Linear_Regression_Multiple_Features.ipynb

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  "metadata": {
    "colab": {
      "name": "Linear Regression Multiple Features.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fgmw6dLmfLFm"
      },
      "source": [
        "# Exploratory Analysis\r\n",
        "# Load\r\n",
        "# Analyse\r\n",
        "# Visualise\r\n",
        "# Normalise\r\n"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4tM7uw-ui6FA"
      },
      "source": [
        "from sklearn.datasets import load_boston"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ytIq2H9ii-ys"
      },
      "source": [
        "boston = load_boston()"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OvKYexNzjO8U"
      },
      "source": [
        "X = boston.data\r\n",
        "y = boston.target"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZblQ4KtVjR2J",
        "outputId": "5c4001e5-5eb8-4950-9f56-0cefb005744f"
      },
      "source": [
        "print(X.shape)\r\n",
        "print(y.shape)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(506, 13)\n",
            "(506,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JRJzhX3cjUXr",
        "outputId": "4c5c344d-f4e1-43fa-cd0a-24a2cb0a05eb"
      },
      "source": [
        "\r\n",
        "print(boston.feature_names)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n",
            " 'B' 'LSTAT']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rCNxpR97jWsT",
        "outputId": "48223f1e-36eb-4646-b65e-38de117c5e98"
      },
      "source": [
        "\r\n",
        "print(boston.DESCR)"
      ],
      "execution_count": 7,
      "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"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "-vTq-Lw-jZcx",
        "outputId": "5301056f-d930-43c0-bb26-f8a40f52e4a7"
      },
      "source": [
        "\r\n",
        "import pandas as pd\r\n",
        "df = pd.DataFrame(X)\r\n",
        "df.columns = boston.feature_names\r\n",
        "df.head()"
      ],
      "execution_count": 8,
      "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",
              "    <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",
              "    </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",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      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",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "qaxQFgsxjdmD",
        "outputId": "f0b4fbd2-8ddc-45d3-c83c-0b39bfe00e5b"
      },
      "source": [
        "df.describe()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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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",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "      <td>506.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>3.613524</td>\n",
              "      <td>11.363636</td>\n",
              "      <td>11.136779</td>\n",
              "      <td>0.069170</td>\n",
              "      <td>0.554695</td>\n",
              "      <td>6.284634</td>\n",
              "      <td>68.574901</td>\n",
              "      <td>3.795043</td>\n",
              "      <td>9.549407</td>\n",
              "      <td>408.237154</td>\n",
              "      <td>18.455534</td>\n",
              "      <td>356.674032</td>\n",
              "      <td>12.653063</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>8.601545</td>\n",
              "      <td>23.322453</td>\n",
              "      <td>6.860353</td>\n",
              "      <td>0.253994</td>\n",
              "      <td>0.115878</td>\n",
              "      <td>0.702617</td>\n",
              "      <td>28.148861</td>\n",
              "      <td>2.105710</td>\n",
              "      <td>8.707259</td>\n",
              "      <td>168.537116</td>\n",
              "      <td>2.164946</td>\n",
              "      <td>91.294864</td>\n",
              "      <td>7.141062</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.006320</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.460000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.385000</td>\n",
              "      <td>3.561000</td>\n",
              "      <td>2.900000</td>\n",
              "      <td>1.129600</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>187.000000</td>\n",
              "      <td>12.600000</td>\n",
              "      <td>0.320000</td>\n",
              "      <td>1.730000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>0.082045</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>5.190000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.449000</td>\n",
              "      <td>5.885500</td>\n",
              "      <td>45.025000</td>\n",
              "      <td>2.100175</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>279.000000</td>\n",
              "      <td>17.400000</td>\n",
              "      <td>375.377500</td>\n",
              "      <td>6.950000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>0.256510</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>9.690000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.538000</td>\n",
              "      <td>6.208500</td>\n",
              "      <td>77.500000</td>\n",
              "      <td>3.207450</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>330.000000</td>\n",
              "      <td>19.050000</td>\n",
              "      <td>391.440000</td>\n",
              "      <td>11.360000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>3.677083</td>\n",
              "      <td>12.500000</td>\n",
              "      <td>18.100000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.624000</td>\n",
              "      <td>6.623500</td>\n",
              "      <td>94.075000</td>\n",
              "      <td>5.188425</td>\n",
              "      <td>24.000000</td>\n",
              "      <td>666.000000</td>\n",
              "      <td>20.200000</td>\n",
              "      <td>396.225000</td>\n",
              "      <td>16.955000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>88.976200</td>\n",
              "      <td>100.000000</td>\n",
              "      <td>27.740000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.871000</td>\n",
              "      <td>8.780000</td>\n",
              "      <td>100.000000</td>\n",
              "      <td>12.126500</td>\n",
              "      <td>24.000000</td>\n",
              "      <td>711.000000</td>\n",
              "      <td>22.000000</td>\n",
              "      <td>396.900000</td>\n",
              "      <td>37.970000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             CRIM          ZN       INDUS  ...     PTRATIO           B       LSTAT\n",
              "count  506.000000  506.000000  506.000000  ...  506.000000  506.000000  506.000000\n",
              "mean     3.613524   11.363636   11.136779  ...   18.455534  356.674032   12.653063\n",
              "std      8.601545   23.322453    6.860353  ...    2.164946   91.294864    7.141062\n",
              "min      0.006320    0.000000    0.460000  ...   12.600000    0.320000    1.730000\n",
              "25%      0.082045    0.000000    5.190000  ...   17.400000  375.377500    6.950000\n",
              "50%      0.256510    0.000000    9.690000  ...   19.050000  391.440000   11.360000\n",
              "75%      3.677083   12.500000   18.100000  ...   20.200000  396.225000   16.955000\n",
              "max     88.976200  100.000000   27.740000  ...   22.000000  396.900000   37.970000\n",
              "\n",
              "[8 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uPWw4i2Kjib0"
      },
      "source": [
        "# Normalise this dataset\r\n",
        "# Each feature must have 0 mean, unit variance\r\n",
        "import numpy as np\r\n",
        "u = np.mean(X,axis=0)\r\n",
        "std = np.std(X,axis=0)\r\n",
        "#print(u.shape,std.shape)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T4-0MlJJjoPM"
      },
      "source": [
        "# Normalise the Data\r\n",
        "X = (X-u)/std"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "3Mql9go4jq5M",
        "outputId": "df9190fc-2d1f-426f-fe55-92fd312781eb"
      },
      "source": [
        "# Normalised Data\r\n",
        "pd.DataFrame(X[:5,:]).head()"
      ],
      "execution_count": 12,
      "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>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>11</th>\n",
              "      <th>12</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.419782</td>\n",
              "      <td>0.284830</td>\n",
              "      <td>-1.287909</td>\n",
              "      <td>-0.272599</td>\n",
              "      <td>-0.144217</td>\n",
              "      <td>0.413672</td>\n",
              "      <td>-0.120013</td>\n",
              "      <td>0.140214</td>\n",
              "      <td>-0.982843</td>\n",
              "      <td>-0.666608</td>\n",
              "      <td>-1.459000</td>\n",
              "      <td>0.441052</td>\n",
              "      <td>-1.075562</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.417339</td>\n",
              "      <td>-0.487722</td>\n",
              "      <td>-0.593381</td>\n",
              "      <td>-0.272599</td>\n",
              "      <td>-0.740262</td>\n",
              "      <td>0.194274</td>\n",
              "      <td>0.367166</td>\n",
              "      <td>0.557160</td>\n",
              "      <td>-0.867883</td>\n",
              "      <td>-0.987329</td>\n",
              "      <td>-0.303094</td>\n",
              "      <td>0.441052</td>\n",
              "      <td>-0.492439</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.417342</td>\n",
              "      <td>-0.487722</td>\n",
              "      <td>-0.593381</td>\n",
              "      <td>-0.272599</td>\n",
              "      <td>-0.740262</td>\n",
              "      <td>1.282714</td>\n",
              "      <td>-0.265812</td>\n",
              "      <td>0.557160</td>\n",
              "      <td>-0.867883</td>\n",
              "      <td>-0.987329</td>\n",
              "      <td>-0.303094</td>\n",
              "      <td>0.396427</td>\n",
              "      <td>-1.208727</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.416750</td>\n",
              "      <td>-0.487722</td>\n",
              "      <td>-1.306878</td>\n",
              "      <td>-0.272599</td>\n",
              "      <td>-0.835284</td>\n",
              "      <td>1.016303</td>\n",
              "      <td>-0.809889</td>\n",
              "      <td>1.077737</td>\n",
              "      <td>-0.752922</td>\n",
              "      <td>-1.106115</td>\n",
              "      <td>0.113032</td>\n",
              "      <td>0.416163</td>\n",
              "      <td>-1.361517</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.412482</td>\n",
              "      <td>-0.487722</td>\n",
              "      <td>-1.306878</td>\n",
              "      <td>-0.272599</td>\n",
              "      <td>-0.835284</td>\n",
              "      <td>1.228577</td>\n",
              "      <td>-0.511180</td>\n",
              "      <td>1.077737</td>\n",
              "      <td>-0.752922</td>\n",
              "      <td>-1.106115</td>\n",
              "      <td>0.113032</td>\n",
              "      <td>0.441052</td>\n",
              "      <td>-1.026501</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         0         1         2   ...        10        11        12\n",
              "0 -0.419782  0.284830 -1.287909  ... -1.459000  0.441052 -1.075562\n",
              "1 -0.417339 -0.487722 -0.593381  ... -0.303094  0.441052 -0.492439\n",
              "2 -0.417342 -0.487722 -0.593381  ... -0.303094  0.396427 -1.208727\n",
              "3 -0.416750 -0.487722 -1.306878  ...  0.113032  0.416163 -1.361517\n",
              "4 -0.412482 -0.487722 -1.306878  ...  0.113032  0.441052 -1.026501\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "id": "jcx_B5zEjuCL",
        "outputId": "230a9a4e-3aec-4ac0-e12c-450200b3c372"
      },
      "source": [
        "# Plot Y vs any feature\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "\r\n",
        "plt.style.use('seaborn')\r\n",
        "plt.scatter(X[:,5],y)\r\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QT-mCqPajxnb",
        "outputId": "850d721a-374a-4be1-b2dd-8498b342344e"
      },
      "source": [
        "X.shape, y.shape"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((506, 13), (506,))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sm8xA4Fcj3is",
        "outputId": "42f084da-f49a-41dd-ba9d-ea9e32122555"
      },
      "source": [
        "\r\n",
        "ones = np.ones((X.shape[0],1))\r\n",
        "X = np.hstack((ones,X))\r\n",
        "print(X.shape)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(506, 14)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pbNBSVrRj54y"
      },
      "source": [
        "# X - Matrix ( m x n)\r\n",
        "# x - Vector (Single Example with n features)\r\n",
        "\r\n",
        "def hypothesis(x,theta):\r\n",
        "    y_ = 0.0\r\n",
        "    n = x.shape[0]\r\n",
        "    for i in range(n):\r\n",
        "        y_  += (theta[i]*x[i])\r\n",
        "    return y_\r\n",
        "\r\n",
        "def error(X,y,theta):\r\n",
        "    e = 0.0\r\n",
        "    m = X.shape[0]\r\n",
        "    \r\n",
        "    for i in range(m):\r\n",
        "        y_ = hypothesis(X[i],theta)\r\n",
        "        e += (y[i] - y_)**2\r\n",
        "        \r\n",
        "    return e/m\r\n",
        "\r\n",
        "def gradient(X,y,theta):\r\n",
        "    m,n = X.shape\r\n",
        "    \r\n",
        "    grad = np.zeros((n,))\r\n",
        "    \r\n",
        "    # for all values of j\r\n",
        "    for j in range(n):\r\n",
        "        #sum over all examples\r\n",
        "        for i in range(m):\r\n",
        "            y_ = hypothesis(X[i],theta)\r\n",
        "            grad[j] += (y_ - y[i])*X[i][j]\r\n",
        "    # Out of the loops\r\n",
        "    return grad/m\r\n",
        "\r\n",
        "def gradient_descent(X,y,learning_rate=0.1,max_epochs=300):\r\n",
        "    m,n = X.shape\r\n",
        "    theta = np.zeros((n,))\r\n",
        "    error_list = []\r\n",
        "    \r\n",
        "    for i in range(max_epochs):\r\n",
        "        e = error(X,y,theta)\r\n",
        "        error_list.append(e)\r\n",
        "        \r\n",
        "        # Gradient Descent\r\n",
        "        grad = gradient(X,y,theta)\r\n",
        "        for j in range(n):\r\n",
        "            theta[j] = theta[j] - learning_rate*grad[j]\r\n",
        "        \r\n",
        "    return theta,error_list"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gvoe2wvOkFij",
        "outputId": "444ec5b0-2436-4df6-c594-9c58853a6b4e"
      },
      "source": [
        "import time\r\n",
        "#def Time():\r\n",
        "start = time.time()\r\n",
        "theta,error_list = gradient_descent(X,y)\r\n",
        "end = time.time()\r\n",
        "print(\"Time taken is \", end-start)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Time taken is  18.95080041885376\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "okIR_-RnkdTV",
        "outputId": "e004ab43-37e8-41aa-d545-775f65a4b668"
      },
      "source": [
        "Time()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Time taken is  18.924753189086914\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ynL-lQQyki3r",
        "outputId": "d833b614-a0db-4a09-87e0-9eb58f32e510"
      },
      "source": [
        "\r\n",
        "print(theta)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 2.25328063e+01 -9.03091692e-01  1.03815625e+00  1.53477685e-02\n",
            "  6.99554920e-01 -2.02101672e+00  2.70014278e+00 -1.93085233e-03\n",
            " -3.10234837e+00  2.34354753e+00 -1.72031485e+00 -2.04614394e+00\n",
            "  8.47845679e-01 -3.73089521e+00]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "id": "LyIPcU7LkqTc",
        "outputId": "91b7348b-6150-4ec2-d95a-f407d7ef753d"
      },
      "source": [
        "plt.plot(error_list)\r\n",
        "plt.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "urBf9Jgdk920"
      },
      "source": [
        "# Predictions\r\n",
        "m,n = X.shape\r\n",
        "y_ = []\r\n",
        "\r\n",
        "for i in range(m):\r\n",
        "    pred = hypothesis(X[i],theta)\r\n",
        "    y_.append(pred)\r\n",
        "y_ = np.array(y_)\r\n",
        "\r\n",
        "\r\n",
        "def r2_score(y,y_):\r\n",
        "    num = np.sum((y-y_)**2)\r\n",
        "    denom = np.sum((y- y.mean())**2)\r\n",
        "    score = (1- num/denom)\r\n",
        "    return score*100"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P9cFDWYXlKDc",
        "outputId": "11c4102d-4f77-4f81-dfa5-a33575ad9158"
      },
      "source": [
        "# score \r\n",
        "r2_score(y,y_)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "74.04541323942743"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5QTSQoSnlpVk"
      },
      "source": [
        "# Vectorized Code\r\n",
        "# Avoid loops in the implemenation, except gradient descent main loop\r\n",
        "# Use numpy functions like np.sum(), np.dot() which are quite fast and already optimised"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o4o63j8Ol6Xs"
      },
      "source": [
        "def hypothesis(X,theta):\r\n",
        "    return np.dot(X,theta)\r\n",
        "\r\n",
        "def error(X,y,theta):\r\n",
        "    e = 0.0\r\n",
        "    y_ = hypothesis(X,theta)\r\n",
        "    e = np.sum((y-y_)**2)\r\n",
        "    \r\n",
        "    return e/m\r\n",
        "    \r\n",
        "def gradient(X,y,theta):\r\n",
        "    \r\n",
        "    y_ = hypothesis(X,theta)\r\n",
        "    grad = np.dot(X.T,(y_ - y))\r\n",
        "    m = X.shape[0]\r\n",
        "    return grad/m\r\n",
        "\r\n",
        "def gradient_descent(X,y,learning_rate = 0.1,max_iters=300):\r\n",
        "    \r\n",
        "    n = X.shape[1]\r\n",
        "    theta = np.zeros((n,))\r\n",
        "    error_list = []\r\n",
        "    \r\n",
        "    for i in range(max_iters):\r\n",
        "        e = error(X,y,theta)\r\n",
        "        error_list.append(e)\r\n",
        "        \r\n",
        "        #Gradient descent\r\n",
        "        grad = gradient(X,y,theta)\r\n",
        "        theta = theta - learning_rate*grad\r\n",
        "        \r\n",
        "    return theta,error_list"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CNCd1qoul-Pj",
        "outputId": "e442aee7-d9c4-4be5-c40b-e74f0f43212a"
      },
      "source": [
        "start = time.time()\r\n",
        "theta,error_list = gradient_descent(X,y)\r\n",
        "end = time.time()\r\n",
        "print(\"Time taken by New Code\",end-start)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Time taken by New Code 0.013743162155151367\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CWjPIjz7mFc-",
        "outputId": "f39255f9-eb5d-407e-b75b-a9091d06e14a"
      },
      "source": [
        "theta"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 2.25328063e+01, -9.03091692e-01,  1.03815625e+00,  1.53477685e-02,\n",
              "        6.99554920e-01, -2.02101672e+00,  2.70014278e+00, -1.93085233e-03,\n",
              "       -3.10234837e+00,  2.34354753e+00, -1.72031485e+00, -2.04614394e+00,\n",
              "        8.47845679e-01, -3.73089521e+00])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "id": "pQAXFS7jmIv0",
        "outputId": "8386f9a6-0855-476a-943c-e62af3d29524"
      },
      "source": [
        "plt.plot(error_list)\r\n",
        "plt.show()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-GyemrSomL07",
        "outputId": "915909e5-703c-4dd4-882f-e3f1748fc0c1"
      },
      "source": [
        "# Prediction & Score\r\n",
        "y_ = hypothesis(X,theta)\r\n",
        "r2_score(y,y_)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "74.04541323942743"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P6PcwzPkmSez"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}