n",
       "3                             50.175802  -47.342078    149.868481  \n",
       "4                           -166.647151 -113.761010  45693.769454  \n",
       "5                             -6.042901  -92.119286    987.171545  \n",
       "6                             24.250157  -62.814818    433.256643  \n",
       "7                             86.202719  -46.894829   2033.543613  \n",
       "8                            -47.929713 -115.697083   6772.809882  \n",
       "9                              1.128506  -92.218764     27.235494  \n",
       "10                            15.453336  -64.136614     83.477714  \n",
       "11                            67.456530  -48.173172    965.541992  \n",
       "12                            80.864803 -117.750564   1913.138297  \n",
       "13                             9.614330  -94.166559    310.938239  \n",
       "14                            -3.813988  -64.706643    639.753932  \n",
       "15                            31.152836  -48.747984     10.575609  \n",
       "16                           449.316648 -164.707202  10863.225340  \n",
       "17                           129.839763 -109.855195  18548.480187  \n",
       "18                            11.836560  -86.798700   9781.467196  \n",
       "19                           -43.508844  -61.663715   8214.936167  \n",
       "20                           -27.115836  -46.453409   3800.302233  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "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>log(x),y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>28.073248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>0.367247</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              log(x),y\n",
       "covariance   28.073248\n",
       "correlation   0.367247"
      ]
     },
     "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>w</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = wlog(x) + t</th>\n",
       "      <td>33.872055</td>\n",
       "      <td>-211.663841</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                w           t\n",
       "y = f(x) = wlog(x) + t  33.872055 -211.663841"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "excel['(y-f(x))**2'] = (excel['y'] - excel['f(x)'])**2\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([covar_logxy, corr_logxy], index=['covariance', 'correlation'], columns=['log(x),y']),\n",
    "        pd.DataFrame([[w, t]], columns=[\"w\", \"t\"], index=[\"y = f(x) = wlog(x) + 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>y</th>\n",
       "      <th>x</th>\n",
       "      <th>log(x)</th>\n",
       "      <th>y-mean(y)</th>\n",
       "      <th>log(x)-mean(log(x))</th>\n",
       "      <th>(y-mean(y))**2</th>\n",
       "      <th>(log(x)-mean(log(x)))**2</th>\n",
       "      <th>(y-mean(y)) * (log(x)-mean(log(x)))</th>\n",
       "      <th>f(x)</th>\n",
       "      <th>(y-f(x))**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>19.500</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.995732</td>\n",
       "      <td>102.398667</td>\n",
       "      <td>-0.805784</td>\n",
       "      <td>10485.486935</td>\n",
       "      <td>0.649288</td>\n",
       "      <td>-82.511226</td>\n",
       "      <td>-110.192233</td>\n",
       "      <td>16820.075290</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>-84.900</td>\n",
       "      <td>36.5</td>\n",
       "      <td>3.597312</td>\n",
       "      <td>-2.001333</td>\n",
       "      <td>-0.204204</td>\n",
       "      <td>4.005335</td>\n",
       "      <td>0.041699</td>\n",
       "      <td>0.408681</td>\n",
       "      <td>-89.815483</td>\n",
       "      <td>24.161969</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>-67.000</td>\n",
       "      <td>80.9</td>\n",
       "      <td>4.393214</td>\n",
       "      <td>15.898667</td>\n",
       "      <td>0.591697</td>\n",
       "      <td>252.767602</td>\n",
       "      <td>0.350106</td>\n",
       "      <td>9.407199</td>\n",
       "      <td>-62.856661</td>\n",
       "      <td>17.167258</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>-35.100</td>\n",
       "      <td>127.9</td>\n",
       "      <td>4.851249</td>\n",
       "      <td>47.798667</td>\n",
       "      <td>1.049732</td>\n",
       "      <td>2284.712535</td>\n",
       "      <td>1.101938</td>\n",
       "      <td>50.175802</td>\n",
       "      <td>-47.342078</td>\n",
       "      <td>149.868481</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>100.000</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.890372</td>\n",
       "      <td>182.898667</td>\n",
       "      <td>-0.911145</td>\n",
       "      <td>33451.922268</td>\n",
       "      <td>0.830185</td>\n",
       "      <td>-166.647151</td>\n",
       "      <td>-113.761010</td>\n",
       "      <td>45693.769454</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>-60.700</td>\n",
       "      <td>34.1</td>\n",
       "      <td>3.529297</td>\n",
       "      <td>22.198667</td>\n",
       "      <td>-0.272219</td>\n",
       "      <td>492.780802</td>\n",
       "      <td>0.074103</td>\n",
       "      <td>-6.042901</td>\n",
       "      <td>-92.119286</td>\n",
       "      <td>987.171545</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>-42.000</td>\n",
       "      <td>81.0</td>\n",
       "      <td>4.394449</td>\n",
       "      <td>40.898667</td>\n",
       "      <td>0.592933</td>\n",
       "      <td>1672.700935</td>\n",
       "      <td>0.351569</td>\n",
       "      <td>24.250157</td>\n",
       "      <td>-62.814818</td>\n",
       "      <td>433.256643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>H2Te</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>-1.800</td>\n",
       "      <td>129.6</td>\n",
       "      <td>4.864453</td>\n",
       "      <td>81.098667</td>\n",
       "      <td>1.062936</td>\n",
       "      <td>6576.993735</td>\n",
       "      <td>1.129834</td>\n",
       "      <td>86.202719</td>\n",
       "      <td>-46.894829</td>\n",
       "      <td>2033.543613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NH3</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-33.400</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.833213</td>\n",
       "      <td>49.498667</td>\n",
       "      <td>-0.968303</td>\n",
       "      <td>2450.118002</td>\n",
       "      <td>0.937611</td>\n",
       "      <td>-47.929713</td>\n",
       "      <td>-115.697083</td>\n",
       "      <td>6772.809882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PH3</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>-87.000</td>\n",
       "      <td>34.0</td>\n",
       "      <td>3.526361</td>\n",
       "      <td>-4.101333</td>\n",
       "      <td>-0.275156</td>\n",
       "      <td>16.820935</td>\n",
       "      <td>0.075711</td>\n",
       "      <td>1.128506</td>\n",
       "      <td>-92.218764</td>\n",
       "      <td>27.235494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>AsH3</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>-55.000</td>\n",
       "      <td>77.9</td>\n",
       "      <td>4.355426</td>\n",
       "      <td>27.898667</td>\n",
       "      <td>0.553909</td>\n",
       "      <td>778.335602</td>\n",
       "      <td>0.306816</td>\n",
       "      <td>15.453336</td>\n",
       "      <td>-64.136614</td>\n",
       "      <td>83.477714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>SbH3</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>-17.100</td>\n",
       "      <td>124.8</td>\n",
       "      <td>4.826712</td>\n",
       "      <td>65.798667</td>\n",
       "      <td>1.025196</td>\n",
       "      <td>4329.464535</td>\n",
       "      <td>1.051027</td>\n",
       "      <td>67.456530</td>\n",
       "      <td>-48.173172</td>\n",
       "      <td>965.541992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>CH4</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-161.490</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.772589</td>\n",
       "      <td>-78.591333</td>\n",
       "      <td>-1.028928</td>\n",
       "      <td>6176.597675</td>\n",
       "      <td>1.058692</td>\n",
       "      <td>80.864803</td>\n",
       "      <td>-117.750564</td>\n",
       "      <td>1913.138297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>SiH4</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>-111.800</td>\n",
       "      <td>32.1</td>\n",
       "      <td>3.468856</td>\n",
       "      <td>-28.901333</td>\n",
       "      <td>-0.332660</td>\n",
       "      <td>835.287068</td>\n",
       "      <td>0.110663</td>\n",
       "      <td>9.614330</td>\n",
       "      <td>-94.166559</td>\n",
       "      <td>310.938239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GeH4</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>-90.000</td>\n",
       "      <td>76.6</td>\n",
       "      <td>4.338597</td>\n",
       "      <td>-7.101333</td>\n",
       "      <td>0.537081</td>\n",
       "      <td>50.428935</td>\n",
       "      <td>0.288456</td>\n",
       "      <td>-3.813988</td>\n",
       "      <td>-64.706643</td>\n",
       "      <td>639.753932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>SnH4</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>-52.000</td>\n",
       "      <td>122.7</td>\n",
       "      <td>4.809742</td>\n",
       "      <td>30.898667</td>\n",
       "      <td>1.008226</td>\n",
       "      <td>954.727602</td>\n",
       "      <td>1.016519</td>\n",
       "      <td>31.152836</td>\n",
       "      <td>-48.747984</td>\n",
       "      <td>10.575609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>He</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-268.934</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>-186.035333</td>\n",
       "      <td>-2.415222</td>\n",
       "      <td>34609.145248</td>\n",
       "      <td>5.833298</td>\n",
       "      <td>449.316648</td>\n",
       "      <td>-164.707202</td>\n",
       "      <td>10863.225340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Ne</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>-246.048</td>\n",
       "      <td>20.2</td>\n",
       "      <td>3.005683</td>\n",
       "      <td>-163.149333</td>\n",
       "      <td>-0.795834</td>\n",
       "      <td>26617.704967</td>\n",
       "      <td>0.633352</td>\n",
       "      <td>129.839763</td>\n",
       "      <td>-109.855195</td>\n",
       "      <td>18548.480187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Ar</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>-185.700</td>\n",
       "      <td>39.9</td>\n",
       "      <td>3.686376</td>\n",
       "      <td>-102.801333</td>\n",
       "      <td>-0.115140</td>\n",
       "      <td>10568.114135</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>11.836560</td>\n",
       "      <td>-86.798700</td>\n",
       "      <td>9781.467196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Kr</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>-152.300</td>\n",
       "      <td>83.8</td>\n",
       "      <td>4.428433</td>\n",
       "      <td>-69.401333</td>\n",
       "      <td>0.626917</td>\n",
       "      <td>4816.545068</td>\n",
       "      <td>0.393024</td>\n",
       "      <td>-43.508844</td>\n",
       "      <td>-61.663715</td>\n",
       "      <td>8214.936167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Xe</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>-108.100</td>\n",
       "      <td>131.3</td>\n",
       "      <td>4.877485</td>\n",
       "      <td>-25.201333</td>\n",
       "      <td>1.075968</td>\n",
       "      <td>635.107202</td>\n",
       "      <td>1.157708</td>\n",
       "      <td>-27.115836</td>\n",
       "      <td>-46.453409</td>\n",
       "      <td>3800.302233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   molecule  boiling point  molecular weight        y      x    log(x)  \\\n",
       "0        HF         19.500              20.0   19.500   20.0  2.995732   \n",
       "1       HCl        -84.900              36.5  -84.900   36.5  3.597312   \n",
       "2       HBr        -67.000              80.9  -67.000   80.9  4.393214   \n",
       "3        HI        -35.100             127.9  -35.100  127.9  4.851249   \n",
       "4       H2O        100.000              18.0  100.000   18.0  2.890372   \n",
       "5       H2S        -60.700              34.1  -60.700   34.1  3.529297   \n",
       "6      H2Se        -42.000              81.0  -42.000   81.0  4.394449   \n",
       "7      H2Te         -1.800             129.6   -1.800  129.6  4.864453   \n",
       "8       NH3        -33.400              17.0  -33.400   17.0  2.833213   \n",
       "9       PH3        -87.000              34.0  -87.000   34.0  3.526361   \n",
       "10     AsH3        -55.000              77.9  -55.000   77.9  4.355426   \n",
       "11     SbH3        -17.100             124.8  -17.100  124.8  4.826712   \n",
       "12      CH4       -161.490              16.0 -161.490   16.0  2.772589   \n",
       "13     SiH4       -111.800              32.1 -111.800   32.1  3.468856   \n",
       "14     GeH4        -90.000              76.6  -90.000   76.6  4.338597   \n",
       "15     SnH4        -52.000             122.7  -52.000  122.7  4.809742   \n",
       "16       He       -268.934               4.0 -268.934    4.0  1.386294   \n",
       "17       Ne       -246.048              20.2 -246.048   20.2  3.005683   \n",
       "18       Ar       -185.700              39.9 -185.700   39.9  3.686376   \n",
       "19       Kr       -152.300              83.8 -152.300   83.8  4.428433   \n",
       "20       Xe       -108.100             131.3 -108.100  131.3  4.877485   \n",
       "\n",
       "     y-mean(y)  log(x)-mean(log(x))  (y-mean(y))**2  (log(x)-mean(log(x)))**2  \\\n",
       "0   102.398667            -0.805784    10485.486935                  0.649288   \n",
       "1    -2.001333            -0.204204        4.005335                  0.041699   \n",
       "2    15.898667             0.591697      252.767602                  0.350106   \n",
       "3    47.798667             1.049732     2284.712535                  1.101938   \n",
       "4   182.898667            -0.911145    33451.922268                  0.830185   \n",
       "5    22.198667            -0.272219      492.780802                  0.074103   \n",
       "6    40.898667             0.592933     1672.700935                  0.351569   \n",
       "7    81.098667             1.062936     6576.993735                  1.129834   \n",
       "8    49.498667            -0.968303     2450.118002                  0.937611   \n",
       "9    -4.101333            -0.275156       16.820935                  0.075711   \n",
       "10   27.898667             0.553909      778.335602                  0.306816   \n",
       "11   65.798667             1.025196     4329.464535                  1.051027   \n",
       "12  -78.591333            -1.028928     6176.597675                  1.058692   \n",
       "13  -28.901333            -0.332660      835.287068                  0.110663   \n",
       "14   -7.101333             0.537081       50.428935                  0.288456   \n",
       "15   30.898667             1.008226      954.727602                  1.016519   \n",
       "16 -186.035333            -2.415222    34609.145248                  5.833298   \n",
       "17 -163.149333            -0.795834    26617.704967                  0.633352   \n",
       "18 -102.801333            -0.115140    10568.114135                  0.013257   \n",
       "19  -69.401333             0.626917     4816.545068                  0.393024   \n",
       "20  -25.201333             1.075968      635.107202                  1.157708   \n",
       "\n",
       "    (y-mean(y)) * (log(x)-mean(log(x)))        f(x)   (y-f(x))**2  \n",
       "0                            -82.511226 -110.192233  16820.075290  \n",
       "1                              0.408681  -89.815483     24.161969  \n",
       "2                              9.407199  -62.856661     17.167258  \n",
       "3                             50.175802  -47.342078    149.868481  \n",
       "4                           -166.647151 -113.761010  45693.769454  \n",
       "5                             -6.042901  -92.119286    987.171545  \n",
       "6                             24.250157  -62.814818    433.256643  \n",
       "7                             86.202719  -46.894829   2033.543613  \n",
       "8                            -47.929713 -115.697083   6772.809882  \n",
       "9                              1.128506  -92.218764     27.235494  \n",
       "10                            15.453336  -64.136614     83.477714  \n",
       "11                            67.456530  -48.173172    965.541992  \n",
       "12                            80.864803 -117.750564   1913.138297  \n",
       "13                             9.614330  -94.166559    310.938239  \n",
       "14                            -3.813988  -64.706643    639.753932  \n",
       "15                            31.152836  -48.747984     10.575609  \n",
       "16                           449.316648 -164.707202  10863.225340  \n",
       "17                           129.839763 -109.855195  18548.480187  \n",
       "18                            11.836560  -86.798700   9781.467196  \n",
       "19                           -43.508844  -61.663715   8214.936167  \n",
       "20                           -27.115836  -46.453409   3800.302233  "
      ]
     },
     "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>log(x)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-82.898667</td>\n",
       "      <td>3.801516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>variance</th>\n",
       "      <td>7050.465101</td>\n",
       "      <td>0.828803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sd</th>\n",
       "      <td>83.967048</td>\n",
       "      <td>0.910386</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    y    log(x)\n",
       "mean       -82.898667  3.801516\n",
       "variance  7050.465101  0.828803\n",
       "sd          83.967048  0.910386"
      ]
     },
     "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>log(x),y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>covariance</th>\n",
       "      <td>28.073248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>correlation</th>\n",
       "      <td>0.367247</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              log(x),y\n",
       "covariance   28.073248\n",
       "correlation   0.367247"
      ]
     },
     "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>w</th>\n",
       "      <th>t</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y = f(x) = wlog(x) + t</th>\n",
       "      <td>33.872055</td>\n",
       "      <td>-211.663841</td>\n",
       "      <td>0.13487</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                w           t       R2\n",
       "y = f(x) = wlog(x) + t  33.872055 -211.663841  0.13487"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r2 = 1. - sum(excel['(y-f(x))**2']) / sum(excel['(y-mean(y))**2'])\n",
    "display(excel, pd.DataFrame([[mean_y, mean_logx], [variance_y, variance_logx], [sd_y, sd_logx]], \n",
    "                            columns=['y','log(x)'], index=['mean', 'variance', 'sd']),\n",
    "        pd.DataFrame([covar_logxy, corr_logxy], index=['covariance', 'correlation'], columns=['log(x),y']),\n",
    "        pd.DataFrame([[w, t, r2]], columns=[\"w\", \"t\", \"R2\"], index=[\"y = f(x) = wlog(x) + t\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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