Linear_Regression_Boston_Housing_dataset.ipynb

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      "name": "Linear Regression - Boston Housing dataset.ipynb",
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        "<a href=\"https://colab.research.google.com/github/PrawinSankar777/Machine-Learning/blob/master/Linear_Regression_Boston_Housing_dataset.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "Function Initialization"
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      "source": [
        "#importing libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.animation import FuncAnimation\n",
        "\n",
        "from sklearn.datasets import load_boston\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "\n",
        "from IPython.display import HTML"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "asshb2PIVBTL",
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          "height": 904
        },
        "outputId": "c002ce87-9516-4c52-d859-3e2ed6fd9f47"
      },
      "source": [
        "boston = load_boston()\n",
        "print(boston.DESCR)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            ".. _boston_dataset:\n",
            "\n",
            "Boston house prices dataset\n",
            "---------------------------\n",
            "\n",
            "**Data Set Characteristics:**  \n",
            "\n",
            "    :Number of Instances: 506 \n",
            "\n",
            "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
            "\n",
            "    :Attribute Information (in order):\n",
            "        - CRIM     per capita crime rate by town\n",
            "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
            "        - INDUS    proportion of non-retail business acres per town\n",
            "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
            "        - NOX      nitric oxides concentration (parts per 10 million)\n",
            "        - RM       average number of rooms per dwelling\n",
            "        - AGE      proportion of owner-occupied units built prior to 1940\n",
            "        - DIS      weighted distances to five Boston employment centres\n",
            "        - RAD      index of accessibility to radial highways\n",
            "        - TAX      full-value property-tax rate per $10,000\n",
            "        - PTRATIO  pupil-teacher ratio by town\n",
            "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
            "        - LSTAT    % lower status of the population\n",
            "        - MEDV     Median value of owner-occupied homes in $1000's\n",
            "\n",
            "    :Missing Attribute Values: None\n",
            "\n",
            "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
            "\n",
            "This is a copy of UCI ML housing dataset.\n",
            "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
            "\n",
            "\n",
            "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
            "\n",
            "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
            "prices and the demand for clean air', J. Environ. Economics & Management,\n",
            "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
            "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
            "pages 244-261 of the latter.\n",
            "\n",
            "The Boston house-price data has been used in many machine learning papers that address regression\n",
            "problems.   \n",
            "     \n",
            ".. topic:: References\n",
            "\n",
            "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
            "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
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          "height": 419
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        "outputId": "103cb28a-58fb-4487-a505-6b24dd093895"
      },
      "source": [
        "features = pd.DataFrame(boston.data,columns = boston.feature_names)\n",
        "features"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
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              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "      <th>501</th>\n",
              "      <td>0.06263</td>\n",
              "      <td>0.0</td>\n",
              "      <td>11.93</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.573</td>\n",
              "      <td>6.593</td>\n",
              "      <td>69.1</td>\n",
              "      <td>2.4786</td>\n",
              "      <td>1.0</td>\n",
              "      <td>273.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>391.99</td>\n",
              "      <td>9.67</td>\n",
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              "    <tr>\n",
              "      <th>502</th>\n",
              "      <td>0.04527</td>\n",
              "      <td>0.0</td>\n",
              "      <td>11.93</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.573</td>\n",
              "      <td>6.120</td>\n",
              "      <td>76.7</td>\n",
              "      <td>2.2875</td>\n",
              "      <td>1.0</td>\n",
              "      <td>273.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.08</td>\n",
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              "      <th>503</th>\n",
              "      <td>0.06076</td>\n",
              "      <td>0.0</td>\n",
              "      <td>11.93</td>\n",
              "      <td>0.0</td>\n",
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              "      <td>2.1675</td>\n",
              "      <td>1.0</td>\n",
              "      <td>273.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.64</td>\n",
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              "      <th>504</th>\n",
              "      <td>0.10959</td>\n",
              "      <td>0.0</td>\n",
              "      <td>11.93</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.573</td>\n",
              "      <td>6.794</td>\n",
              "      <td>89.3</td>\n",
              "      <td>2.3889</td>\n",
              "      <td>1.0</td>\n",
              "      <td>273.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>393.45</td>\n",
              "      <td>6.48</td>\n",
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              "      <td>0.04741</td>\n",
              "      <td>0.0</td>\n",
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              "      <td>0.573</td>\n",
              "      <td>6.030</td>\n",
              "      <td>80.8</td>\n",
              "      <td>2.5050</td>\n",
              "      <td>1.0</td>\n",
              "      <td>273.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>396.90</td>\n",
              "      <td>7.88</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "<p>506 rows × 13 columns</p>\n",
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              "        CRIM    ZN  INDUS  CHAS    NOX  ...  RAD    TAX  PTRATIO       B  LSTAT\n",
              "0    0.00632  18.0   2.31   0.0  0.538  ...  1.0  296.0     15.3  396.90   4.98\n",
              "1    0.02731   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  396.90   9.14\n",
              "2    0.02729   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  392.83   4.03\n",
              "3    0.03237   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  394.63   2.94\n",
              "4    0.06905   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  396.90   5.33\n",
              "..       ...   ...    ...   ...    ...  ...  ...    ...      ...     ...    ...\n",
              "501  0.06263   0.0  11.93   0.0  0.573  ...  1.0  273.0     21.0  391.99   9.67\n",
              "502  0.04527   0.0  11.93   0.0  0.573  ...  1.0  273.0     21.0  396.90   9.08\n",
              "503  0.06076   0.0  11.93   0.0  0.573  ...  1.0  273.0     21.0  396.90   5.64\n",
              "504  0.10959   0.0  11.93   0.0  0.573  ...  1.0  273.0     21.0  393.45   6.48\n",
              "505  0.04741   0.0  11.93   0.0  0.573  ...  1.0  273.0     21.0  396.90   7.88\n",
              "\n",
              "[506 rows x 13 columns]"
            ]
          },
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          "execution_count": 3
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          "height": 221
        },
        "outputId": "bc12fd88-cb2b-4882-c514-77ba0a515078"
      },
      "source": [
        "features['AGE']"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      65.2\n",
              "1      78.9\n",
              "2      61.1\n",
              "3      45.8\n",
              "4      54.2\n",
              "       ... \n",
              "501    69.1\n",
              "502    76.7\n",
              "503    91.0\n",
              "504    89.3\n",
              "505    80.8\n",
              "Name: AGE, Length: 506, dtype: float64"
            ]
          },
          "metadata": {
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          "execution_count": 4
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      ]
    },
    {
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      "metadata": {
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        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "outputId": "2a920bd4-8403-4690-af7b-9e5e1a064897"
      },
      "source": [
        "target = pd.DataFrame(boston.target,columns = ['target'])\n",
        "target"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "      <th></th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>501</th>\n",
              "      <td>22.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>502</th>\n",
              "      <td>20.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>503</th>\n",
              "      <td>23.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>504</th>\n",
              "      <td>22.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>505</th>\n",
              "      <td>11.9</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "<p>506 rows × 1 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "     target\n",
              "0      24.0\n",
              "1      21.6\n",
              "2      34.7\n",
              "3      33.4\n",
              "4      36.2\n",
              "..      ...\n",
              "501    22.4\n",
              "502    20.6\n",
              "503    23.9\n",
              "504    22.0\n",
              "505    11.9\n",
              "\n",
              "[506 rows x 1 columns]"
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          "execution_count": 5
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          "height": 34
        },
        "outputId": "5e23cbce-b690-41ad-f714-9699017ca112"
      },
      "source": [
        "max(target['target'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "50.0"
            ]
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          "metadata": {
            "tags": []
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          "execution_count": 6
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      "source": [
        "min(target['target'])"
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.0"
            ]
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          "metadata": {
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          "execution_count": 7
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        "outputId": "e1512de8-6a50-4bc6-bdb5-1c7806ea0614"
      },
      "source": [
        "df = pd.concat((features,target),axis = 1)\n",
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
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              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      CRIM    ZN  INDUS  CHAS    NOX  ...    TAX  PTRATIO       B  LSTAT  target\n",
              "0  0.00632  18.0   2.31   0.0  0.538  ...  296.0     15.3  396.90   4.98    24.0\n",
              "1  0.02731   0.0   7.07   0.0  0.469  ...  242.0     17.8  396.90   9.14    21.6\n",
              "2  0.02729   0.0   7.07   0.0  0.469  ...  242.0     17.8  392.83   4.03    34.7\n",
              "3  0.03237   0.0   2.18   0.0  0.458  ...  222.0     18.7  394.63   2.94    33.4\n",
              "4  0.06905   0.0   2.18   0.0  0.458  ...  222.0     18.7  396.90   5.33    36.2\n",
              "\n",
              "[5 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0lvXUmjLVBTt",
        "colab_type": "text"
      },
      "source": [
        "**Use describe() to generate a summary of the dataset**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nuPiqaAwVBTu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "5fda36c6-6520-4e47-f84a-d3c89acb4181"
      },
      "source": [
        "#Using rounding off of decimals(2 places)to set the precision\n",
        "df.describe().round(decimals = 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "      <td>506.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>3.61</td>\n",
              "      <td>11.36</td>\n",
              "      <td>11.14</td>\n",
              "      <td>0.07</td>\n",
              "      <td>0.55</td>\n",
              "      <td>6.28</td>\n",
              "      <td>68.57</td>\n",
              "      <td>3.80</td>\n",
              "      <td>9.55</td>\n",
              "      <td>408.24</td>\n",
              "      <td>18.46</td>\n",
              "      <td>356.67</td>\n",
              "      <td>12.65</td>\n",
              "      <td>22.53</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>8.60</td>\n",
              "      <td>23.32</td>\n",
              "      <td>6.86</td>\n",
              "      <td>0.25</td>\n",
              "      <td>0.12</td>\n",
              "      <td>0.70</td>\n",
              "      <td>28.15</td>\n",
              "      <td>2.11</td>\n",
              "      <td>8.71</td>\n",
              "      <td>168.54</td>\n",
              "      <td>2.16</td>\n",
              "      <td>91.29</td>\n",
              "      <td>7.14</td>\n",
              "      <td>9.20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.01</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.46</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.38</td>\n",
              "      <td>3.56</td>\n",
              "      <td>2.90</td>\n",
              "      <td>1.13</td>\n",
              "      <td>1.00</td>\n",
              "      <td>187.00</td>\n",
              "      <td>12.60</td>\n",
              "      <td>0.32</td>\n",
              "      <td>1.73</td>\n",
              "      <td>5.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>0.08</td>\n",
              "      <td>0.00</td>\n",
              "      <td>5.19</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.45</td>\n",
              "      <td>5.89</td>\n",
              "      <td>45.02</td>\n",
              "      <td>2.10</td>\n",
              "      <td>4.00</td>\n",
              "      <td>279.00</td>\n",
              "      <td>17.40</td>\n",
              "      <td>375.38</td>\n",
              "      <td>6.95</td>\n",
              "      <td>17.02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>0.26</td>\n",
              "      <td>0.00</td>\n",
              "      <td>9.69</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.54</td>\n",
              "      <td>6.21</td>\n",
              "      <td>77.50</td>\n",
              "      <td>3.21</td>\n",
              "      <td>5.00</td>\n",
              "      <td>330.00</td>\n",
              "      <td>19.05</td>\n",
              "      <td>391.44</td>\n",
              "      <td>11.36</td>\n",
              "      <td>21.20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>3.68</td>\n",
              "      <td>12.50</td>\n",
              "      <td>18.10</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.62</td>\n",
              "      <td>6.62</td>\n",
              "      <td>94.07</td>\n",
              "      <td>5.19</td>\n",
              "      <td>24.00</td>\n",
              "      <td>666.00</td>\n",
              "      <td>20.20</td>\n",
              "      <td>396.22</td>\n",
              "      <td>16.96</td>\n",
              "      <td>25.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>88.98</td>\n",
              "      <td>100.00</td>\n",
              "      <td>27.74</td>\n",
              "      <td>1.00</td>\n",
              "      <td>0.87</td>\n",
              "      <td>8.78</td>\n",
              "      <td>100.00</td>\n",
              "      <td>12.13</td>\n",
              "      <td>24.00</td>\n",
              "      <td>711.00</td>\n",
              "      <td>22.00</td>\n",
              "      <td>396.90</td>\n",
              "      <td>37.97</td>\n",
              "      <td>50.00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         CRIM      ZN   INDUS    CHAS  ...  PTRATIO       B   LSTAT  target\n",
              "count  506.00  506.00  506.00  506.00  ...   506.00  506.00  506.00  506.00\n",
              "mean     3.61   11.36   11.14    0.07  ...    18.46  356.67   12.65   22.53\n",
              "std      8.60   23.32    6.86    0.25  ...     2.16   91.29    7.14    9.20\n",
              "min      0.01    0.00    0.46    0.00  ...    12.60    0.32    1.73    5.00\n",
              "25%      0.08    0.00    5.19    0.00  ...    17.40  375.38    6.95   17.02\n",
              "50%      0.26    0.00    9.69    0.00  ...    19.05  391.44   11.36   21.20\n",
              "75%      3.68   12.50   18.10    0.00  ...    20.20  396.22   16.96   25.00\n",
              "max     88.98  100.00   27.74    1.00  ...    22.00  396.90   37.97   50.00\n",
              "\n",
              "[8 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OSFMdOj0VBTx",
        "colab_type": "text"
      },
      "source": [
        "**Correlation between Attributes and Target Variables**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "StW1r-eGVBTz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "outputId": "0b0b00bd-566f-4b06-859f-4342890eac11"
      },
      "source": [
        "#calculate correlation between every column on the data \n",
        "corr  = df.corr('pearson')\n",
        "\n",
        "#Take absolute valuea of correlations\n",
        "corrs = [abs(corr[attr]['target']) for attr in list(features)]\n",
        "\n",
        "#Make a list of pairs [(corr, feature)]\n",
        "l = list(zip(corrs, list(features)))\n",
        "\n",
        "#Sort the list of pairs in reverse/descending order,\n",
        "#with the correlation value as the key for sorting \n",
        "l.sort(key = lambda x : x[0], reverse=True)\n",
        "\n",
        "\n",
        "#Unzip pairs to two lists\n",
        "#zip(*l) - takes a list that looks like [[a,b,c], [d,e,f], [g,h,i]]\n",
        "#and returns [[a,d,g],[b,e,h],[c,f,i]]\n",
        "corrs, labels = list(zip((*l)))\n",
        "        \n",
        "#Plot correlations w.r.t. target variable as bar graph\n",
        "import numpy as np\n",
        "index = np.arange(len(labels))\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "plt.bar(index, corrs, width=0.5)\n",
        "plt.xlabel('Attributes')\n",
        "plt.ylabel('Correlations with Target variable')\n",
        "plt.xticks(index, labels)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QZ-jctguVBT2",
        "colab_type": "text"
      },
      "source": [
        "From the above bar graph we can observe that LSTAT and RAM have two highest absolute correlation values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7Q2TjwXFVBT3",
        "colab_type": "text"
      },
      "source": [
        "<h2>`Normalizing the Data<h2>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-10JSbgGVBT4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = df['LSTAT'].values\n",
        "Y = df['target'].values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yq4w2E9wVBT_",
        "colab_type": "code",
        "colab": {},
        "outputId": "80f8722e-c830-4f98-c4ad-41d41e2cf1fb"
      },
      "source": [
        "#Before normalization\n",
        "print(Y[:5])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[24.  21.6 34.7 33.4 36.2]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5GNJR_4LVBUD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_scaler = MinMaxScaler()\n",
        "X = x_scaler.fit_transform(x.reshape(-1,1))\n",
        "X = X[:, -1]\n",
        "y_scaler = MinMaxScaler()\n",
        "Y = y_scaler.fit_transform(Y.reshape(-1, 1))\n",
        "Y = Y[:, -1]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "43Jha8bBVBUH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "0be5fcd0-f714-494b-9d6c-2730efa32b3f"
      },
      "source": [
        "#After normalization\n",
        "print(Y[:5])\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.42222222 0.36888889 0.66       0.63111111 0.69333333]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MliOJM5zVBUL",
        "colab_type": "text"
      },
      "source": [
        "<h2>Defining Error<h2>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KNg5V3IHVBUM",
        "colab_type": "text"
      },
      "source": [
        "**MSE - Mean Squared Error**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Euala3fvVBUM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from sklearn.metrics import mean_squared_error"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LPBY0VD2VBUP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "e890de48-3bf2-44d4-a74d-f2a84c054ecf"
      },
      "source": [
        "# Generate n evenly spaced values from zero radians to 2PI radians\n",
        "n = 200\n",
        "x = np.linspace(0, 2 * np.pi, n)\n",
        "sine_values = np.sin(x)\n",
        "\n",
        "#plotting sine wave\n",
        "plt.plot(x, sine_values)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f966c645630>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h7e89rQPVBUT",
        "colab_type": "text"
      },
      "source": [
        "# Add some noise to the sine wave\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H91prZT8VBUT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "538ca5d1-2c8d-4b03-dfcf-f06c71e77ece"
      },
      "source": [
        "noise = 0.5 \n",
        "noisy_sine_values = sine_values + np.random.uniform(-noise, noise, n)\n",
        "\n",
        "#Plot the noisy values\n",
        "plt.plot(x, noisy_sine_values, color='r')\n",
        "plt.plot(x, sine_values, linewidth=3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f966c5fb400>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "errCxsbCVBUX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a8da12e2-df08-4912-d941-99850d2c45c8"
      },
      "source": [
        "#calc MSE using function from sklearn library\n",
        "mean_squared_error(sine_values, noisy_sine_values)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.08940732518757459"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GFyebIcPVBUe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f31cd025-d2e1-4fca-db49-7e39b5df36c6"
      },
      "source": [
        "#Calc MSE using the equation\n",
        "error_value = (1/n) * sum(np.power(sine_values  - noisy_sine_values, 2))\n",
        "error_value"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.08940732518757459"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LC2kwPZZVBUh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def error(m, x, c, t):\n",
        "    N = x.size\n",
        "    e = sum(((m * x + c) - t) ** 2)\n",
        "    return e * 1/(2 * N)\n",
        "    "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "frL6N-X4VBUk",
        "colab_type": "text"
      },
      "source": [
        "# Splitting the dataset\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t--WAGeeVBUl",
        "colab_type": "text"
      },
      "source": [
        "Splitting data into fixed sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ti7f4zCtVBUm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#0.2 indicates 20% of the data is randomly sampled as testing data\n",
        "xtrain, xtest, ytrain, ytest = train_test_split(X, Y, test_size = 0.2)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJlzEQwOVBUp",
        "colab_type": "text"
      },
      "source": [
        "Update Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pAKvi1ZyVBUq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def update (m, x, c, t, learning_rate):##updating the update function\n",
        "    grad_m = sum(2 * ((m * x + c) -t) * x)\n",
        "    grad_c = sum(2 * ((m * x + c) -t))\n",
        "    m = m - grad_m * learning_rate\n",
        "    c = c - grad_c * learning_rate\n",
        "    return m, c"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qIKv46e7VBUu",
        "colab_type": "text"
      },
      "source": [
        "**Error Threshold** : If the error falls below the threshold, the gradient descent process is stopped and the weights are returned."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZRh0VyAqVBUv",
        "colab_type": "text"
      },
      "source": [
        "Gradient Descent Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d226k0o6VBUw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradient_descent(init_m, init_c, x, t, learning_rate, iterations, error_threshold):\n",
        "    m = init_m\n",
        "    c = init_c\n",
        "    error_values  = list()\n",
        "    mc_values = list()\n",
        "    for i in range(iterations):\n",
        "        e = error(m, x, c, t)\n",
        "        if e < error_threshold:\n",
        "            print('Error less than the threshold. Stopping gradient descent')\n",
        "            break\n",
        "        error_values.append(e)\n",
        "        m, c = update(m, x, c, t, learning_rate)\n",
        "        mc_values.append((m,c))\n",
        "    return m, c, error_values, mc_values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_jcvJg2jVBU0",
        "colab_type": "text"
      },
      "source": [
        "*#magic function to identify the time of execution*\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jg48LqN9VBU1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "3c599dba-9a34-4cb6-e7c6-3d82676e9de3"
      },
      "source": [
        "%%time\n",
        "init_m = 0.9\n",
        "init_c = 0\n",
        "learning_rate = 0.001\n",
        "iterations = 250\n",
        "error_threshold = 0.001\n",
        "\n",
        "m, c, error_values, mc_values = gradient_descent(init_m, init_c, xtrain, ytrain, learning_rate, iterations, error_threshold)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPU times: user 62.3 ms, sys: 1.7 ms, total: 64 ms\n",
            "Wall time: 64.6 ms\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7xUGO6UAVBU5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "942d685c-67fc-4e9b-a808-9cafd85f5c78"
      },
      "source": [
        "print(m,c)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-0.7699103418190527 0.6207227268250588\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v5ThwlFMVBU9",
        "colab_type": "text"
      },
      "source": [
        "*Animating the model visualisation*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a663ijJAVBU9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#As the number of iterations increases, changes in the line are less noticeable. \n",
        "#Inorder to reduce the processing time for animation, it is prefered to choose small\n",
        "mc_values_anim = mc_values[0:250:5]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V21XTTrHVBVA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 561
        },
        "outputId": "4484e7df-594b-4c72-8cf7-42b28c4243c6"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "ln, = plt.plot([], [], 'ro-', animated = True)\n",
        "\n",
        "def init():\n",
        "    plt.scatter(xtest, ytest, color = 'g')\n",
        "    ax.set_xlim(0, 1.0)\n",
        "    ax.set_ylim(0, 1.0)\n",
        "    return ln,\n",
        "\n",
        "def update_frame(frame):\n",
        "    m, c = mc_values_anim[frame]\n",
        "    x1, y1 = -0.5, m * -.5 + c\n",
        "    x2, y2 = 1.5, m * 1.5 + c\n",
        "    ln.set_data([x1, x2], [y1, y2])\n",
        "    return ln,\n",
        "\n",
        "anim = FuncAnimation(fig, update_frame, frames = range(len(mc_values_anim)),\n",
        "                                init_func = init, blit = True)\n",
        "HTML(anim.to_html5_video())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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            "text/plain": [
              "<IPython.core.display.HTML object>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gcuf8RHEVBVE",
        "colab_type": "text"
      },
      "source": [
        "<h2>Error Visualization</h2>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cZb16ha5VBVE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "7bf2dad0-5bd8-47b3-ad01-fb5f09673ef7"
      },
      "source": [
        "plt.scatter(xtrain,ytrain,color = \"r\")\n",
        "plt.plot(xtrain,(m*xtrain+c),color = 'b')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f966c63eb38>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_5IU4wQ3VBVK",
        "colab_type": "text"
      },
      "source": [
        "<h2>Plotting error values</h2>\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mDJpC91WVBVL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "533ee33d-c331-46e6-b71e-ded5511437c8"
      },
      "source": [
        "plt.plot(np.arange(len(error_values)), error_values)\n",
        "plt.ylabel('Error')\n",
        "plt.xlabel('Iterations')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Iterations')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iWbUCXVkVBVN",
        "colab_type": "text"
      },
      "source": [
        "# Prediction\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9oUHv58wVBVO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#  Calculate the predictions on the test set as a vectorized operation\n",
        "predicted = (m * xtest) + c\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "49t1mrmrVBVQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "fc311888-7165-4edb-aacc-dc50516a9b25"
      },
      "source": [
        "# Compute MSE for the predicted valus on testing_set\n",
        "mean_squared_error(ytest, predicted)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.01601048093116738"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vH2TS8PhVBVT",
        "colab_type": "raw"
      },
      "source": [
        "# Put xtest, ytest and predicted values into a single DataFrame so that we\n",
        "# can see the predicted values alongside testing set\n",
        "p = pd.DataFrame(list(zip(xtest, ytest, predicted)), columns = ['x', 'target_y', 'predictions'] )"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nLoOSa4ZVBVU",
        "colab_type": "code",
        "colab": {},
        "outputId": "e77f4706-571b-4245-d3e0-e26ac1c6b158"
      },
      "source": [
        "# Put xtest, ytest and predicted values into a single DataFrame so that we\n",
        "# can see the predicted values alongside testing set\n",
        "p = pd.DataFrame(list(zip(xtest, ytest, predicted)), columns = ['x', 'target_y', 'predicted_y'] )\n",
        "p.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>target_y</th>\n",
              "      <th>predicted_y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.323124</td>\n",
              "      <td>0.222222</td>\n",
              "      <td>0.368816</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.161976</td>\n",
              "      <td>0.557778</td>\n",
              "      <td>0.488818</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.178532</td>\n",
              "      <td>0.377778</td>\n",
              "      <td>0.476489</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.220199</td>\n",
              "      <td>0.482222</td>\n",
              "      <td>0.445461</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.174393</td>\n",
              "      <td>0.293333</td>\n",
              "      <td>0.479571</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          x  target_y  predicted_y\n",
              "0  0.323124  0.222222     0.368816\n",
              "1  0.161976  0.557778     0.488818\n",
              "2  0.178532  0.377778     0.476489\n",
              "3  0.220199  0.482222     0.445461\n",
              "4  0.174393  0.293333     0.479571"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BTYyXQpfVBVW",
        "colab_type": "code",
        "colab": {},
        "outputId": "acd758a9-fdb6-4cfb-950c-3ac43dfcea0c"
      },
      "source": [
        "plt.scatter(xtest, ytest, color = 'r')\n",
        "plt.plot(xtest,predicted,color = 'g')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x2466881d358>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 111
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QcwKxe1JVBVZ",
        "colab_type": "code",
        "colab": {},
        "outputId": "c999993f-cab5-44b8-e62f-6e8a0dfa593d"
      },
      "source": [
        "predicted = predicted.reshape(-1, 1)\n",
        "xtest = xtest.reshape(-1, 1)\n",
        "ytest = ytest.reshape(-1, 1)\n",
        "xtest_scaled = x_scaler.inverse_transform(xtest)\n",
        "ytest_scaled = y_scaler.inverse_transform(ytest)\n",
        "predicted_scaled = y_scaler.inverse_transform(predicted)\n",
        "p = pd.DataFrame(list(zip(xtest_scaled, ytest_scaled, predicted_scaled)),\n",
        "                 columns = ['x', 'target_y', 'predicted_y'])\n",
        "p = p.round(decimals = 2)\n",
        "p.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>target_y</th>\n",
              "      <th>predicted_y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>[13.44]</td>\n",
              "      <td>[15.000000000000002]</td>\n",
              "      <td>[21.59672291764394]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>[7.6]</td>\n",
              "      <td>[30.1]</td>\n",
              "      <td>[26.996811080953233]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>[8.2]</td>\n",
              "      <td>[22.0]</td>\n",
              "      <td>[26.442007502531045]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>[9.71]</td>\n",
              "      <td>[26.7]</td>\n",
              "      <td>[25.04575183016854]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>[8.05]</td>\n",
              "      <td>[18.2]</td>\n",
              "      <td>[26.580708397136593]</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         x              target_y           predicted_y\n",
              "0  [13.44]  [15.000000000000002]   [21.59672291764394]\n",
              "1    [7.6]                [30.1]  [26.996811080953233]\n",
              "2    [8.2]                [22.0]  [26.442007502531045]\n",
              "3   [9.71]                [26.7]   [25.04575183016854]\n",
              "4   [8.05]                [18.2]  [26.580708397136593]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G4MgogOOVBVd",
        "colab_type": "text"
      },
      "source": [
        "<h1>Plot the predicted values against the Target values</h1>\n",
        "\n",
        "<h2>1. Predicted values are represented by red colored line.</h2>\n",
        "<h2>2.Target values are represenetd by blue colored points</h2>\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rc7YbsdeVBVd",
        "colab_type": "code",
        "colab": {},
        "outputId": "01602ca1-d1e0-459b-b03b-c5734cdf2266"
      },
      "source": [
        "plt.scatter(xtest, ytest, color = 'b')\n",
        "plt.plot(xtest, predicted, color = 'r')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x24668824828>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 113
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KY_OQ63CVBVg",
        "colab_type": "text"
      },
      "source": [
        "<h2>Reverting normalization to obtain the predicted price of the houses in $1000s</h2>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tVvpJx-0VBVh",
        "colab_type": "code",
        "colab": {},
        "outputId": "cc03832e-ad79-41d5-8311-870f7d2ae4ca"
      },
      "source": [
        "# Reshape to change the shape to the shape that is required by the scaler\n",
        "predicted = predicted.reshape(-1, 1)\n",
        "xtest = xtest.reshape(-1, 1)\n",
        "ytest = ytest.reshape(-1, 1)\n",
        "xtest_scaled = x_scaler.inverse_transform(xtest)\n",
        "ytest_scaled = y_scaler.inverse_transform(ytest)\n",
        "\n",
        "predicted_scaled = y_scaler.inverse_transform(predicted)\n",
        "\n",
        "# This is to remove the extra dimensions\n",
        "xtest_scaled = xtest_scaled[:, -1]\n",
        "ytest_scaled = ytest_scaled[:, -1]\n",
        "predicted_scaled = predicted[:, -1]\n",
        "\n",
        "p = pd.DataFrame(list(zip(xtest_scaled, ytest_scaled, predicted_scaled)), columns = ['x', 'target_y', 'predicted_y'])\n",
        "p = p.round(decimals = 2)\n",
        "p.head()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>x</th>\n",
              "      <th>target_y</th>\n",
              "      <th>predicted_y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>13.44</td>\n",
              "      <td>15.0</td>\n",
              "      <td>0.37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>7.60</td>\n",
              "      <td>30.1</td>\n",
              "      <td>0.49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>8.20</td>\n",
              "      <td>22.0</td>\n",
              "      <td>0.48</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>9.71</td>\n",
              "      <td>26.7</td>\n",
              "      <td>0.45</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8.05</td>\n",
              "      <td>18.2</td>\n",
              "      <td>0.48</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       x  target_y  predicted_y\n",
              "0  13.44      15.0         0.37\n",
              "1   7.60      30.1         0.49\n",
              "2   8.20      22.0         0.48\n",
              "3   9.71      26.7         0.45\n",
              "4   8.05      18.2         0.48"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OU_nvDhGVBVj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}