RandomSet(Q11,12,13,14).ipynb

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      "name": "RandomSet(Q11,12,13,14).ipynb",
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      "authorship_tag": "ABX9TyOdlXvbRwjwttGOtTMGwT3Y",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/PhantomBlade009/ISLR_LinReg_Solutions/blob/main/RandomSet(Q11%2C12%2C13%2C14).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ObtoPEjOfS4K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f6d30080-db98-4cfa-db9d-74f6b23c5ef6"
      },
      "source": [
        "import numpy as np \n",
        "import pandas as pd \n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns \n",
        "import statsmodels.api as sm"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "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"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IwDV1vKKpSU4"
      },
      "source": [
        "#Q11"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xgcm3fgpiiDk",
        "outputId": "17a80938-b20e-4835-94cc-5d417d2ff1cf"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1)\n",
        "y = (2*X +np.random.randn(100).reshape(-1,1)).reshape(-1,1)\n",
        "print(X.shape, y.shape)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(100, 1) (100, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nw6U-biRi22q",
        "outputId": "71d02cc4-e8a9-456e-a9d5-38413cc1b8a7"
      },
      "source": [
        "model = sm.OLS(y,X).fit() \n",
        "print(model.summary())"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                                 OLS Regression Results                                \n",
            "=======================================================================================\n",
            "Dep. Variable:                      y   R-squared (uncentered):                   0.827\n",
            "Model:                            OLS   Adj. R-squared (uncentered):              0.826\n",
            "Method:                 Least Squares   F-statistic:                              474.8\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):                    1.48e-39\n",
            "Time:                        14:22:07   Log-Likelihood:                         -149.59\n",
            "No. Observations:                 100   AIC:                                      301.2\n",
            "Df Residuals:                      99   BIC:                                      303.8\n",
            "Df Model:                           1                                                  \n",
            "Covariance Type:            nonrobust                                                  \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "x1             2.3359      0.107     21.789      0.000       2.123       2.549\n",
            "==============================================================================\n",
            "Omnibus:                        0.864   Durbin-Watson:                   1.908\n",
            "Prob(Omnibus):                  0.649   Jarque-Bera (JB):                0.883\n",
            "Skew:                          -0.054   Prob(JB):                        0.643\n",
            "Kurtosis:                       2.553   Cond. No.                         1.00\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": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-B0zCIJakLbh",
        "outputId": "284fd1fa-795d-42ee-fa60-506f2529d319"
      },
      "source": [
        "model2 = sm.OLS(X,y).fit()\n",
        "print(model2.summary())"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                                 OLS Regression Results                                \n",
            "=======================================================================================\n",
            "Dep. Variable:                      y   R-squared (uncentered):                   0.827\n",
            "Model:                            OLS   Adj. R-squared (uncentered):              0.826\n",
            "Method:                 Least Squares   F-statistic:                              474.8\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):                    1.48e-39\n",
            "Time:                        14:22:09   Log-Likelihood:                         -55.278\n",
            "No. Observations:                 100   AIC:                                      112.6\n",
            "Df Residuals:                      99   BIC:                                      115.2\n",
            "Df Model:                           1                                                  \n",
            "Covariance Type:            nonrobust                                                  \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "x1             0.3542      0.016     21.789      0.000       0.322       0.386\n",
            "==============================================================================\n",
            "Omnibus:                        0.619   Durbin-Watson:                   1.852\n",
            "Prob(Omnibus):                  0.734   Jarque-Bera (JB):                0.749\n",
            "Skew:                           0.106   Prob(JB):                        0.688\n",
            "Kurtosis:                       2.633   Cond. No.                         1.00\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": "HOi6t3oqkfVI"
      },
      "source": [
        "Xnew = sm.add_constant(X)"
      ],
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9dxd6E4-mMjZ",
        "outputId": "0f7a56d3-029d-42c0-d555-6b27de3eb4ab"
      },
      "source": [
        "model3 = sm.OLS(y,Xnew).fit()\n",
        "print(model3.summary())"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.832\n",
            "Model:                            OLS   Adj. R-squared:                  0.831\n",
            "Method:                 Least Squares   F-statistic:                     486.3\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           8.87e-40\n",
            "Time:                        14:22:15   Log-Likelihood:                -148.13\n",
            "No. Observations:                 100   AIC:                             300.3\n",
            "Df Residuals:                      98   BIC:                             305.5\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.1835      0.108     -1.704      0.091      -0.397       0.030\n",
            "x1             2.3443      0.106     22.053      0.000       2.133       2.555\n",
            "==============================================================================\n",
            "Omnibus:                        0.898   Durbin-Watson:                   1.963\n",
            "Prob(Omnibus):                  0.638   Jarque-Bera (JB):                0.903\n",
            "Skew:                          -0.054   Prob(JB):                        0.637\n",
            "Kurtosis:                       2.547   Cond. No.                         1.05\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": "ADofw2YHmzDA"
      },
      "source": [
        "ynew = sm.add_constant(y)"
      ],
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gwue2kzcm5Fw",
        "outputId": "316874ee-0b89-4f8f-97a7-38d541785473"
      },
      "source": [
        "model4 = sm.OLS(X, ynew).fit()\n",
        "print(model4.summary())"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.832\n",
            "Model:                            OLS   Adj. R-squared:                  0.831\n",
            "Method:                 Least Squares   F-statistic:                     486.3\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           8.87e-40\n",
            "Time:                        14:22:18   Log-Likelihood:                -53.749\n",
            "No. Observations:                 100   AIC:                             111.5\n",
            "Df Residuals:                      98   BIC:                             116.7\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          0.0730      0.042      1.744      0.084      -0.010       0.156\n",
            "x1             0.3550      0.016     22.053      0.000       0.323       0.387\n",
            "==============================================================================\n",
            "Omnibus:                        0.633   Durbin-Watson:                   1.910\n",
            "Prob(Omnibus):                  0.729   Jarque-Bera (JB):                0.759\n",
            "Skew:                           0.105   Prob(JB):                        0.684\n",
            "Kurtosis:                       2.628   Cond. No.                         2.60\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PHOJfsWApA8H"
      },
      "source": [
        "All results are statistically significant and t values corresponding to model and model2, model3 and model4 are same suggesting the conjecture that has been given in the question"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0hrBTuaYpV83"
      },
      "source": [
        "#Q12"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uepezgE7pdwt"
      },
      "source": [
        "# Part a is a proof \n",
        "# For part b solution of question 11 suffices \n",
        "# For part c see below"
      ],
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pqla4mijr1lK",
        "outputId": "3df4bc6c-de72-461e-dbfb-18b452f1424a"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1) \n",
        "y = X + 0.01*np.random.randn(100).reshape(-1,1)\n",
        "print(X.shape, y.shape)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(100, 1) (100, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VEEJZ8EKsti5",
        "outputId": "9d2194d8-9fca-4f1b-e5a4-f7804ada7521"
      },
      "source": [
        "model1 = sm.OLS(y,X).fit()\n",
        "print(model1.summary())"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                                 OLS Regression Results                                \n",
            "=======================================================================================\n",
            "Dep. Variable:                      y   R-squared (uncentered):                   1.000\n",
            "Model:                            OLS   Adj. R-squared (uncentered):              1.000\n",
            "Method:                 Least Squares   F-statistic:                          9.063e+05\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):                   6.32e-198\n",
            "Time:                        14:58:24   Log-Likelihood:                          303.49\n",
            "No. Observations:                 100   AIC:                                     -605.0\n",
            "Df Residuals:                      99   BIC:                                     -602.4\n",
            "Df Model:                           1                                                  \n",
            "Covariance Type:            nonrobust                                                  \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "x1             0.9994      0.001    951.981      0.000       0.997       1.001\n",
            "==============================================================================\n",
            "Omnibus:                        0.435   Durbin-Watson:                   1.817\n",
            "Prob(Omnibus):                  0.805   Jarque-Bera (JB):                0.241\n",
            "Skew:                          -0.118   Prob(JB):                        0.887\n",
            "Kurtosis:                       3.044   Cond. No.                         1.00\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": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a5A4E9NktQ9j",
        "outputId": "e0e1915e-a0ba-406e-972e-68d30fde23f5"
      },
      "source": [
        "model2 = sm.OLS(X,y).fit()\n",
        "print(model2.summary())"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                                 OLS Regression Results                                \n",
            "=======================================================================================\n",
            "Dep. Variable:                      y   R-squared (uncentered):                   1.000\n",
            "Model:                            OLS   Adj. R-squared (uncentered):              1.000\n",
            "Method:                 Least Squares   F-statistic:                          9.063e+05\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):                   6.32e-198\n",
            "Time:                        14:58:28   Log-Likelihood:                          303.44\n",
            "No. Observations:                 100   AIC:                                     -604.9\n",
            "Df Residuals:                      99   BIC:                                     -602.3\n",
            "Df Model:                           1                                                  \n",
            "Covariance Type:            nonrobust                                                  \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "x1             1.0005      0.001    951.981      0.000       0.998       1.003\n",
            "==============================================================================\n",
            "Omnibus:                        0.481   Durbin-Watson:                   1.816\n",
            "Prob(Omnibus):                  0.786   Jarque-Bera (JB):                0.262\n",
            "Skew:                           0.122   Prob(JB):                        0.877\n",
            "Kurtosis:                       3.060   Cond. No.                         1.00\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zgdIXxj61Lxx"
      },
      "source": [
        "As it can be seen above coeeficient corresponding to both regression of Y on X as well as X on Y are same "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KRPvUIzi1VhX"
      },
      "source": [
        "#Q13"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F06Z9j8dtVyR",
        "outputId": "501fbef4-7ceb-4fa7-eda8-60fbf8422f29"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1)\n",
        "eps = 0.25*np.random.randn(100).reshape(-1,1)\n",
        "y = -1 + 0.5*X + eps \n",
        "y.shape"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JPYdOuUq25d6"
      },
      "source": [
        "a) Done above  \n",
        "b) Done above  \n",
        "c) Done above, length of y is 100, beta_0 is -1 and beta_1 is 0.5 "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mW47UehO3QNl",
        "outputId": "ca624f83-6cc1-45b5-d209-c55842bacde0"
      },
      "source": [
        "Xtemp = sm.add_constant(X)\n",
        "model = sm.OLS(y,Xtemp).fit()\n",
        "y_predict = model.predict(Xtemp)\n",
        "print(model.summary())"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.747\n",
            "Model:                            OLS   Adj. R-squared:                  0.745\n",
            "Method:                 Least Squares   F-statistic:                     289.7\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           5.00e-31\n",
            "Time:                        15:49:42   Log-Likelihood:                -6.6712\n",
            "No. Observations:                 100   AIC:                             17.34\n",
            "Df Residuals:                      98   BIC:                             22.55\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.9808      0.026    -37.493      0.000      -1.033      -0.929\n",
            "x1             0.5242      0.031     17.022      0.000       0.463       0.585\n",
            "==============================================================================\n",
            "Omnibus:                        0.610   Durbin-Watson:                   2.055\n",
            "Prob(Omnibus):                  0.737   Jarque-Bera (JB):                0.293\n",
            "Skew:                          -0.114   Prob(JB):                        0.864\n",
            "Kurtosis:                       3.136   Cond. No.                         1.19\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": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 354
        },
        "id": "AN_IV1sZ3102",
        "outputId": "e074c2cc-2452-4aa8-976e-11a2adee4898"
      },
      "source": [
        "sns.regplot(X, y_predict )\n",
        "sns.regplot(X,y)\n",
        "plt.show()"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N216SR8Q7XmA"
      },
      "source": [
        "The scatter plot and line plots for both targets and predictions are above, it can be seen the model is an extremely good fit, the predicted values of coefficients is very clode to real values\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AoWmjk578oqL",
        "outputId": "e32c8f77-c4fa-4766-ffc0-0c34790ab009"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1)\n",
        "eps = 0.05*np.random.randn(100).reshape(-1,1)\n",
        "y = -1 + 0.5*X + eps \n",
        "y.shape"
      ],
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6jjbiMic8oqX"
      },
      "source": [
        "a) Done above  \n",
        "b) Done above  \n",
        "c) Done above, length of y is 100, beta_0 is -1 and beta_1 is 0.5 "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JEuzvnna8oqa",
        "outputId": "5d042622-4975-4e43-a35b-1550114183f1"
      },
      "source": [
        "Xtemp = sm.add_constant(X)\n",
        "model = sm.OLS(y,Xtemp).fit()\n",
        "y_predict = model.predict(Xtemp)\n",
        "print(model.summary())"
      ],
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.991\n",
            "Model:                            OLS   Adj. R-squared:                  0.990\n",
            "Method:                 Least Squares   F-statistic:                 1.027e+04\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):          5.15e-101\n",
            "Time:                        15:57:04   Log-Likelihood:                 164.54\n",
            "No. Observations:                 100   AIC:                            -325.1\n",
            "Df Residuals:                      98   BIC:                            -319.9\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -1.0041      0.005   -212.675      0.000      -1.013      -0.995\n",
            "x1             0.5037      0.005    101.332      0.000       0.494       0.514\n",
            "==============================================================================\n",
            "Omnibus:                        0.092   Durbin-Watson:                   2.023\n",
            "Prob(Omnibus):                  0.955   Jarque-Bera (JB):                0.245\n",
            "Skew:                           0.048   Prob(JB):                        0.885\n",
            "Kurtosis:                       2.778   Cond. No.                         1.07\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": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 354
        },
        "id": "q7k5-tPK8oqc",
        "outputId": "21da5b75-6229-4a99-9adb-5709736d2467"
      },
      "source": [
        "sns.regplot(X, y_predict )\n",
        "sns.regplot(X,y)\n",
        "plt.show()"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xJdbWr4H8_ib"
      },
      "source": [
        "We see that decreasing the noise cause R2 scores and F statistics to increase by a great factor means the model fits even better"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RvqlSw7T88bA",
        "outputId": "ee105d54-0002-4bc3-8359-64d04efbae01"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1)\n",
        "eps = 0.5*np.random.randn(100).reshape(-1,1)\n",
        "y = -1 + 0.5*X + eps \n",
        "y.shape"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9TFn_qHf88bC"
      },
      "source": [
        "a) Done above  \n",
        "b) Done above  \n",
        "c) Done above, length of y is 100, beta_0 is -1 and beta_1 is 0.5 "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G_dTWCLy88bD",
        "outputId": "196db90b-165c-4cc1-ff89-fe1328cae6e5"
      },
      "source": [
        "Xtemp = sm.add_constant(X)\n",
        "model = sm.OLS(y,Xtemp).fit()\n",
        "y_predict = model.predict(Xtemp)\n",
        "print(model.summary())"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.536\n",
            "Model:                            OLS   Adj. R-squared:                  0.531\n",
            "Method:                 Least Squares   F-statistic:                     113.1\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           5.09e-18\n",
            "Time:                        15:58:38   Log-Likelihood:                -72.226\n",
            "No. Observations:                 100   AIC:                             148.5\n",
            "Df Residuals:                      98   BIC:                             153.7\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.9612      0.050    -19.075      0.000      -1.061      -0.861\n",
            "x1             0.5370      0.050     10.635      0.000       0.437       0.637\n",
            "==============================================================================\n",
            "Omnibus:                        1.342   Durbin-Watson:                   1.902\n",
            "Prob(Omnibus):                  0.511   Jarque-Bera (JB):                0.868\n",
            "Skew:                          -0.196   Prob(JB):                        0.648\n",
            "Kurtosis:                       3.233   Cond. No.                         1.05\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": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 354
        },
        "id": "-38w39h688bE",
        "outputId": "c0a50581-0867-4afe-d722-42bac7d32df7"
      },
      "source": [
        "sns.regplot(X, y_predict )\n",
        "sns.regplot(X,y)\n",
        "plt.show()"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzBcegSK9ODq"
      },
      "source": [
        "We see that increasing the noise causes the R2 score and F statistics to decrease drastically causing the model to fit worse"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AR3dl0Qw9kPc",
        "outputId": "501fbef4-7ceb-4fa7-eda8-60fbf8422f29"
      },
      "source": [
        "X = np.random.randn(100).reshape(-1,1)\n",
        "eps = 0.25*np.random.randn(100).reshape(-1,1)\n",
        "y = -1 + 0.5*X + eps \n",
        "y.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TYpRf0D09kQB"
      },
      "source": [
        "a) Done above  \n",
        "b) Done above  \n",
        "c) Done above, length of y is 100, beta_0 is -1 and beta_1 is 0.5 "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gvUynvjS9kQC",
        "outputId": "f1c5e74f-b1ba-4d4a-88b0-e966abda015a"
      },
      "source": [
        "Xtemp = np.column_stack((X,X**2))\n",
        "Xtemp = sm.add_constant(Xtemp)\n",
        "model = sm.OLS(y,Xtemp).fit()\n",
        "y_predict = model.predict(Xtemp)\n",
        "print(model.summary())"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.544\n",
            "Model:                            OLS   Adj. R-squared:                  0.535\n",
            "Method:                 Least Squares   F-statistic:                     57.97\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           2.74e-17\n",
            "Time:                        16:01:21   Log-Likelihood:                -71.282\n",
            "No. Observations:                 100   AIC:                             148.6\n",
            "Df Residuals:                      97   BIC:                             156.4\n",
            "Df Model:                           2                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.9109      0.062    -14.623      0.000      -1.035      -0.787\n",
            "x1             0.5534      0.052     10.703      0.000       0.451       0.656\n",
            "x2            -0.0512      0.038     -1.360      0.177      -0.126       0.024\n",
            "==============================================================================\n",
            "Omnibus:                        2.434   Durbin-Watson:                   1.879\n",
            "Prob(Omnibus):                  0.296   Jarque-Bera (JB):                1.813\n",
            "Skew:                          -0.265   Prob(JB):                        0.404\n",
            "Kurtosis:                       3.392   Cond. No.                         2.48\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": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 354
        },
        "id": "K_LjWWUb9kQE",
        "outputId": "f965cc86-2926-4d3d-80c4-42c79933b220"
      },
      "source": [
        "sns.regplot(X, y_predict )\n",
        "sns.regplot(X,y)\n",
        "plt.show()"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hr33Hse3933X"
      },
      "source": [
        "There is no imporvement from introducing qudratic feature since R2 score and Fstats decrease and also the coefficient corresponding to X**2 can be neglected since p value is high"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TiCsqknGAX1g"
      },
      "source": [
        "#Q14"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LXdVaPs-91po",
        "outputId": "31e0d61f-b355-4cb5-cd83-11265568c971"
      },
      "source": [
        "x1 = np.random.uniform( size=(100,1))\n",
        "x2 = 0.5*x1 + 0.1*np.random.randn(100).reshape(-1,1)\n",
        "y = 2 + 2*x1 + 0.3*x2 + np.random.randn(100).reshape(-1,1)\n",
        "print(x1.shape, x2.shape, y.shape)"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(100, 1) (100, 1) (100, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 567
        },
        "id": "yhu9wtBVB3pV",
        "outputId": "760962b9-7a5d-4c35-d11b-13e77e638ecc"
      },
      "source": [
        "df = pd.DataFrame(np.column_stack((x1,x2,y)))\n",
        "sns.pairplot(df)"
      ],
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<seaborn.axisgrid.PairGrid at 0x7f4800b4de90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 540x540 with 12 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "UMw5nOdRC1yX",
        "outputId": "5ba9cd64-06a2-45ff-e952-7a092c61dc3e"
      },
      "source": [
        "sns.heatmap(df.corr())"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4801075250>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1INuYjzyD0xs",
        "outputId": "0e900ea6-b338-40cb-95c9-cf8ca12b7305"
      },
      "source": [
        "X = np.column_stack((x1,x2))\n",
        "X = sm.add_constant(X)\n",
        "model = sm.OLS(y,X).fit()\n",
        "print(model.summary())"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.227\n",
            "Model:                            OLS   Adj. R-squared:                  0.211\n",
            "Method:                 Least Squares   F-statistic:                     14.23\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           3.82e-06\n",
            "Time:                        16:32:09   Log-Likelihood:                -153.07\n",
            "No. Observations:                 100   AIC:                             312.1\n",
            "Df Residuals:                      97   BIC:                             320.0\n",
            "Df Model:                           2                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          2.0877      0.228      9.164      0.000       1.636       2.540\n",
            "x1             2.1935      0.620      3.539      0.001       0.963       3.424\n",
            "x2            -0.1108      1.105     -0.100      0.920      -2.303       2.082\n",
            "==============================================================================\n",
            "Omnibus:                        1.544   Durbin-Watson:                   1.971\n",
            "Prob(Omnibus):                  0.462   Jarque-Bera (JB):                1.335\n",
            "Skew:                           0.121   Prob(JB):                        0.513\n",
            "Kurtosis:                       2.488   Cond. No.                         12.2\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": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y6JBDEBsE27c",
        "outputId": "80ffd22f-8dfb-421c-e80c-d2576043480c"
      },
      "source": [
        "X = sm.add_constant(x1)\n",
        "model = sm.OLS(y,X).fit()\n",
        "print(model.summary())"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.227\n",
            "Model:                            OLS   Adj. R-squared:                  0.219\n",
            "Method:                 Least Squares   F-statistic:                     28.74\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           5.52e-07\n",
            "Time:                        16:33:06   Log-Likelihood:                -153.07\n",
            "No. Observations:                 100   AIC:                             310.1\n",
            "Df Residuals:                      98   BIC:                             315.4\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          2.0847      0.225      9.277      0.000       1.639       2.531\n",
            "x1             2.1462      0.400      5.361      0.000       1.352       2.941\n",
            "==============================================================================\n",
            "Omnibus:                        1.598   Durbin-Watson:                   1.976\n",
            "Prob(Omnibus):                  0.450   Jarque-Bera (JB):                1.363\n",
            "Skew:                           0.121   Prob(JB):                        0.506\n",
            "Kurtosis:                       2.482   Cond. No.                         4.44\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": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1pgKQJRAFE4n",
        "outputId": "9ee662ce-874d-4a94-acfb-6d6beafdcd6a"
      },
      "source": [
        "X = sm.add_constant(x2)\n",
        "model = sm.OLS(y,X).fit()\n",
        "print(model.summary())"
      ],
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       0.127\n",
            "Model:                            OLS   Adj. R-squared:                  0.118\n",
            "Method:                 Least Squares   F-statistic:                     14.25\n",
            "Date:                Tue, 13 Apr 2021   Prob (F-statistic):           0.000274\n",
            "Time:                        16:33:27   Log-Likelihood:                -159.14\n",
            "No. Observations:                 100   AIC:                             322.3\n",
            "Df Residuals:                      98   BIC:                             327.5\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const          2.4564      0.214     11.469      0.000       2.031       2.881\n",
            "x1             2.8629      0.758      3.776      0.000       1.358       4.368\n",
            "==============================================================================\n",
            "Omnibus:                        3.655   Durbin-Watson:                   2.077\n",
            "Prob(Omnibus):                  0.161   Jarque-Bera (JB):                2.274\n",
            "Skew:                           0.148   Prob(JB):                        0.321\n",
            "Kurtosis:                       2.323   Cond. No.                         6.67\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CCu-84qOFdVg"
      },
      "source": [
        "The values for coefficient do not match in any model, however for x1 they are close, for x2 the first  model suggest extremely different value of coefficient. \n",
        "Also for the first model NULL hypothesis cannot be rejected for x2, in all other models null hypothesis can be rejected for all variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cZf1OchGFJ4e"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}