Linear_Regression_Models_to_Predict_Boston_Housing_Price.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Linear Regression Models to Predict Boston Housing Price",
      "provenance": [],
      "authorship_tag": "ABX9TyOwcC0SRmpJq0qQlA1aY7w3",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/juansvas/testing_repo/blob/master/Linear_Regression_Models_to_Predict_Boston_Housing_Price.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BR-eWe9rtyzR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Import libraries\n",
        "import sklearn as sk\n",
        "from sklearn.datasets import load_boston\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z83sZUXVuAT0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 918
        },
        "outputId": "4cea4ef6-64e8-4f00-bd0f-627ab0b4b672"
      },
      "source": [
        "# Load data\n",
        "boston = load_boston()\n",
        "print(boston.DESCR)"
      ],
      "execution_count": 9,
      "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": {
        "id": "TsOI0pwlu_S1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 198
        },
        "outputId": "b2259482-c972-4d38-aa2e-6518f95e3662"
      },
      "source": [
        "# Prepare data\n",
        "data = pd.DataFrame(boston.data, columns=boston.feature_names)\n",
        "data['Price'] = boston.target\n",
        "data.head()"
      ],
      "execution_count": 10,
      "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>Price</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  Price\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": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "17KzrG2GvURS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 654
        },
        "outputId": "abb5da1c-37f7-4cf8-db9c-5dc0caa6ac40"
      },
      "source": [
        "# Explore data\n",
        "display(data.describe())\n",
        "display(data.info())"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "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>Price</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",
              "      <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",
              "      <td>22.532806</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",
              "      <td>9.197104</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",
              "      <td>5.000000</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",
              "      <td>17.025000</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",
              "      <td>21.200000</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",
              "      <td>25.000000</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",
              "      <td>50.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             CRIM          ZN       INDUS  ...           B       LSTAT       Price\n",
              "count  506.000000  506.000000  506.000000  ...  506.000000  506.000000  506.000000\n",
              "mean     3.613524   11.363636   11.136779  ...  356.674032   12.653063   22.532806\n",
              "std      8.601545   23.322453    6.860353  ...   91.294864    7.141062    9.197104\n",
              "min      0.006320    0.000000    0.460000  ...    0.320000    1.730000    5.000000\n",
              "25%      0.082045    0.000000    5.190000  ...  375.377500    6.950000   17.025000\n",
              "50%      0.256510    0.000000    9.690000  ...  391.440000   11.360000   21.200000\n",
              "75%      3.677083   12.500000   18.100000  ...  396.225000   16.955000   25.000000\n",
              "max     88.976200  100.000000   27.740000  ...  396.900000   37.970000   50.000000\n",
              "\n",
              "[8 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 506 entries, 0 to 505\n",
            "Data columns (total 14 columns):\n",
            "CRIM       506 non-null float64\n",
            "ZN         506 non-null float64\n",
            "INDUS      506 non-null float64\n",
            "CHAS       506 non-null float64\n",
            "NOX        506 non-null float64\n",
            "RM         506 non-null float64\n",
            "AGE        506 non-null float64\n",
            "DIS        506 non-null float64\n",
            "RAD        506 non-null float64\n",
            "TAX        506 non-null float64\n",
            "PTRATIO    506 non-null float64\n",
            "B          506 non-null float64\n",
            "LSTAT      506 non-null float64\n",
            "Price      506 non-null float64\n",
            "dtypes: float64(14)\n",
            "memory usage: 55.5 KB\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "None"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mnqDZLrguCzH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Split, train and test data\n",
        "from sklearn.model_selection import train_test_split\n",
        "X = data.drop('Price', axis=1)\n",
        "y = data['Price']\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=5)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y8hKF8rguJL4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "25fd1551-eeff-42c1-8a01-abff145ec102"
      },
      "source": [
        "# Run Linear Regresion Model\n",
        "from sklearn.linear_model import LinearRegression\n",
        "linear_reg = LinearRegression()\n",
        "linear_reg.fit(X_train, y_train)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xHcFelaQyhYp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Predict\n",
        "y_pred = linear_reg.predict(X_test)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5ulhBKdmypgY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "e70e146b-1b75-485d-9206-e5c845c79456"
      },
      "source": [
        "# Check Prediction\n",
        "from sklearn import metrics \n",
        "plt.scatter(y_test, y_pred)\n",
        "plt.show()\n",
        "mse = metrics.mean_squared_error(y_test, y_pred)\n",
        "print('MSE:', mse)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSzGAExFZigGciMhS/w+nz2CkUtsJrgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "MSE: 30.697037704088626\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tHDBp3b80BRT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Tutorial https://medium.com/@haydar_ai/learning-data-science-day-9-linear-regression-on-boston-housing-dataset-cd62a80775ef"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}