Linear_Regression.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Linear Regression.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMtvXZM29V3H+LKyZGphXdj",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/philsaurabh/Tutorials/blob/main/Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o2mzBgA8B-2B"
      },
      "source": [
        "# Importing Libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b2iRX35_B1ib",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a589bfe9-0b92-428a-d560-836cffb29b24"
      },
      "source": [
        "import pandas as pd\n",
        "import scipy.stats as st\n",
        "import statsmodels.api as sm\n",
        "from statsmodels.formula.api import ols"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Po3bju8yEGAT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 203
        },
        "outputId": "e59e5544-5430-470d-e655-dbf1b5801835"
      },
      "source": [
        "# To read data as dataframe\n",
        "df = pd.read_csv('https://raw.githubusercontent.com/philsaurabh/Tutorials/main/Advertising.csv')\n",
        "df.head()"
      ],
      "execution_count": 2,
      "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>Unnamed: 0</th>\n",
              "      <th>TV</th>\n",
              "      <th>radio</th>\n",
              "      <th>newspaper</th>\n",
              "      <th>sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>230.1</td>\n",
              "      <td>37.8</td>\n",
              "      <td>69.2</td>\n",
              "      <td>22.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>44.5</td>\n",
              "      <td>39.3</td>\n",
              "      <td>45.1</td>\n",
              "      <td>10.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>17.2</td>\n",
              "      <td>45.9</td>\n",
              "      <td>69.3</td>\n",
              "      <td>9.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>151.5</td>\n",
              "      <td>41.3</td>\n",
              "      <td>58.5</td>\n",
              "      <td>18.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>180.8</td>\n",
              "      <td>10.8</td>\n",
              "      <td>58.4</td>\n",
              "      <td>12.9</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Unnamed: 0     TV  radio  newspaper  sales\n",
              "0           1  230.1   37.8       69.2   22.1\n",
              "1           2   44.5   39.3       45.1   10.4\n",
              "2           3   17.2   45.9       69.3    9.3\n",
              "3           4  151.5   41.3       58.5   18.5\n",
              "4           5  180.8   10.8       58.4   12.9"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fLWYrUDvyu_E"
      },
      "source": [
        "# Check Null Values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zw6GzbJRyyBE",
        "outputId": "f6e7ae71-b268-4f28-b75e-574b5602d3bc"
      },
      "source": [
        "df.isnull().sum()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Unnamed: 0    0\n",
              "TV            0\n",
              "radio         0\n",
              "newspaper     0\n",
              "sales         0\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mtWnAVzsz06x"
      },
      "source": [
        "# Model Building\n",
        "For Simple Linear Regression,\n",
        "\n",
        "Equation of linear regression\n",
        "\n",
        "*y=c+m<sub>1</sub>x<sub>1</sub>+m<sub>2</sub>x<sub>2</sub>+...+m<sub>n</sub>x<sub>n</sub>*\n",
        "\n",
        "*y*  is the response\n",
        "*c*  is the intercept\n",
        "*m<sub>1</sub>*  is the coefficient for the first feature\n",
        "*m<sub>n</sub>*  is the coefficient for the nth feature\n",
        "In our case:\n",
        "\n",
        "*y=c+m<sub>1</sub>×TV*\n",
        "\n",
        "The  *m*  values are called the model coefficients or model parameters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eTek6buP0xCJ"
      },
      "source": [
        "X = df['TV']#df.iloc[: , 1:3]\n",
        "y = df['sales']"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sLEHEaKq03C9"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.8, test_size = 0.2)# random_state = 100"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tA7Cfwf-04Bn",
        "outputId": "fce7f109-932f-4732-93af-9f2590e09f55"
      },
      "source": [
        "# The training dataset\n",
        "print(X_train.head())\n",
        "print(y_train.head())"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "11     214.7\n",
            "87     110.7\n",
            "80      76.4\n",
            "190     39.5\n",
            "146    240.1\n",
            "Name: TV, dtype: float64\n",
            "11     17.4\n",
            "87     16.0\n",
            "80     11.8\n",
            "190    10.8\n",
            "146    13.2\n",
            "Name: sales, dtype: float64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QOm6xnG_1OLA"
      },
      "source": [
        "import statsmodels.api as sm\n",
        "# Add a constant to get an intercept\n",
        "X_train_sm = sm.add_constant(X_train)\n",
        "\n",
        "# Fit the resgression line using 'OLS'\n",
        "lr = sm.OLS(y_train, X_train_sm).fit()"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jnlG6vBn1R3F",
        "outputId": "30d08401-2374-4129-803e-051a2e7cc96a"
      },
      "source": [
        "# Print the parameters, i.e. the intercept and the slope of the regression line fitted\n",
        "lr.params"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "const    7.066184\n",
              "TV       0.046658\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e5ch4kjK1VdZ",
        "outputId": "797677df-2962-41b9-e10a-51cef6d194c0"
      },
      "source": [
        "# Performing a summary operation lists out all the different parameters of the regression line fitted\n",
        "print(lr.summary())"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                  sales   R-squared:                       0.616\n",
            "Model:                            OLS   Adj. R-squared:                  0.614\n",
            "Method:                 Least Squares   F-statistic:                     253.8\n",
            "Date:                Sun, 14 Nov 2021   Prob (F-statistic):           1.10e-34\n",
            "Time:                        05:06:33   Log-Likelihood:                -411.71\n",
            "No. Observations:                 160   AIC:                             827.4\n",
            "Df Residuals:                     158   BIC:                             833.6\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          7.0662      0.499     14.151      0.000       6.080       8.052\n",
            "TV             0.0467      0.003     15.931      0.000       0.041       0.052\n",
            "==============================================================================\n",
            "Omnibus:                        0.783   Durbin-Watson:                   1.944\n",
            "Prob(Omnibus):                  0.676   Jarque-Bera (JB):                0.888\n",
            "Skew:                          -0.154   Prob(JB):                        0.641\n",
            "Kurtosis:                       2.805   Cond. No.                         337.\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PiUtWl8C1y3i"
      },
      "source": [
        "# Model Evaluation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sFe1c96k1yOv"
      },
      "source": [
        "y_train_pred = lr.predict(X_train_sm)\n",
        "res = (y_train - y_train_pred)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NB8eBmIv12d8"
      },
      "source": [
        "# Add a constant to X_test\n",
        "X_test_sm = sm.add_constant(X_test)\n",
        "\n",
        "# Predict the y values corresponding to X_test_sm\n",
        "y_pred = lr.predict(X_test_sm)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "joYCnGwZ18vs",
        "outputId": "73553e76-3743-4755-a19f-75f1ff015d43"
      },
      "source": [
        "y_pred.head()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "195     8.848504\n",
              "159    13.210990\n",
              "97     15.693174\n",
              "29     10.360210\n",
              "128    17.344853\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aTf6sGRD1-wk",
        "outputId": "14b170dc-8dfe-47ef-90d8-abbcb9443113"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.metrics import r2_score\n",
        "import numpy as np\n",
        "#Returns the mean squared error; we'll take a square root\n",
        "np.sqrt(mean_squared_error(y_test, y_pred))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.521641260199283"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ntH4tqb_2H9P",
        "outputId": "e50425e1-dea9-4d10-d235-0001f63a493a"
      },
      "source": [
        "# Checking the R-squared on the test set\n",
        "r_squared = r2_score(y_test, y_pred)\n",
        "r_squared"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5919992773757194"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    }
  ]
}