lr-assumptions-notebook.ipynb

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    "colab": {
      "name": "Untitled1.ipynb",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "OJ6g6vuhGquZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import scipy as sp\n",
        "import seaborn as sns\n",
        "import statsmodels.api as sm\n",
        "import statsmodels.tsa.api as smt\n",
        "import warnings\n",
        "from google.colab import drive\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from statsmodels.stats.outliers_influence import variance_inflation_factor"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hAuRD0LuGsuA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "warnings.filterwarnings(\"ignore\")\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o3IUV044G7Mc",
        "colab_type": "code",
        "outputId": "b5768a2d-fa73-4d60-fa2e-318a12cd8932",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "drive.mount('/content/drive')"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S5vMtmcMG8c_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "path = \"/content/drive/My Drive/data.csv\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eET-2BJYHClY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = pd.read_csv(path)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xuycFHBFHFMA",
        "colab_type": "code",
        "outputId": "eedbedfb-b108-41ec-fa45-80aa1577fa94",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "print (\"Total number of rows in dataset = {}\".format(df.shape[0]))\n",
        "print (\"Total number of columns in dataset = {}\".format(df.shape[1]))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Total number of rows in dataset = 200\n",
            "Total number of columns in dataset = 4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4hI1HSMYHGva",
        "colab_type": "code",
        "outputId": "8d2a9c7f-22ec-4944-89b2-d2aebdcbfe2e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 7,
      "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>Feature 1</th>\n",
              "      <th>Feature 2</th>\n",
              "      <th>Feature 3</th>\n",
              "      <th>Target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\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>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>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>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>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": [
              "   Feature 1  Feature 2  Feature 3  Target\n",
              "0      230.1       37.8       69.2    22.1\n",
              "1       44.5       39.3       45.1    10.4\n",
              "2       17.2       45.9       69.3     9.3\n",
              "3      151.5       41.3       58.5    18.5\n",
              "4      180.8       10.8       58.4    12.9"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "18qrj1qVHIJp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "target_col = \"Target\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TUxWcUiCHLiI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = df.loc[:, df.columns != target_col]\n",
        "y = df.loc[:, target_col]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vNlJ3qaSxqUJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Split the data into train and test with 70% data being used for training\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
        "                                                    test_size=0.30, \n",
        "                                                    random_state=42)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kL_0pbTeIZ80",
        "colab_type": "text"
      },
      "source": [
        "# Linear Regression using statsmodels "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zpxeNJZ2HS3I",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_with_constant = sm.add_constant(X_train)\n",
        "model = sm.OLS(y_train, X_with_constant)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "60yAyWlfHZJc",
        "colab_type": "code",
        "outputId": "e60283c2-f63f-4574-90b8-967bc974671d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "results = model.fit()\n",
        "results.params"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "const        2.708949\n",
              "Feature 1    0.044059\n",
              "Feature 2    0.199287\n",
              "Feature 3    0.006882\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XwX1CvbIHjaf",
        "colab_type": "code",
        "outputId": "c12453f7-4574-4501-f5f5-1ad7c0cc0a9a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        }
      },
      "source": [
        "print(results.summary())"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                 Target   R-squared:                       0.906\n",
            "Model:                            OLS   Adj. R-squared:                  0.903\n",
            "Method:                 Least Squares   F-statistic:                     434.5\n",
            "Date:                Sun, 01 Dec 2019   Prob (F-statistic):           1.88e-69\n",
            "Time:                        11:56:48   Log-Likelihood:                -262.21\n",
            "No. Observations:                 140   AIC:                             532.4\n",
            "Df Residuals:                     136   BIC:                             544.2\n",
            "Df Model:                           3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          2.7089      0.374      7.250      0.000       1.970       3.448\n",
            "Feature 1      0.0441      0.002     27.219      0.000       0.041       0.047\n",
            "Feature 2      0.1993      0.010     20.195      0.000       0.180       0.219\n",
            "Feature 3      0.0069      0.007      0.988      0.325      -0.007       0.021\n",
            "==============================================================================\n",
            "Omnibus:                       68.437   Durbin-Watson:                   2.285\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              325.342\n",
            "Skew:                          -1.709   Prob(JB):                     2.25e-71\n",
            "Kurtosis:                       9.640   Cond. No.                         500.\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_EEHKVDWyAM_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_test = sm.add_constant(X_test)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DMrfPYNyx7OU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_pred = results.predict(X_test)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ViGVFhjTLwaB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "residual = y_test - y_pred"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kdm-Nl5B8-gW",
        "colab_type": "text"
      },
      "source": [
        "# No Multicolinearity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g0Mbh6kZ3t3a",
        "colab_type": "code",
        "outputId": "29d0f7cd-0927-4ecb-d03a-4c5faf68aedc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        }
      },
      "source": [
        "vif = [variance_inflation_factor(X_train.values, i) for i in range(X_train.shape[1])]\n",
        "pd.DataFrame({'vif': vif[0:]}, index=X_train.columns).T"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
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              "        vertical-align: middle;\n",
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              "\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>Feature 1</th>\n",
              "      <th>Feature 2</th>\n",
              "      <th>Feature 3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>vif</th>\n",
              "      <td>2.697679</td>\n",
              "      <td>3.473818</td>\n",
              "      <td>3.162643</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     Feature 1  Feature 2  Feature 3\n",
              "vif   2.697679   3.473818   3.162643"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rDPab8cb9Nrd",
        "colab_type": "text"
      },
      "source": [
        "# Normailty of Residual"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_kV6rdj3zF8q",
        "colab_type": "code",
        "outputId": "ba96c88d-fdec-4ac5-c5ca-2df4798feb28",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "sns.distplot(residual)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f5f86785e10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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n5O26dq65/3XqWnv49SfO58bFk5wuyUxgd1w8he7+QR7eeMTpUgKKBb05ay+U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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k9kK7sVr9Ulu",
        "colab_type": "code",
        "outputId": "f82c0647-af00-4928-a092-39cc377ba657",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 214
        }
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(6,2.5))\n",
        "_, (__, ___, r) = sp.stats.probplot(residual, plot=ax, fit=True)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0aV6dyznXCGaW8gd4g2iMoMb2IuCNdJ/L9Ae4BdgfWEooOlPvZwYPHmwtassW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\nUN4AOOdcgfIGwDnnCpQ3AM45V6D+H743LJgBtGA6AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x180 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a4xGnyoJ9mpf",
        "colab_type": "code",
        "outputId": "0f01c027-c3ea-40e3-f59e-e684b87dcd5d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "np.mean(residual)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-0.038488952534398074"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7PX4FfxH_TlK",
        "colab_type": "text"
      },
      "source": [
        "# Homoscedasticity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xb11PpM59XM1",
        "colab_type": "code",
        "outputId": "4a6e60b6-69f2-432c-e899-c50944e0f98e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 184
        }
      },
      "source": [
        "fig, ax = plt.subplots(figsize=(6,2.5))\n",
        "_ = ax.scatter(y_pred, residual)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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OBD4IbAJuMTOLex533+bus+4+u3Llylz/EyKgRcpFkgzsunH385JuM7NPA7e5uwP/YWaH\ngRWADtmldFqkXCRe1q6b7cA5AGb2HuAY4JWsQYmMQ4uUi8TLmuhvAN5pZo8BNwGXRUf3IqXTIuUi\n8TJV3bj7T4DfyykWkUy0SLlIPC0OLo2iRcpFjqYpEEREGk6JXkSk4SzE2KmZHQS+V/DLrKCaFUCK\na3RVjU1xjaaqcUF1Y1sc18+6+8gXIgVJ9GUws53uPhs6jsUU1+iqGpviGk1V44LqxpZXXOq6ERFp\nOCV6EZGGa3Ki3xY6gASKa3RVjU1xjaaqcUF1Y8slrsb20YuISFeTj+hFRIQGJHoze87M9pnZHjPb\nGXO7mdnfmNkBM3vUzM4qIabVUTy9n9fM7KpF9/momb3ad5/rC4rlBjN7OZqPqLftRDO7x8yejv5d\nnvDYy6L7PG1ml5UQ19ZoWcpHzex2M5tKeGzqPi8ots+ZWadvf12Y8NgLzGx/1N42lxDXzX0xPWdm\nexIeW9h7Zmanmdn9ZvZEtKToZ6LtQdtZSlxB21lKXMW1MXev9Q/wHLAi5fYLgW8DRnfe/IdKjm8p\n8CLd+tf+7R8F/qWE1/8IcBbwWN+2LwKbo983A1+IedyJwLPRv8uj35cXHNf5wLLo9y/ExTXMPi8o\nts8BfzbEvn4GeCfdmVz3Au8tMq5Ft/8FcH3Z7xlwMnBW9PsJwHeA94ZuZylxBW1nKXEV1sZqf0Q/\nhPXAP3nXg8CUmZ1c4ut/DHjG3Yu+QCyWu/878MNFm9cDX49+/zqwIeah64B73P2H7v7fwD3ABUXG\n5e53u/sb0Z8PAqfm9XqjSHjPhnE2cMDdn/XuhH830X2vC4/LzAz4TeCbeb3esNz9BXd/JPr9R8CT\nwDSB21lSXKHbWcr7NYyx2lgTEr0Dd5vZLjPbGHP7NPD9vr+fZ/g3NQ+Xkvzh+xUz22tm3zazny8x\npne4+wvR7y8C74i5T+j37XK6Z2JxBu3zolwZne7fkNANEfI9+zDwkrs/nXB7Ke+Zma0C1gAPUaF2\ntiiufkHbWUxchbSxJiT6D7n7WcDHgT82s4+EDqjHzI4BLgb+OebmR+h257wP+Fu6i7iUzrvng5Uq\nvTKz64A3gBsT7hJin/8d8C7g/cALdLtJquS3ST+aL/w9M7PjgVuBq9z9tf7bQrazpLhCt7OYuApr\nY7VP9O7eif59Gbid7qlNvw5wWt/fp0bbyvBx4BF3f2nxDe7+mrv/T/T7XcCEma0oKa6Xet1X0b8v\nx9wnyPtmZp8CPgH8bpQcjjLEPs+du7/k7gvufhj4h4TXDPWeLQMuAW5Ouk/R75mZTdBNWje6+23R\n5uDtLCGu4O0sLq4i21itE72ZHWdmJ/R+pzvI8tiiu90J/IF1fRB4te90smiJR1lmdlLUr4qZnU13\nX/xXSXHdCfSqGy4D7oi5zw7gfDNbHp1Cnh9tK4yZXQBcA1zs7q8n3GeYfV5EbP3jOr+e8JoPA+82\ns9Ojs7lL6b7XRTsPeMrdn4+7sej3LGrHXwOedPcv9d0UtJ0lxRW6naXEVVwby3tEucwfuiPPe6Of\nx4Hrou1XAFdEvxvwFboj1fuA2ZJiO45u4n5b37b+uK6MYt5Ld0DoVwuK45t0TwPn6fbn/RHwM8C/\nAk8D9wInRvedBb7a99jLgQPRzx+WENcBuv2Pe6Kfv4/uewpwV9o+LyG2b0Tt59Hog3Xy4tiivy+k\nW0XxTN6xxcUVbf/HXrvqu29p7xnwIbrdMo/27bsLQ7ezlLiCtrOUuAprY7oyVkSk4WrddSMiIoMp\n0YuINJwSvYhIwynRi4g0nBK9iEjDKdGLiDScEr2ISMMp0YuINNz/A27KTjU9FIf8AAAAAElFTkSu\nQmCC\n",
            "text/plain": [
              "<Figure size 432x180 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8uwQaKeH7dT-",
        "colab_type": "text"
      },
      "source": [
        "# No autocorrelation of residuals"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQr_qb793cl_",
        "colab_type": "code",
        "outputId": "ce114842-8ac9-410e-f4b6-f080d6bc8955",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "acf = smt.graphics.plot_acf(residual, lags=40 , alpha=0.05)\n",
        "acf.show()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7/wEMAj8Dng0MAXcBq8uOK4vtQWBpBeJ4JXAKcE9u3p8DF2fPLwY+UYGYPgL8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\nQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}