Analysing_student_performance.ipynb

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      "name": "Analysing-student-performance.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/divijsingh02/Analysing-student-performance/blob/main/Analysing_student_performance.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XL0Wfjid3m15"
      },
      "source": [
        "Importing libraries and dataset\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VbG0Fdburzla"
      },
      "source": [
        "\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "\n",
        "dataset = pd.read_csv('StudentsPerformance.csv')\n",
        "X = dataset.iloc[:, :-1].values\n",
        "y = dataset.iloc[:, -1].values"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kXseIsg130Wd"
      },
      "source": [
        "Encoding the variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jWYSrTxirzlg"
      },
      "source": [
        "from sklearn.compose import ColumnTransformer\n",
        "from sklearn.preprocessing import OneHotEncoder\n",
        "ct = ColumnTransformer(transformers=[('encoder', OneHotEncoder(), list(range(5)))], remainder='passthrough')\n",
        "X = np.array(ct.fit_transform(X))"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nVyuXjHQrzlh"
      },
      "source": [
        "##### Spliting dataset\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WWt1K-Mxrzlh"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 1)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K8C82rmH4SNh"
      },
      "source": [
        "Scaling the values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i0OAz0xqrzlh"
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "sc = StandardScaler()\n",
        "X_train = sc.fit_transform(X_train)\n",
        "X_test = sc.transform(X_test)\n"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E14RHGuM4VF8"
      },
      "source": [
        "Implementing neural network model \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NNg4cw9Urzli"
      },
      "source": [
        "ann = tf.keras.models.Sequential()"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "27HpmTJ12CE0"
      },
      "source": [
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "ann.add(tf.keras.layers.Dense(units=2048, activation='relu'))\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "51FQRRTQrzli"
      },
      "source": [
        "ann.add(tf.keras.layers.Dense(units=1, activation='linear'))"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rDqAJBv4rzli"
      },
      "source": [
        "ann.compile(optimizer = 'adam', loss = 'mean_squared_error', metrics = ['mean_squared_error'])"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bE1O0Yc84kgw"
      },
      "source": [
        "  Training the model with batch size =128 and epoch = 50\n",
        "  \n",
        "  Best result achieved by this model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J0VSnXB5rzlj",
        "outputId": "e0fa2d7d-6bed-4090-c108-02829c69d58f"
      },
      "source": [
        "ann.fit(X_train, y_train, batch_size = 128, epochs = 50 ,validation_split=0.1 )  #8 , 200"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/50\n",
            "6/6 [==============================] - 4s 95ms/step - loss: 14428.2113 - mean_squared_error: 14428.2113 - val_loss: 4999.4854 - val_mean_squared_error: 4999.4854\n",
            "Epoch 2/50\n",
            "6/6 [==============================] - 0s 23ms/step - loss: 4970.8186 - mean_squared_error: 4970.8186 - val_loss: 4638.5234 - val_mean_squared_error: 4638.5234\n",
            "Epoch 3/50\n",
            "6/6 [==============================] - 0s 22ms/step - loss: 3488.2695 - mean_squared_error: 3488.2695 - val_loss: 737.5457 - val_mean_squared_error: 737.5457\n",
            "Epoch 4/50\n",
            "6/6 [==============================] - 0s 20ms/step - loss: 751.6541 - mean_squared_error: 751.6541 - val_loss: 1242.9326 - val_mean_squared_error: 1242.9326\n",
            "Epoch 5/50\n",
            "6/6 [==============================] - 0s 19ms/step - loss: 778.4428 - mean_squared_error: 778.4428 - val_loss: 553.6439 - val_mean_squared_error: 553.6439\n",
            "Epoch 6/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 344.3437 - mean_squared_error: 344.3437 - val_loss: 330.5439 - val_mean_squared_error: 330.5439\n",
            "Epoch 7/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 212.7440 - mean_squared_error: 212.7440 - val_loss: 140.6303 - val_mean_squared_error: 140.6303\n",
            "Epoch 8/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 85.9963 - mean_squared_error: 85.9963 - val_loss: 78.7422 - val_mean_squared_error: 78.7422\n",
            "Epoch 9/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 64.9921 - mean_squared_error: 64.9921 - val_loss: 43.3292 - val_mean_squared_error: 43.3292\n",
            "Epoch 10/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 42.2333 - mean_squared_error: 42.2333 - val_loss: 35.5902 - val_mean_squared_error: 35.5902\n",
            "Epoch 11/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 33.0565 - mean_squared_error: 33.0565 - val_loss: 34.3170 - val_mean_squared_error: 34.3170\n",
            "Epoch 12/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 31.5894 - mean_squared_error: 31.5894 - val_loss: 35.5835 - val_mean_squared_error: 35.5835\n",
            "Epoch 13/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 24.4329 - mean_squared_error: 24.4329 - val_loss: 30.3644 - val_mean_squared_error: 30.3644\n",
            "Epoch 14/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 21.3144 - mean_squared_error: 21.3144 - val_loss: 29.2835 - val_mean_squared_error: 29.2835\n",
            "Epoch 15/50\n",
            "6/6 [==============================] - 0s 15ms/step - loss: 19.9999 - mean_squared_error: 19.9999 - val_loss: 28.3318 - val_mean_squared_error: 28.3318\n",
            "Epoch 16/50\n",
            "6/6 [==============================] - 0s 15ms/step - loss: 19.5113 - mean_squared_error: 19.5113 - val_loss: 27.6932 - val_mean_squared_error: 27.6932\n",
            "Epoch 17/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 18.1766 - mean_squared_error: 18.1766 - val_loss: 26.3810 - val_mean_squared_error: 26.3810\n",
            "Epoch 18/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 17.5431 - mean_squared_error: 17.5431 - val_loss: 26.4460 - val_mean_squared_error: 26.4460\n",
            "Epoch 19/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 16.5801 - mean_squared_error: 16.5801 - val_loss: 25.8478 - val_mean_squared_error: 25.8478\n",
            "Epoch 20/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 16.4904 - mean_squared_error: 16.4904 - val_loss: 25.1250 - val_mean_squared_error: 25.1250\n",
            "Epoch 21/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 14.9257 - mean_squared_error: 14.9257 - val_loss: 24.8039 - val_mean_squared_error: 24.8039\n",
            "Epoch 22/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 15.9343 - mean_squared_error: 15.9343 - val_loss: 24.5788 - val_mean_squared_error: 24.5788\n",
            "Epoch 23/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 14.8616 - mean_squared_error: 14.8616 - val_loss: 25.0331 - val_mean_squared_error: 25.0331\n",
            "Epoch 24/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 14.0902 - mean_squared_error: 14.0902 - val_loss: 23.9133 - val_mean_squared_error: 23.9133\n",
            "Epoch 25/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 13.7712 - mean_squared_error: 13.7712 - val_loss: 24.1570 - val_mean_squared_error: 24.1570\n",
            "Epoch 26/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 13.9060 - mean_squared_error: 13.9060 - val_loss: 23.5773 - val_mean_squared_error: 23.5773\n",
            "Epoch 27/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 13.2973 - mean_squared_error: 13.2973 - val_loss: 23.5590 - val_mean_squared_error: 23.5590\n",
            "Epoch 28/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 13.7954 - mean_squared_error: 13.7954 - val_loss: 23.2742 - val_mean_squared_error: 23.2742\n",
            "Epoch 29/50\n",
            "6/6 [==============================] - 0s 19ms/step - loss: 13.0906 - mean_squared_error: 13.0906 - val_loss: 23.1121 - val_mean_squared_error: 23.1121\n",
            "Epoch 30/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 12.2757 - mean_squared_error: 12.2757 - val_loss: 23.5214 - val_mean_squared_error: 23.5214\n",
            "Epoch 31/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.9948 - mean_squared_error: 12.9948 - val_loss: 23.1729 - val_mean_squared_error: 23.1729\n",
            "Epoch 32/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 11.5551 - mean_squared_error: 11.5551 - val_loss: 22.5169 - val_mean_squared_error: 22.5169\n",
            "Epoch 33/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.2925 - mean_squared_error: 12.2925 - val_loss: 22.2878 - val_mean_squared_error: 22.2878\n",
            "Epoch 34/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.6090 - mean_squared_error: 12.6090 - val_loss: 25.5799 - val_mean_squared_error: 25.5799\n",
            "Epoch 35/50\n",
            "6/6 [==============================] - 0s 18ms/step - loss: 13.2192 - mean_squared_error: 13.2192 - val_loss: 22.5893 - val_mean_squared_error: 22.5893\n",
            "Epoch 36/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 12.8359 - mean_squared_error: 12.8359 - val_loss: 22.6740 - val_mean_squared_error: 22.6740\n",
            "Epoch 37/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 11.5782 - mean_squared_error: 11.5782 - val_loss: 22.5107 - val_mean_squared_error: 22.5107\n",
            "Epoch 38/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 11.7622 - mean_squared_error: 11.7622 - val_loss: 22.1418 - val_mean_squared_error: 22.1418\n",
            "Epoch 39/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.4394 - mean_squared_error: 12.4394 - val_loss: 22.5668 - val_mean_squared_error: 22.5668\n",
            "Epoch 40/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 11.6909 - mean_squared_error: 11.6909 - val_loss: 22.9203 - val_mean_squared_error: 22.9203\n",
            "Epoch 41/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 11.1084 - mean_squared_error: 11.1084 - val_loss: 22.8614 - val_mean_squared_error: 22.8614\n",
            "Epoch 42/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 11.3902 - mean_squared_error: 11.3902 - val_loss: 23.3925 - val_mean_squared_error: 23.3925\n",
            "Epoch 43/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 12.4558 - mean_squared_error: 12.4558 - val_loss: 22.5447 - val_mean_squared_error: 22.5447\n",
            "Epoch 44/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 11.2325 - mean_squared_error: 11.2325 - val_loss: 23.6538 - val_mean_squared_error: 23.6538\n",
            "Epoch 45/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.4412 - mean_squared_error: 12.4412 - val_loss: 22.6493 - val_mean_squared_error: 22.6493\n",
            "Epoch 46/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 12.2946 - mean_squared_error: 12.2946 - val_loss: 22.1996 - val_mean_squared_error: 22.1996\n",
            "Epoch 47/50\n",
            "6/6 [==============================] - 0s 15ms/step - loss: 11.5314 - mean_squared_error: 11.5314 - val_loss: 22.6042 - val_mean_squared_error: 22.6042\n",
            "Epoch 48/50\n",
            "6/6 [==============================] - 0s 17ms/step - loss: 11.3366 - mean_squared_error: 11.3366 - val_loss: 23.2801 - val_mean_squared_error: 23.2801\n",
            "Epoch 49/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 10.8425 - mean_squared_error: 10.8425 - val_loss: 22.1326 - val_mean_squared_error: 22.1326\n",
            "Epoch 50/50\n",
            "6/6 [==============================] - 0s 16ms/step - loss: 10.3637 - mean_squared_error: 10.3637 - val_loss: 23.2571 - val_mean_squared_error: 23.2571\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7f366006d950>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mqlfl11R5Iur"
      },
      "source": [
        "Mean squared loss = 2.45 which is quite less hence our model works great\n",
        "It shows that there is a great correlation between reading score and the rest of the features of the data\n",
        "\n",
        "\n",
        "\n",
        "**Here , I have compared predicted values with test values**\n",
        "\n",
        "Mean absolute error = 3.355 , Which far more impressive than I expected"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qN71P1krrzlj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "68ad3352-fec7-4d7a-fa55-3e8970160ba4"
      },
      "source": [
        "y_pred = ann.predict(X_test)\n",
        "test_mean_sq_error=0\n",
        "n=len(y_pred)\n",
        "for i in range(n):\n",
        "\n",
        "  if y_pred[i]-int(y_pred[i])>=0.5:\n",
        "    y_pred[i]=int(y_pred[i])+1\n",
        "  else:\n",
        "    y_pred[i]=int(y_pred[i])\n",
        "for i in range(n):\n",
        "  test_mean_sq_error+=abs(y_pred[i]-y_test[i])\n",
        "print(test_mean_sq_error/n)\n",
        "print(np.concatenate((y_pred.reshape(len(y_pred),1), y_test.reshape(len(y_test),1)),1))"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3.355]\n",
            "[[ 55.  59.]\n",
            " [ 75.  72.]\n",
            " [ 76.  77.]\n",
            " [ 60.  64.]\n",
            " [ 59.  52.]\n",
            " [ 55.  56.]\n",
            " [ 54.  50.]\n",
            " [ 42.  31.]\n",
            " [ 69.  71.]\n",
            " [ 83.  84.]\n",
            " [ 62.  66.]\n",
            " [ 57.  55.]\n",
            " [ 67.  76.]\n",
            " [ 76.  80.]\n",
            " [ 75.  72.]\n",
            " [ 84.  81.]\n",
            " [ 91.  86.]\n",
            " [ 95.  95.]\n",
            " [ 62.  60.]\n",
            " [ 56.  48.]\n",
            " [ 88.  84.]\n",
            " [ 82.  86.]\n",
            " [ 74.  77.]\n",
            " [ 58.  61.]\n",
            " [ 53.  59.]\n",
            " [ 65.  69.]\n",
            " [ 72.  76.]\n",
            " [ 72.  62.]\n",
            " [ 68.  66.]\n",
            " [ 73.  70.]\n",
            " [ 50.  42.]\n",
            " [ 76.  76.]\n",
            " [ 51.  55.]\n",
            " [ 70.  64.]\n",
            " [ 63.  59.]\n",
            " [ 82.  85.]\n",
            " [ 68.  74.]\n",
            " [ 58.  59.]\n",
            " [ 63.  65.]\n",
            " [100.  93.]\n",
            " [ 79.  84.]\n",
            " [ 80.  76.]\n",
            " [ 74.  72.]\n",
            " [ 70.  74.]\n",
            " [ 92.  86.]\n",
            " [ 94.  91.]\n",
            " [ 64.  66.]\n",
            " [ 70.  73.]\n",
            " [ 55.  58.]\n",
            " [ 94.  99.]\n",
            " [ 83.  81.]\n",
            " [ 88.  87.]\n",
            " [ 77.  74.]\n",
            " [ 77.  81.]\n",
            " [ 78.  75.]\n",
            " [ 51.  56.]\n",
            " [ 79.  76.]\n",
            " [ 73.  82.]\n",
            " [ 58.  47.]\n",
            " [ 99.  99.]\n",
            " [ 51.  52.]\n",
            " [ 55.  52.]\n",
            " [ 43.  45.]\n",
            " [ 61.  58.]\n",
            " [ 53.  52.]\n",
            " [ 65.  64.]\n",
            " [ 66.  58.]\n",
            " [ 67.  59.]\n",
            " [ 51.  41.]\n",
            " [ 34.  32.]\n",
            " [ 58.  61.]\n",
            " [ 77.  77.]\n",
            " [ 84.  83.]\n",
            " [ 59.  57.]\n",
            " [ 52.  54.]\n",
            " [ 65.  64.]\n",
            " [ 76.  83.]\n",
            " [ 55.  57.]\n",
            " [ 43.  37.]\n",
            " [ 79.  76.]\n",
            " [ 70.  73.]\n",
            " [ 84.  84.]\n",
            " [ 53.  58.]\n",
            " [ 72.  68.]\n",
            " [ 81.  77.]\n",
            " [ 77.  76.]\n",
            " [ 94.  90.]\n",
            " [ 80.  77.]\n",
            " [ 63.  66.]\n",
            " [ 47.  53.]\n",
            " [ 80.  79.]\n",
            " [ 86.  88.]\n",
            " [ 73.  74.]\n",
            " [ 81.  87.]\n",
            " [ 78.  72.]\n",
            " [ 54.  57.]\n",
            " [ 66.  66.]\n",
            " [ 78.  76.]\n",
            " [ 78.  75.]\n",
            " [ 63.  67.]\n",
            " [ 69.  68.]\n",
            " [ 72.  72.]\n",
            " [ 84.  84.]\n",
            " [ 80.  74.]\n",
            " [ 60.  59.]\n",
            " [ 56.  58.]\n",
            " [ 77.  72.]\n",
            " [ 73.  66.]\n",
            " [ 67.  66.]\n",
            " [ 64.  68.]\n",
            " [ 68.  71.]\n",
            " [ 47.  51.]\n",
            " [ 80.  73.]\n",
            " [ 25.  17.]\n",
            " [ 72.  74.]\n",
            " [ 88.  91.]\n",
            " [ 84.  85.]\n",
            " [ 75.  73.]\n",
            " [ 89.  92.]\n",
            " [ 53.  52.]\n",
            " [ 71.  68.]\n",
            " [ 61.  60.]\n",
            " [ 48.  57.]\n",
            " [ 83.  84.]\n",
            " [ 76.  66.]\n",
            " [ 45.  40.]\n",
            " [ 60.  55.]\n",
            " [ 73.  75.]\n",
            " [ 98.  97.]\n",
            " [ 81.  74.]\n",
            " [ 90.  90.]\n",
            " [ 66.  64.]\n",
            " [ 88.  87.]\n",
            " [100.  95.]\n",
            " [ 65.  71.]\n",
            " [ 58.  62.]\n",
            " [ 74.  72.]\n",
            " [ 79.  79.]\n",
            " [ 62.  62.]\n",
            " [ 58.  60.]\n",
            " [ 63.  57.]\n",
            " [ 80.  82.]\n",
            " [ 82.  81.]\n",
            " [ 83.  83.]\n",
            " [ 55.  55.]\n",
            " [ 88.  92.]\n",
            " [ 56.  49.]\n",
            " [100. 100.]\n",
            " [ 39.  39.]\n",
            " [ 51.  48.]\n",
            " [ 69.  71.]\n",
            " [100. 100.]\n",
            " [ 64.  64.]\n",
            " [ 80.  79.]\n",
            " [ 86.  85.]\n",
            " [ 53.  51.]\n",
            " [ 66.  72.]\n",
            " [ 79.  80.]\n",
            " [ 39.  39.]\n",
            " [ 70.  72.]\n",
            " [ 67.  62.]\n",
            " [ 77.  71.]\n",
            " [ 92.  95.]\n",
            " [ 47.  58.]\n",
            " [ 62.  72.]\n",
            " [ 63.  67.]\n",
            " [ 72.  74.]\n",
            " [ 52.  54.]\n",
            " [ 82.  84.]\n",
            " [ 57.  55.]\n",
            " [ 71.  77.]\n",
            " [ 48.  45.]\n",
            " [ 55.  52.]\n",
            " [ 77.  83.]\n",
            " [ 59.  56.]\n",
            " [ 77.  81.]\n",
            " [ 70.  76.]\n",
            " [ 83.  89.]\n",
            " [ 92.  90.]\n",
            " [ 61.  63.]\n",
            " [ 89.  86.]\n",
            " [ 51.  55.]\n",
            " [ 63.  59.]\n",
            " [ 75.  78.]\n",
            " [ 57.  54.]\n",
            " [ 75.  64.]\n",
            " [ 84.  84.]\n",
            " [ 80.  80.]\n",
            " [ 64.  63.]\n",
            " [ 93.  87.]\n",
            " [ 64.  66.]\n",
            " [ 69.  68.]\n",
            " [ 86.  87.]\n",
            " [ 76.  77.]\n",
            " [ 69.  63.]\n",
            " [ 62.  66.]\n",
            " [ 63.  62.]\n",
            " [ 76.  76.]\n",
            " [ 64.  64.]\n",
            " [ 80.  80.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aoTIG3O1FTEu"
      },
      "source": [
        "Graphical Representation of predicted values and true values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X0hnoBoNrzlj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 668
        },
        "outputId": "b1d6b0d1-b620-4906-ccd0-f1e9b297c0a0"
      },
      "source": [
        "plt.figure(figsize=(10,10))\n",
        "plt.scatter(y_test, y_pred, c='crimson')\n",
        "plt.yscale('log')\n",
        "plt.xscale('log')\n",
        "\n",
        "p1 = max(max(y_pred), max(y_test))\n",
        "p2 = min(min(y_pred), min(y_test))\n",
        "plt.plot([p1, p2], [p1, p2], 'b-')\n",
        "plt.xlabel('True Values', fontsize=15)\n",
        "plt.ylabel('Predictions', fontsize=15)\n",
        "plt.axis('equal')\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_asarray.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
            "  return array(a, dtype, copy=False, order=order, subok=True)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PYUq-swvFFuu"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}