MultiLinearRegression.ipynb

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        "<a href=\"https://colab.research.google.com/github/DivyaWadehra/AI-LAB/blob/master/MultiLinearRegression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "metadata": {
        "id": "IRLsK5SuKPDB",
        "colab_type": "code",
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      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n0hVvuaSLWkp",
        "colab_type": "code",
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      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6EqGP2otLakQ",
        "colab_type": "code",
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      },
      "source": [
        "import pandas as pd"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R_0_ReOcLeRP",
        "colab_type": "code",
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      },
      "source": [
        "dataset=pd.read_csv('50_Startups.csv')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ENPKyvn1LkhK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X=dataset.iloc[:,:-1].values"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "metadata": {
        "id": "azzX-RmpLqIM",
        "colab_type": "code",
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      },
      "source": [
        "y=dataset.iloc[:,-1].values"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNcchzTyLyZp",
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        "y"
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    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H2JiyR2xLzAm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.preprocessing import LabelEncoder,OneHotEncoder"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qu2BM9ARL1yV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "labelencoder_X=LabelEncoder()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qQJfjER2MaLE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X[:,3]=labelencoder_X.fit_transform(X[:,3])"
      ],
      "execution_count": 0,
      "outputs": []
    },
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        "X"
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    {
      "cell_type": "code",
      "metadata": {
        "id": "PWl4HXTuMsd5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "onehotencoder=OneHotEncoder(categorical_features=[3])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q5MsFQRpM7Sh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 139
        },
        "outputId": "7fd3319b-8da2-4baf-ad44-8ba606736705"
      },
      "source": [
        "X=onehotencoder.fit_transform(X).toarray()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/preprocessing/_encoders.py:415: FutureWarning: The handling of integer data will change in version 0.22. Currently, the categories are determined based on the range [0, max(values)], while in the future they will be determined based on the unique values.\n",
            "If you want the future behaviour and silence this warning, you can specify \"categories='auto'\".\n",
            "In case you used a LabelEncoder before this OneHotEncoder to convert the categories to integers, then you can now use the OneHotEncoder directly.\n",
            "  warnings.warn(msg, FutureWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/preprocessing/_encoders.py:451: DeprecationWarning: The 'categorical_features' keyword is deprecated in version 0.20 and will be removed in 0.22. You can use the ColumnTransformer instead.\n",
            "  \"use the ColumnTransformer instead.\", DeprecationWarning)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3Emlm4EPNBRh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "46614e49-b0ba-43ed-8243-117ba6545044"
      },
      "source": [
        "X[0]"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.000000e+00, 0.000000e+00, 1.000000e+00, 1.653492e+05,\n",
              "       1.368978e+05, 4.717841e+05])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H5ISpJz-NRGD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X=X[:,1:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u0liM8lzNpHM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "8b13cab4-d9a6-422c-e8b7-b3c25f5c0260"
      },
      "source": [
        "X[0]"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.000000e+00, 1.000000e+00, 1.653492e+05, 1.368978e+05,\n",
              "       4.717841e+05])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YnSTE4zxNp7S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.model_selection import train_test_split"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RRLKap1JNxaZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6myYwCq2OMth",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.linear_model import LinearRegression"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4pizamPfOf1U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "regressor=LinearRegression()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Er4gAL-jOla9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d257e079-fa75-4639-9460-3197548b70cd"
      },
      "source": [
        "regressor.fit(X_train,y_train)"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PXDB-9GuOqvP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_pred=regressor.predict(X_test)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y_FZD5hzO6Cy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b6c5f02e-76bc-4033-80f1-b5b51b127096"
      },
      "source": [
        "y_pred[0]"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "103015.20159796216"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LuNKbhPcO-8z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1879ab70-3b65-4305-88d4-d6784d9f8da8"
      },
      "source": [
        "y_test[0]"
      ],
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "103282.38"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DIrfG-7ePAi6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Backward Elimination (Fastest)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j0ZT0nklPIJy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.formula.api as sm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pbVHffskPUwV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X=np.append(arr=np.ones((50,1)).astype(int),values=X,axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lSC1E4LKQIGI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "e8e3658a-77ea-407e-cc42-2bfc10a3f090"
      },
      "source": [
        "X[0]"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.000000e+00, 0.000000e+00, 1.000000e+00, 1.653492e+05,\n",
              "       1.368978e+05, 4.717841e+05])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zb4KkjCTQShk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sf1e5HweQq1l",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "95ZOkfUYQkrX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ga4dFOy4Q1r-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.api as sm\n",
        "X_opt = X[:,[0,1,2,3,4,5]]\n",
        "#OrdinaryLeastSquares\n",
        "regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "utysoBrRRILm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 562
        },
        "outputId": "28536fb1-6fc2-49ee-9db1-494cb6b704f9"
      },
      "source": [
        "regressor_OLS.summary()"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.951</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.945</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   169.9</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Sun, 01 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>1.34e-27</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>19:19:51</td>     <th>  Log-Likelihood:    </th> <td> -525.38</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   1063.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    44</td>      <th>  BIC:               </th> <td>   1074.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     5</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td> 5.013e+04</td> <td> 6884.820</td> <td>    7.281</td> <td> 0.000</td> <td> 3.62e+04</td> <td>  6.4e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x1</th>    <td>  198.7888</td> <td> 3371.007</td> <td>    0.059</td> <td> 0.953</td> <td>-6595.030</td> <td> 6992.607</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x2</th>    <td>  -41.8870</td> <td> 3256.039</td> <td>   -0.013</td> <td> 0.990</td> <td>-6604.003</td> <td> 6520.229</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x3</th>    <td>    0.8060</td> <td>    0.046</td> <td>   17.369</td> <td> 0.000</td> <td>    0.712</td> <td>    0.900</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x4</th>    <td>   -0.0270</td> <td>    0.052</td> <td>   -0.517</td> <td> 0.608</td> <td>   -0.132</td> <td>    0.078</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x5</th>    <td>    0.0270</td> <td>    0.017</td> <td>    1.574</td> <td> 0.123</td> <td>   -0.008</td> <td>    0.062</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>14.782</td> <th>  Durbin-Watson:     </th> <td>   1.283</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  21.266</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.948</td> <th>  Prob(JB):          </th> <td>2.41e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 5.572</td> <th>  Cond. No.          </th> <td>1.45e+06</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.45e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   R-squared:                       0.951\n",
              "Model:                            OLS   Adj. R-squared:                  0.945\n",
              "Method:                 Least Squares   F-statistic:                     169.9\n",
              "Date:                Sun, 01 Sep 2019   Prob (F-statistic):           1.34e-27\n",
              "Time:                        19:19:51   Log-Likelihood:                -525.38\n",
              "No. Observations:                  50   AIC:                             1063.\n",
              "Df Residuals:                      44   BIC:                             1074.\n",
              "Df Model:                           5                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const       5.013e+04   6884.820      7.281      0.000    3.62e+04     6.4e+04\n",
              "x1           198.7888   3371.007      0.059      0.953   -6595.030    6992.607\n",
              "x2           -41.8870   3256.039     -0.013      0.990   -6604.003    6520.229\n",
              "x3             0.8060      0.046     17.369      0.000       0.712       0.900\n",
              "x4            -0.0270      0.052     -0.517      0.608      -0.132       0.078\n",
              "x5             0.0270      0.017      1.574      0.123      -0.008       0.062\n",
              "==============================================================================\n",
              "Omnibus:                       14.782   Durbin-Watson:                   1.283\n",
              "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.266\n",
              "Skew:                          -0.948   Prob(JB):                     2.41e-05\n",
              "Kurtosis:                       5.572   Cond. No.                     1.45e+06\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.45e+06. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I2mvJAKyRPKN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.api as sm\n",
        "X_opt = X[:,[0,3,4,5]]\n",
        "#OrdinaryLeastSquares\n",
        "regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ks2frAbeRmql",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "outputId": "46ddf7ad-318c-4ff1-c57a-172f1dceb1cb"
      },
      "source": [
        "regressor_OLS.summary()"
      ],
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.951</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.948</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   296.0</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Sun, 01 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>4.53e-30</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>19:21:36</td>     <th>  Log-Likelihood:    </th> <td> -525.39</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   1059.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    46</td>      <th>  BIC:               </th> <td>   1066.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td> 5.012e+04</td> <td> 6572.353</td> <td>    7.626</td> <td> 0.000</td> <td> 3.69e+04</td> <td> 6.34e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x1</th>    <td>    0.8057</td> <td>    0.045</td> <td>   17.846</td> <td> 0.000</td> <td>    0.715</td> <td>    0.897</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x2</th>    <td>   -0.0268</td> <td>    0.051</td> <td>   -0.526</td> <td> 0.602</td> <td>   -0.130</td> <td>    0.076</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x3</th>    <td>    0.0272</td> <td>    0.016</td> <td>    1.655</td> <td> 0.105</td> <td>   -0.006</td> <td>    0.060</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>14.838</td> <th>  Durbin-Watson:     </th> <td>   1.282</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  21.442</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.949</td> <th>  Prob(JB):          </th> <td>2.21e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 5.586</td> <th>  Cond. No.          </th> <td>1.40e+06</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.4e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   R-squared:                       0.951\n",
              "Model:                            OLS   Adj. R-squared:                  0.948\n",
              "Method:                 Least Squares   F-statistic:                     296.0\n",
              "Date:                Sun, 01 Sep 2019   Prob (F-statistic):           4.53e-30\n",
              "Time:                        19:21:36   Log-Likelihood:                -525.39\n",
              "No. Observations:                  50   AIC:                             1059.\n",
              "Df Residuals:                      46   BIC:                             1066.\n",
              "Df Model:                           3                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const       5.012e+04   6572.353      7.626      0.000    3.69e+04    6.34e+04\n",
              "x1             0.8057      0.045     17.846      0.000       0.715       0.897\n",
              "x2            -0.0268      0.051     -0.526      0.602      -0.130       0.076\n",
              "x3             0.0272      0.016      1.655      0.105      -0.006       0.060\n",
              "==============================================================================\n",
              "Omnibus:                       14.838   Durbin-Watson:                   1.282\n",
              "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.442\n",
              "Skew:                          -0.949   Prob(JB):                     2.21e-05\n",
              "Kurtosis:                       5.586   Cond. No.                     1.40e+06\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.4e+06. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "81hZ0ZLkRooQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.api as sm\n",
        "X_opt = X[:,[0,3,5]]\n",
        "#OrdinaryLeastSquares\n",
        "regressor_OLS = sm.OLS(endog=y, exog=X_opt).fit()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2UFbdaITRyWk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 499
        },
        "outputId": "93ee82f8-ca0e-4a73-f15e-ade23bf56d1f"
      },
      "source": [
        "regressor_OLS.summary()"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.950</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.948</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   450.8</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Sun, 01 Sep 2019</td> <th>  Prob (F-statistic):</th> <td>2.16e-31</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>19:22:25</td>     <th>  Log-Likelihood:    </th> <td> -525.54</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    50</td>      <th>  AIC:               </th> <td>   1057.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    47</td>      <th>  BIC:               </th> <td>   1063.</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td> 4.698e+04</td> <td> 2689.933</td> <td>   17.464</td> <td> 0.000</td> <td> 4.16e+04</td> <td> 5.24e+04</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x1</th>    <td>    0.7966</td> <td>    0.041</td> <td>   19.266</td> <td> 0.000</td> <td>    0.713</td> <td>    0.880</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>x2</th>    <td>    0.0299</td> <td>    0.016</td> <td>    1.927</td> <td> 0.060</td> <td>   -0.001</td> <td>    0.061</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>14.677</td> <th>  Durbin-Watson:     </th> <td>   1.257</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  21.161</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.939</td> <th>  Prob(JB):          </th> <td>2.54e-05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 5.575</td> <th>  Cond. No.          </th> <td>5.32e+05</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 5.32e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   R-squared:                       0.950\n",
              "Model:                            OLS   Adj. R-squared:                  0.948\n",
              "Method:                 Least Squares   F-statistic:                     450.8\n",
              "Date:                Sun, 01 Sep 2019   Prob (F-statistic):           2.16e-31\n",
              "Time:                        19:22:25   Log-Likelihood:                -525.54\n",
              "No. Observations:                  50   AIC:                             1057.\n",
              "Df Residuals:                      47   BIC:                             1063.\n",
              "Df Model:                           2                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const       4.698e+04   2689.933     17.464      0.000    4.16e+04    5.24e+04\n",
              "x1             0.7966      0.041     19.266      0.000       0.713       0.880\n",
              "x2             0.0299      0.016      1.927      0.060      -0.001       0.061\n",
              "==============================================================================\n",
              "Omnibus:                       14.677   Durbin-Watson:                   1.257\n",
              "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               21.161\n",
              "Skew:                          -0.939   Prob(JB):                     2.54e-05\n",
              "Kurtosis:                       5.575   Cond. No.                     5.32e+05\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 5.32e+05. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QHE8xVq5R0j7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "c12aa36f-3e25-46fa-82dd-aa3c592b6bb8"
      },
      "source": [
        "#Backward Elimination with p value\n",
        "import statsmodels.formula.api as sm\n",
        "def backwardElimination(x, sl):\n",
        "    numVars = len(x[0])\n",
        "    for i in range(0, numVars):\n",
        "        regressor_OLS = sm.OLS(y, x).fit()\n",
        "        maxVar = max(regressor_OLS.pvalues).astype(float)\n",
        "        if maxVar > sl:\n",
        "            for j in range(0, numVars - i):\n",
        "                if (regressor_OLS.pvalues[j].astype(float) == maxVar):\n",
        "                    x = np.delete(x, j, 1)\n",
        "    regressor_OLS.summary()\n",
        "    return x\n",
        " \n",
        "SL = 0.05\n",
        "X_opt = X[:, [0, 1, 2, 3, 4, 5]]\n",
        "X_Modeled = backwardElimination(X_opt, SL)"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-98-046309c9fd14>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0mSL\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.05\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0mX_opt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mX_Modeled\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbackwardElimination\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_opt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m<ipython-input-98-046309c9fd14>\u001b[0m in \u001b[0;36mbackwardElimination\u001b[0;34m(x, sl)\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnumVars\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumVars\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m         \u001b[0mregressor_OLS\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOLS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m         \u001b[0mmaxVar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mregressor_OLS\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpvalues\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mmaxVar\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0msl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mAttributeError\u001b[0m: module 'statsmodels.formula.api' has no attribute 'OLS'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r4oIv9jzSKKc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}