linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "linear_regression.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "upqWMBuzHmnn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7d8f8931-2836-45a1-a294-089f2541bac3"
      },
      "source": [
        "# Load the boston housing data set from sklearn.datasets \n",
        "import pandas as pd\n",
        "from sklearn.datasets import load_boston\n",
        "boston = load_boston()\n",
        "\n",
        "df = pd.DataFrame(boston.data,columns= boston.feature_names)\n",
        "df_target = pd.DataFrame(boston.target)\n",
        "\n",
        "print(df.head())\n",
        "\n",
        "df_target = df_target.rename(columns={0: 'target'})\n",
        "print(df_target.head())\n",
        "print(boston.DESCR)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "      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]\n",
            "   target\n",
            "0    24.0\n",
            "1    21.6\n",
            "2    34.7\n",
            "3    33.4\n",
            "4    36.2\n",
            ".. _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/"
        },
        "id": "Qn6-zs8_jTtC",
        "outputId": "b09ffd7e-c4b2-4426-c175-515fe0412bbb"
      },
      "source": [
        "# aim to find the most correlated columns in our feature set, with the target column\n",
        "df = pd.concat([df,df_target],axis=1)\n",
        "#print(ex.head())\n",
        "df[df.columns[1:]].corr()['target'][:]"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "ZN         0.360445\n",
              "INDUS     -0.483725\n",
              "CHAS       0.175260\n",
              "NOX       -0.427321\n",
              "RM         0.695360\n",
              "AGE       -0.376955\n",
              "DIS        0.249929\n",
              "RAD       -0.381626\n",
              "TAX       -0.468536\n",
              "PTRATIO   -0.507787\n",
              "B          0.333461\n",
              "LSTAT     -0.737663\n",
              "target     1.000000\n",
              "Name: target, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1lraDHXuljV3",
        "outputId": "ffcd95d2-b29c-4a5e-943e-506b8b71c063"
      },
      "source": [
        "# Based on results of the correlation check, we select RM and LSTAT as the most correlated columns to our target set\n",
        "# and use them to predict the house prices\n",
        "\n",
        "df = df[['RM','target']]\n",
        "df.insert(0,'ones',1)\n",
        "\n",
        "#print(len(df))\n",
        "# Divide it into train and test sets\n",
        "\n",
        "from sklearn.utils import shuffle\n",
        "df = shuffle(df)\n",
        "\n",
        "\n",
        "# for testing our model, we will begin with less number of data for train and test and then include more row.\n",
        "\n",
        "train_df = df[0:350]\n",
        "test_df = df[350:506]\n",
        "\n",
        "print(len(train_df))\n",
        "print(len(test_df))\n",
        "\n",
        "print(train_df.head())"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "350\n",
            "156\n",
            "     ones     RM  target\n",
            "324     1  6.415    25.0\n",
            "128     1  6.431    18.0\n",
            "422     1  5.648    20.8\n",
            "268     1  7.470    43.5\n",
            "413     1  5.155    16.3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "_fg7IKS4ntOS",
        "outputId": "fb49f5a3-fc90-41c6-8325-d729b65d23dc"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.Figure(figsize=(8, 8))\n",
        "plt.scatter(train_df['RM'], train_df['target']) # positively correlated with house prices\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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U8mgaxNfu+Pj4rKqO2t3PU4mhqpYAbBWRDIDvA9jotSGqeh+A+wBgdHRUx8bGvP5qKGZmZhD1Nvph0M+zUnaXbLk9m0nixFTr/d04lRF+yVDil82kceKWHcbfvXLqEajNh2WrZ9/8szs3L+GvTyfw7N722x8ng/7abdZWdYqq5gE8DuBPAGRExLoIXA6An+MoNvysh3YrI+y04sOp3M/0s4QIp8sPGNcgLiLrqj1wiEgawMcBPI1KML+xerdbAfwgqEYS+c2Pemgrp377wZOOZYT1JX4AkBSp/fzL06eNFwCn4G/3MwAoqdaOc/vBk9i650cM5n3OS0/8UgCPi8g/AfgpgB+r6sMAvgjgCyLyK1TKDL8VXDOJ/NVtPXR979ukuVefX6xU4FoLW+XyBXz7iRccp7nfsC2LpFQSKEmR2ibGzbXf1n2a5QtF3zejoGhxzYmr6j8BGLG5/dcAPhxEo4iC1m09tJf6bqtXb7chsRtrn8yDP32xFvRLqjj40+VNjOtLAa+cesR4LK590t+4dgoNrG7qod1y5/W9etN+l04uy6RtNzIulhR7js63tLtywXij4/ZSfHHaPVEHnHLnzdPaOwmg4xvXGVcztLt9cucGJAwpFYBrn/SzyAdxLlBPUWTKqd+7aytOTO1o6Cl3EkAff+Y1x583vw8mRrLIrk1jrc1a41z7pL9FOoj3Ysdwok60u6hUu17KF5BOmd+edu+DTDqFua9cjXt3bfXULuoPkc6Jc4F6ijKnnHrzBJ52XZZJY/H8EgrF1hmbgPP7gGufDJZI98S5QD3Fkd0nSFO2eu1QyljqmHfZ4YfvAwIi3hPvdsdwojDYfYJUVKbL19eapFNJ3H3tptrv5PKFholAmaGU41Zt1uxMqzwy4/+pUAxEuifOBeopTqxBeNMEIAVsc9UTI9naa71+ItC5t5aQSporTupnZ9710GnkC849d+pPke6Jc4F6iovmXeLtZDNp293lrV54s2JZkUmnsPqCFbVeekm19n+9QrGEV84yiA+iSAdxgIM0FA9uMzjtPkF6CfxnC0WcvPvqhttMszPtlq2l/hfpdApRXDgNMprK/NqZuu92G7C8zjgNFj7rRD5w2qGnefKPpZ2p+/VMY0XDF61qo8XULxjEaaD5NSO4k0H4dqbu1zNNNPJ7RyKKh8jnxImC0pyTzuULmDx0CruPzONsodjWQHong/CTOze05MTTqaSnGZZ2Y0UzM790bSf1HwZxGij1MykTNlUexZLWSvWs0j0ALQGzvqrEqhbJZtIY37gOjz/zGl7KF7D7yDz2HJ1HftH+guA18Dtt/eZ0fqzmGgwM4tRXWoLYllLDz+p7vs0B3E6hWMLuI/MNxxzfuA6HZ3Mtx7E2ebDU122bLghu1Vd2nxZMF5Z8oYi7HvN2X+ofDOLUF6bncth9ZL4lcOYWSrU8950PnvIUuJvlC8WG3nl9oG5HJ+v+tLN+0Ctn30KhmPB0X+ofDOIUe0711mWtbKLwVrHcUQD3W7vrnbSzflClTry1VoFrrPQ3BnGKPbd6a6f1R3pNAWzfe9xzrtpp/aDm1NEt77Gfos+1hvobSwwpttzWKokqu3XxTaWOptLF8Y3rWlZKLCuQSkjLfbnWUH9jEKdY8rLbPFBZ6S+K9dNWrhpw3vzEVBP++DOvta6UqIqSVtZb4YYQg4PpFIolL1PWRSo58aiyctVug5d2FSx3HDxpe8yyAm8vlbF/11YG7wHBIE49Z6plbqfG2WmwTqr/ytX4HdUlWjPV/TA72fzElCsHWJEyaBjEqaem53KYPHQKxdJybfXkoVN46vnXG2qv3WqcnYKYonHzhahSrfw97CYdAc4DknazPeuxImVwMCdOPbXn6HwtgFuKJcV3nnzBmFKws/6S+Fdc5AtF3PXQadsA7jYgaeXKk8KKlEHHnjj1lKncz5S6tnqU03M57Dk6H6lywW5ZW7HZ3e51/RQAtuuvsCJlcDCIU6RZ9dD1KZh+kEqK8XzKqp7z2fXrrwBvIMv1UgYOgzj1VCadsh1oHEoloBDbHuW+Y2dCC+DpVNK1CqYTq1euqG271syUCjEN/Fr/ZmZm8LlbxnxvK3WuFwuSMSdOPbX7uk0tE1JSCcF/vf6DtXpoAA27vvd6Mo/VOqvOutvj2MkXim2tQe5US07R1KvnjEGcempiJIt9N21pmLyy76Ytjru+OwVDv6USgv27tuLeXVsBVOqxEx02YP+urcaBx6SIcSKPXU/NqZacoqlXzxnTKdRzTsuv2r3we5lIKZYVtzdNpOl0vtDESLblWBbrIuV1I/BOaskpXL16ztgTp0hxeoGvHYre9HkTa6p/1pDfNt1uYsqTs5Qwunr1nDGIU9f82KfSOoap05vNpDH3lavx3N5r8OdXvbu7BgcslRDsvm4TgM723rTj13God3r1nDGdQl1pZ+cZr8do1vzCf+DJF7tsdXCSIrUcP9DZ3pt2/DoO9U6vnjMGcepKOzvPtHMMi13dc9ibO2TSKYi0TlwybXLsNe/txq/jUO/04jljEKeuOA3eeK2RdcqDv5Qv1Ebzrd9NGtYa6YV0Kond120yLtgFVDZ9YG+ZesU1iIvIFQD+HsAwKoUC96nq10XkYgAHAawH8ByAm1V1IbimUhSZFqLKDKU8p1ncFrPK5QuY/N6p2s7xq1IJFIq9D+LNnwqae1l+pJaI2uVlYHMJwJ2q+n4AVwH4rIi8H8AUgMdU9X0AHqt+TwPGNHijCs81snbHaFYsKxYWi1AAhWK563a3a+1QCiemdhiD8fRcDnc+eIq13NRzrkFcVX+rqj+rfv0GgKcBZAF8CsD91bvdD2AiqEZSdDVPWFk7lMIFKxLGNbztUifNx4ii/GLRWH1j9cBNKR7WclOQRNvILYrIegA/AfABAC+oaqZ6uwBYsL5v+p3bANwGAMPDw9sOHDjQfasDdO7cOaxZsybsZgQuiPPMF4rILRQcd9NZmUxgw7suNP78pXwBv3/zvG9tGk4Dr/gcQxMiyK5N12rBf/HbP6BU7vyc/cLXbn+pP8/x8fFZVR21u5/ngU0RWQPgMIDbVfUPUjedWFVVRGxfxap6H4D7AGB0dFTHxsa8PmQoZmZmEPU2+iGI86xsWmxOi1jVG2MOKYkvPXoS6uN4+52bl/C10/6P32czSZyYGsP0XA7/7VH7WZmA+zn7ia/d/uL1PD1N9hGRFCoB/Duq+lD15ldE5NLqzy8F8GpnTaV+4ZQ28LJp775jZ2KxIw/QuD+midd1wYm64RrEq6mSbwF4WlX/uu5HRwDcWv36VgA/8L95FCem6cTZTNpxUNASp9yxda5Obf7azVsYwClwXnri2wH8BYAdInKy+u8TAPYC+LiI/BLAx6rf0wDrdppx2OuArEx6G1atPydTmw2LFxL5zkt1yj+qqqjqB1V1a/XfP6jq71X1o6r6PlX9mKq+3osGU3S1s7SqncmdG0KrTkklxXG1wvp2rUotv21M5ZGq4Hrf1BOcsRlRvdgRJAjdTDN2Wro1aKtXrjCWRQKNy+EuLFY2OH7q+dfx+DOvGZcMaHf5AaJOMIhHUFRm/gV9IbE7ftZh9maQnAK4nUKxhG8/8YLr/eKU57cT187EIOFStBEUhV1cgtxaanouh617foTbD55sOP7koVMY37iu6+ObvO+dq11nhvot7Dx/N7glXDwwiEdQFHZxCepCYgUGu55vsaR4aPY3gW3+8NzvFnHDtmxbGzKIdL4ZRdzX+45CZ4LcMYhHUBR2cQnqQuK07CwALBbLeP+lF7YMcKaSUpsh2engZ7GsePyZ13Biaof3X1Lg7ms3td2Db3dQN4qi0JkgdwziERSFXVyCupB4CQD/559fbxhIFAC7/sUV2H3dJmQz6a4mBOWqS+R6vRBclknXqm5Mmx43s56rOAdwIBqdCXLHIB5B3Zbq+SGoC4mXANAcpBXAw6d+W8vPunELtbuPzHu6ENSf78RIFl+7eYunHnmhWMKeo/Ndb1kXtih0Jsgdq1MiKsxdXKyKhEKxVNuAwW6HnU5M7tzguBWbidfqkUw6hU9uuRQHf/oiiiX7UO10rGwmbazEsL72Uga5sFis7fxjqi6KeuUHt4SLBwZxatBc3lhS9TU9UB8Y/CwlFAC3XPVufHViMwBg9D0Xt11zbi0PUM+0e0+7mmvGo1JG6oZbwkUfgzg18GPPTDf1gaE+SGaGUi37VlqGUgksGjaDqP+UUH88J+lUsuE87dIEpkDr1BYn9W3qxd+ZBgODODXwsyKh3XTBHwpLxp8tFssQNObL6zcmtmrPvaRd1g6lcPe1m7D7yHzt/vVT6S2mQJtJp1AsKYo2a4hnM2m8+faSbTvqxwNY+UF+YRCnBqb9LtutSPCSLvjy9Gl854kXaoHZbfNjBWqBvLn37TXPnkoK7r52EwDg7aXl3rQ1lb6+faaAerZQxP5dW40XKLv2NPf0/fo7E7E6ZQBNz+Vw5uU3bCsn/KpIcJsoMj2XawjgXlkBvH5pW7facwC1Kp99N1aWh/UykcWpxG5iJIsTUzvw7N5rWpbZ9VJdxMoP8gt74gPG6iX+h41lKBItPWS/KhLc0gXdbADRfGy3FITdgKWXdIZdJU0qIVg8v4Qrpx5x/Nu4DQhGsfIj6tUyZI9BfMB4GVDzoyLBLV3gFHhF4LgsbKZpGrzpsYDKfpjjG9dh+97jDcHJSzpjYiSLp55/HQ88+SJKqhCppHzcSge9sv7OVvC84+BJ7Dt2JpTgGZdqGWrFdEqfm57LNUw6MQU7vwfU3NIFxs0UAOy/eSue23tNbZp9s4XFYkMayLSm99qhFNYOpXB4NtewiNMdB09i/SVp13TG9FwOh2dztVy9KtA8ltntWiJRWWSK66TEF4N4H7MLEKbZjH4PqLnlhU2Bt75K5KxDpUl9sLN7rHt3bcXcV67GG28ttQQnRWVqv7UYlilv7SXXDnR3AYxK8GS1THwxndLH7AKEKUsRxBKwTmkZ6/Y9R+cbasMLxXLtY7xTmqRy3+U0kN1jTc/lcL5Uhl1fRQHXxbC8BrDmC2A7uWWn4NnLHDWrZeKLQdyjuA36TM/l2poR+fgzr/n62F7/Vna14VZw9jJF3xQElwdwze10C5RuFxFLcwrGKbfc/HimCU4XpVM9zVHb/a1ZLRMPDOIexG3Qx2pvO/z62OzlbzU9l2uYaGNqj5cp+qaeopdUSGbIOVB6uYhk0inXFEx9eqT58VIJQSopDeu8pFNJiKCnMzqjWC1D3jCIexC3KdJOAax51qPFj4/N03M53PngqZZJO/V/K68Tc6z21FdwuPUU63u5XsoX84ViSxVMc4oGWL6I2M0Y3X3dpobfd0qP7Dk633LexbIik05h9QUrGoLnHYZ1X4LMUXOdlHhiEPcgboM+Tu265ap34/BsDsByGsOPj81WkDXNuqyvD3cL4Hbtae4pZoZSUEWtLG984zrHlQvtmMoY6/9+pnVeTD1VUwrGaV2Ys4UiTt59dcNtpk8fzFFTMwZxD+I26GNqbzaTxlcnNmP0PRfjlTM/g1Tv287HZlMgcwvOXurDASApYlw73dQrz+ULnjYtNn0KMbXV7vGB5QvJ7iPz2HN0HvnFIi5KpyBSKX+067E71b3bPR5z1OQVg7gHcXtDubV3YiSLmbO/xLN7x9o6rlO+2yk4N9eHOw0WXrhqRe2xTL1er6V/Futi5WWQ0ul5bT7/+px+/dd2a7yY0iMAbB+POWryikHcg7i9oYJqr9PYgClINves3QYL84UiJg+dAhS1VQKbBxzbTWM9u/caADBOdkqKoKzasF548wxPL5826tWv8QKY0yPNA6P1mKMmLxjEPYrbGyqI9jqNDezftdW291+/VGx9PvuCFQmcLRSRqO4cVM8ur10/4Oi1Vw0AycTy9CbTJ5T6i0ynnzbsuK3DYjcwStQuztgkz0y54kR1A2HTDM3mmaMLi0W8vVTG/l1bUXZZfraeFRRNsz2bpRLSshaK2+qCbp822tHuYxN1gj1xj+I22ScIplRISRV3PXQa91y/2XYGZCdpGDv1ZYcAbMsZLVYuGi//oiU10sksTdOnDRNThc2gvWYoeOyJexCVRYrCZvUmk9K6AovTeh+mwJjLF3EgYc4AAAm1SURBVLB4fgmpROPxUklpua05KJp2n0+nkrh319ZaoM4tFDw9b9ZCYabPBdYa4qbzrycAbtjGgE29wSDuQVQWKYqCiZGsMQWSyxcaVky0gqVTGmJhsQhIZYCvfuOGfTdtcU09uKUo9h0709JWu+et/iJtp7myxy0FZK3LQtQLTKd4ELfJPkEzpUAEqN1ePyDoVpFSLClWX7CiZcKLl56sU4ripXwBuMJwex2nqpOsTerMSwpoUF8b1HvsiXvgtE3XILIbWLSbSFNfUXLDtqxxGVwgmKDn9XkzPbYALVuvAd4GVjNDKdtPJUR+YxD3gPshNrJLY5gSDFaAfPyZ1xxnSwZxQZzcuaFWOWOxe96adwpyu73+/AG0XJxSScG5t5YGfgyFeoPpFA/iNtmnF5rTGKaJNF6m2wd1QZwYyWL65V8gm0k6Pm+mFLdT6ttpTZU3315qWaExygumUbwxiHvE8rBGzYFrfOM6HJ7NGaf6e53R2cljO11QM+kUTkyNOR7PtIOQ01K59ZpfG1dOPWJ7P79TRi1/hy3elyKg/uGaThGR/ykir4rIz+tuu1hEfiwiv6z+vzbYZlKU2JVcHp7NOW53ZkpJfe3mLW0HcL/LPZ32++zkuL0YQ7H7O+QWCkzZDCAvOfG/A/Bvmm6bAvCYqr4PwGPV72lAmEoure3Ont17TcuAoF8zFoMo95zcucF20FWrj9fJ8YIeQ7H7O5RVB7LsddC5plNU9Scisr7p5k8BGKt+fT+AGQBf9LFdFLB8oWi7yJMXnZZc+pGSCqLcc2Iki9t93IShF2MoLHsli6iHtSuqQfxhVf1A9fu8qmaqXwuABet7m9+9DcBtADA8PLztwIED/rQ8IOfOncOaNWvCbkag8oUiioVFvFz3fk+IILs2jUzaviKj3pmX36huQNxoZTKBDe+60M+mdv3YXp9Pr8fNF4p45exbOF8qY2UygeGLVnn6m/nNrr3DaWDhfPDPQdgG4T0KNJ7n+Pj4rKqO2t2v64FNVVURMV4JVPU+APcBwOjoqI6NjXX7kIGamZlB1NvYre17j+PTVwBfO9349GczSddBQADIG7ZKu+f6zRgLePC33cf2+nx6Oe70XA53PXYahWICViYynSrhnuvf3/NBb7v2Tn6whOwffyjw5yBsg/AeBbyfZ6d14q+IyKUAUP3/1Q6PQyHo9qN4mCvyBfXY3a5w2Gt27c2uTbOCagB12hM/AuBWAHur///Atxb1kaiufFipknjDcLs3YZZc+vXYds9PpyschqH57zAzMxNKOyhcrkFcRB5AZRDzHSLyGwB3oxK8HxSRzwB4HsDNQTYyjpw2Fwg7kE/u3IDc07MNt/ViBmqULmqdPD+93Gs1Sn8rijYv1Sl/ZvjRR31uS19x+ugd9pvR60xGL7wGm6Auap0Gu06en17ttRrlDgBFD2dsBiRqH72b1c9ktALhHQdPthUI2wk2QVzUugl2nTw/vVp+IcodAIoeBvGA9PKjdze6CYTtBJsgLmrdBLtOn59ejAVEvQNA0cJVDAMSl5UPu6m4aCfYBDEVvZtgF9XnZ3ou17LyoiVqHQCKBgbxgMRlY9xuAmE7gTmIoNnNhSGKz4/1qchu39AoXGAomphOCVAcVj5sN61QP5CYGUohlRAUy8tBxxRsgsgndzvQ2M7zYxpA9bOKxLTDUCcrPdLgYBAPWdilZO0Ewub8+cJiEamkIJNO4Wyh6Np+vy9qvRpoNI0bPPX86w3L73ZbRWL69FNWZQAnIwbxEEWhlKydQGjXUzTtj9krvfi0Yxo3eODJF1tSH91UkcRlMJyihUE8RFEpJfMaCAe1asJ0fna5a6f7u+lVHTr1FwbxEMUtKEapp9jLNJTTrkR2gbzTvwe3AaROMIiHKEpB0Yuo9BR7nYYynfcN27KOW9J1Ig6D4RQtLDEMUVRrlU2iUpbX69UETef91YnNkfh70GBjTzxEcfz4HIWeopc0lJVu+fQVb+BLe493/Xc1nXcU/h402BjEQ8Yg0D63NFRDuuUKLiBF/Y3pFIodtzRUlDZvIAoae+IUO25pqLhV/RB1g0GcYskpDRW3qh+ibjCdQn0nblU/RN1gT5z6Tn26BXgD2RhU/RB1ikGc+pKVbpmZmcHnbhkLuzlEgWE6hYgoxhjEiYhijEGciCjGGMSJiGKMQZyIKMZEDQvbB/JgIq8BeL5nD9iZdwD4XdiN6AGeZ/8ZlHMdxPN8j6qus7tTT4N4HIjIU6o6GnY7gsbz7D+Dcq48z0ZMpxARxRiDOBFRjDGIt7ov7Ab0CM+z/wzKufI86zAnTkQUY+yJExHFGIM4EVGMMYjXEZGkiMyJyMNhtyVIIvKciJwWkZMi8lTY7QmKiGRE5JCIPCMiT4vIn4TdJr+JyIbq82j9+4OI3B52u4IgIneIyLyI/FxEHhCRVWG3KSgi8vnqec67PZ9cirbR5wE8DeCPwm5ID4yrar9PmPg6gEdV9UYRWQlgKOwG+U1VzwDYClQ6IQByAL4faqMCICJZAP8RwPtVtSAiDwL4NIC/C7VhARCRDwD4dwA+DOA8gEdF5GFV/ZXd/dkTrxKRywFcA+CbYbeFuiciFwH4CIBvAYCqnlfVfLitCtxHAfyzqkZ9VnSnVgBIi8gKVC7IL4XcnqD8MYAnVXVRVZcA/G8A15vuzCC+7F4A/xlAOeyG9IAC+JGIzIrIbWE3JiBXAngNwP+qpsi+KSKrw25UwD4N4IGwGxEEVc0B+O8AXgDwWwBnVfVH4bYqMD8H8K9F5BIRGQLwCQBXmO7MIA5ARD4J4FVVnQ27LT3yr1T1QwD+FMBnReQjYTcoACsAfAjAN1R1BMCbAKbCbVJwqumi6wB8L+y2BEFE1gL4FCoX58sArBaRPw+3VcFQ1acB/BWAHwF4FMBJACXT/RnEK7YDuE5EngNwAMAOEfl2uE0KTrVXA1V9FZX86YfDbVEgfgPgN6r6ZPX7Q6gE9X71pwB+pqqvhN2QgHwMwLOq+pqqFgE8BOBfhtymwKjqt1R1m6p+BMACgP9nui+DOABVvUtVL1fV9ah8JD2uqn15lReR1SJyofU1gKtR+fjWV1T1ZQAvioi1xf1HAfwixCYF7c/Qp6mUqhcAXCUiQyIiqDyfT4fcpsCIyDur/78blXz4d033ZXXK4BkG8P3K+wArAHxXVR8Nt0mB+RyA71RTDb8G8JchtycQ1YvxxwH8+7DbEhRVfVJEDgH4GYAlAHPo7+n3h0XkEgBFAJ91GpTntHsiohhjOoWIKMYYxImIYoxBnIgoxhjEiYhijEGciCjGGMSJiGKMQZyIKMb+P00yTrO2o/YsAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_OYbmU1g-8jk"
      },
      "source": [
        "# With the intercept and fixed learning rate\n",
        "def linear_regression(df,y,theta,alpha,iter,eps):\n",
        "\n",
        "\n",
        "  n = df.shape[0]\n",
        "  df = np.array(df)\n",
        "  y = y.reshape(len(y),1)\n",
        "\n",
        "  for i in range(0,iter):\n",
        "    \n",
        "    y_hat = np.dot(df,theta)  \n",
        "    err = y-y_hat\n",
        "    \n",
        "    loss = 1/n * np.sum((err)**2)\n",
        "    #print(\"iter:\",i,\"loss:\",loss)\n",
        "\n",
        "    if abs(loss) < eps:\n",
        "      return theta\n",
        "\n",
        "    else:\n",
        "  \n",
        "      g = -2/n * np.dot(df.T,err)\n",
        "      d = np.array(g/np.linalg.norm(g))\n",
        "      theta =  theta - alpha*g\n",
        "  return loss,theta\n",
        "    "
      ],
      "execution_count": 82,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mHHVpWTGWfLT"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "df = train_df[['ones','RM']]\n",
        "y = np.array(train_df['target'])\n",
        "alpha = 0.009\n",
        "c = df.shape[1]\n",
        "iter = 20000\n",
        "theta = np.random.rand(c,1) # Specifying random values for theta\n",
        "#theta = np.ones((1,c))\n",
        "loss,theta = linear_regression(df,y,theta,alpha,iter,eps=1e-4)"
      ],
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YzMkEdM-egFd"
      },
      "source": [
        "# Predict values \n",
        "\n",
        "X = test_df[['RM']]\n",
        "test_target = test_df[['target']]\n",
        "x = test_df[['ones',  'RM']]\n",
        "y_pred = np.dot(x,theta)\n"
      ],
      "execution_count": 86,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 413
        },
        "id": "Y6gozpGofzPT",
        "outputId": "2e446a1b-79f2-4d22-8c94-3aa3ed5249b5"
      },
      "source": [
        "plt.figure(figsize=(8, 6), dpi=80)\n",
        "plt.scatter(X,test_target,color='green')\n",
        "plt.plot(X,y_pred,color='red')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}