Boston(Lab_and_Q15).ipynb

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  "metadata": {
    "colab": {
      "name": "Boston(Lab and Q15).ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOHqZiyDiZlK1i9oNo3WY/F",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/PhantomBlade009/ISLR_LinReg_Solutions/blob/main/Boston(Lab_and_Q15).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l0F6AhbHNdfT"
      },
      "source": [
        "#Question 15 solution below"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lk-MIdOXZ5xS"
      },
      "source": [
        "#Lab part and Self "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5Be-iF6hyrin"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        " "
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1TIHXme6zyog"
      },
      "source": [
        "df = pd.read_csv('https://raw.githubusercontent.com/mscaudill/IntroStatLearn/master/data/Boston.csv')"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fCY2DEXoz8jj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "outputId": "1ef953d4-4ac2-4a7f-aaea-18f55bb14642"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "      <th></th>\n",
              "      <th>Unnamed: 0</th>\n",
              "      <th>crim</th>\n",
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              "      <th>indus</th>\n",
              "      <th>chas</th>\n",
              "      <th>nox</th>\n",
              "      <th>rm</th>\n",
              "      <th>age</th>\n",
              "      <th>dis</th>\n",
              "      <th>rad</th>\n",
              "      <th>tax</th>\n",
              "      <th>ptratio</th>\n",
              "      <th>black</th>\n",
              "      <th>lstat</th>\n",
              "      <th>medv</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1</td>\n",
              "      <td>296</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
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            ],
            "text/plain": [
              "   Unnamed: 0     crim    zn  indus  chas  ...  tax  ptratio   black  lstat  medv\n",
              "0           1  0.00632  18.0   2.31     0  ...  296     15.3  396.90   4.98  24.0\n",
              "1           2  0.02731   0.0   7.07     0  ...  242     17.8  396.90   9.14  21.6\n",
              "2           3  0.02729   0.0   7.07     0  ...  242     17.8  392.83   4.03  34.7\n",
              "3           4  0.03237   0.0   2.18     0  ...  222     18.7  394.63   2.94  33.4\n",
              "4           5  0.06905   0.0   2.18     0  ...  222     18.7  396.90   5.33  36.2\n",
              "\n",
              "[5 rows x 15 columns]"
            ]
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          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "id": "ObA2s5WpC0op",
        "outputId": "47558b66-a182-49fa-955f-cf80374a5794"
      },
      "source": [
        "#Dropped the first column\n",
        "df.drop(axis=1, columns= df.columns[0], inplace = True )\n",
        "df.head()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>crim</th>\n",
              "      <th>zn</th>\n",
              "      <th>indus</th>\n",
              "      <th>chas</th>\n",
              "      <th>nox</th>\n",
              "      <th>rm</th>\n",
              "      <th>age</th>\n",
              "      <th>dis</th>\n",
              "      <th>rad</th>\n",
              "      <th>tax</th>\n",
              "      <th>ptratio</th>\n",
              "      <th>black</th>\n",
              "      <th>lstat</th>\n",
              "      <th>medv</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1</td>\n",
              "      <td>296</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "      crim    zn  indus  chas    nox  ...  tax  ptratio   black  lstat  medv\n",
              "0  0.00632  18.0   2.31     0  0.538  ...  296     15.3  396.90   4.98  24.0\n",
              "1  0.02731   0.0   7.07     0  0.469  ...  242     17.8  396.90   9.14  21.6\n",
              "2  0.02729   0.0   7.07     0  0.469  ...  242     17.8  392.83   4.03  34.7\n",
              "3  0.03237   0.0   2.18     0  0.458  ...  222     18.7  394.63   2.94  33.4\n",
              "4  0.06905   0.0   2.18     0  0.458  ...  222     18.7  396.90   5.33  36.2\n",
              "\n",
              "[5 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HuHasqI5DQzW",
        "outputId": "2d3d8041-137c-4fcd-c232-214ec85fb746"
      },
      "source": [
        "df.isnull().sum()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "crim       0\n",
              "zn         0\n",
              "indus      0\n",
              "chas       0\n",
              "nox        0\n",
              "rm         0\n",
              "age        0\n",
              "dis        0\n",
              "rad        0\n",
              "tax        0\n",
              "ptratio    0\n",
              "black      0\n",
              "lstat      0\n",
              "medv       0\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XIzWWonMD4CE",
        "outputId": "dee10f35-73a9-4bae-8e8e-4d2edce2f145"
      },
      "source": [
        "X = df.iloc[:,0:df.shape[1]-1].values\n",
        "y = df.iloc[:,df.shape[1]-1].values.reshape(-1,1)\n",
        "print(X.shape, y.shape)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(506, 13) (506, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z2v0EiWUG58G"
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler \n",
        "scaler = StandardScaler()\n",
        "X_norm = scaler.fit_transform(X)"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SKuioVW2ExsQ"
      },
      "source": [
        "from sklearn.linear_model import LinearRegression \n",
        "lr = LinearRegression()"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4U04Qd4Bc_Ym"
      },
      "source": [
        "lr.fit(X_norm, y)\n",
        "y_predict = lr.predict(X_norm)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mFZ12PK6fUml"
      },
      "source": [
        "def summary(X, y, y_predict, lr):\n",
        "  from scipy import stats\n",
        "  from sklearn.metrics import r2_score \n",
        "  from sklearn.metrics import mean_squared_error\n",
        "\n",
        "  n = X.shape[0] \n",
        "  p = X.shape[1] \n",
        "  R2 = r2_score(y,y_predict) \n",
        "  adjusted_r2 = 1- (1-R2)*((n-1)/(n-p-1)) \n",
        "  RMSE = mean_squared_error(y,y_predict)**(1/2) \n",
        "  print(\"RMSE = \", RMSE) \n",
        "  print(\"R2 Score = \", R2)\n",
        "  print(\"Adjusted R2 =\" ,adjusted_r2) \n",
        "\n",
        "  weights = np.append(lr.intercept_,lr.coef_)\n",
        "\n",
        "  #newX = pd.DataFrame({\"Constant\":np.ones(len(X))}).join(pd.DataFrame(X))\n",
        "  #MSE = (mean_squared_error(y, y_predict_tot))/(len(newX)-len(newX.columns))\n",
        "\n",
        "  # Note if you don't want to use a DataFrame replace the two lines above with\n",
        "  newX = np.append(np.ones((len(X),1)), X, axis=1)\n",
        "  MSE = (sum((y-y_predict)**2))/(newX.shape[0]-newX.shape[1])\n",
        "\n",
        "\n",
        "  var_b = MSE*(np.linalg.pinv(np.dot(newX.T,newX)).diagonal())\n",
        "  sd_b = np.sqrt(var_b)\n",
        "  ts_b = weights/ sd_b\n",
        "\n",
        "  p_values =[2.0*(1.0-stats.t.cdf(np.abs(i),(newX.shape[0]-newX.shape[1]))) for i in ts_b]\n",
        "\n",
        "  sd_b = np.round(sd_b,3)\n",
        "  ts_b = np.round(ts_b,3)\n",
        "  p_values = np.round(p_values,100)\n",
        "  weights = np.round(weights,4)\n",
        "\n",
        "  myDF3 = pd.DataFrame()\n",
        "  myDF3[\"Coefficients\"],myDF3[\"Standard Errors\"],myDF3[\"t values\"],myDF3[\"Probabilities\"] = [weights,sd_b,ts_b,p_values]\n",
        "  print(myDF3)\n",
        "\n",
        "  interval_95 = pd.DataFrame(np.column_stack((weights-2*sd_b, weights+2*sd_b)), columns=['LowerBound', 'UpperBound'])\n",
        "  print('95 per intervals')\n",
        "  print(interval_95)\n",
        "  return"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ohq7P2GPdMq2",
        "outputId": "ec4aa264-ea4e-4393-e5cf-420a9fb910f1"
      },
      "source": [
        "summary(X_norm,y,y_predict,lr)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE =  4.679191295697282\n",
            "R2 Score =  0.7406426641094094\n",
            "Adjusted R2 = 0.7337897263724629\n",
            "    Coefficients  Standard Errors  t values  Probabilities\n",
            "0        36.4595            0.211   172.831       0.000000\n",
            "1        -0.1080            0.282    -0.382       0.702283\n",
            "2         0.0464            0.320     0.145       0.884663\n",
            "3         0.0206            0.421     0.049       0.961115\n",
            "4         2.6867            0.219    12.290       0.000000\n",
            "5       -17.7666            0.442   -40.179       0.000000\n",
            "6         3.8099            0.293    12.987       0.000000\n",
            "7         0.0007            0.371     0.002       0.998514\n",
            "8        -1.4756            0.420    -3.517       0.000477\n",
            "9         0.3060            0.577     0.530       0.596143\n",
            "10       -0.0123            0.633    -0.019       0.984465\n",
            "11       -0.9527            0.283    -3.367       0.000819\n",
            "12        0.0093            0.245     0.038       0.969694\n",
            "13       -0.5248            0.362    -1.450       0.147585\n",
            "95 per intervals\n",
            "    LowerBound  UpperBound\n",
            "0      36.0375     36.8815\n",
            "1      -0.6720      0.4560\n",
            "2      -0.5936      0.6864\n",
            "3      -0.8214      0.8626\n",
            "4       2.2487      3.1247\n",
            "5     -18.6506    -16.8826\n",
            "6       3.2239      4.3959\n",
            "7      -0.7413      0.7427\n",
            "8      -2.3156     -0.6356\n",
            "9      -0.8480      1.4600\n",
            "10     -1.2783      1.2537\n",
            "11     -1.5187     -0.3867\n",
            "12     -0.4807      0.4993\n",
            "13     -1.2488      0.1992\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vugnVoQNdROP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "c34104bf-eaba-41b9-bcb8-f6398d6f0da6"
      },
      "source": [
        "import matplotlib.pyplot as plt \n",
        "plt.scatter(y_predict-y, y_predict)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f4f10604a90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        },
        {
          "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": "code",
      "metadata": {
        "id": "tygq46ZPaPsR"
      },
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures \n",
        "poly = PolynomialFeatures(degree = 2, include_bias = False, interaction_only = True) \n",
        "X_norm = poly.fit_transform(X_norm)"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bgAZRleXKMaA"
      },
      "source": [
        "lr.fit(X_norm, y)\n",
        "y_predict = lr.predict(X_norm)"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GbxJLEGZLGw3",
        "outputId": "75bf8a66-258b-4251-dbdd-8a912307e23c"
      },
      "source": [
        "summary(X_norm,y,y_predict,lr)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE =  2.5794001227398327\n",
            "R2 Score =  0.9211876335753\n",
            "Adjusted R2 = 0.9038641424046534\n",
            "    Coefficients  Standard Errors  t values  Probabilities\n",
            "0        36.3908            6.527     5.575   4.467968e-08\n",
            "1        36.8834           16.227     2.273   2.354193e-02\n",
            "2        32.6516           14.596     2.237   2.581169e-02\n",
            "3        -0.8710           10.552    -0.083   9.342576e-01\n",
            "4         1.8761            0.481     3.899   1.126197e-04\n",
            "..           ...              ...       ...            ...\n",
            "87       -0.0073            3.070    -0.002   9.980915e-01\n",
            "88       -1.6854            1.451    -1.162   2.459402e-01\n",
            "89        0.2374            0.663     0.358   7.205080e-01\n",
            "90        0.0602            0.461     0.131   8.960685e-01\n",
            "91       -0.3980            0.270    -1.472   1.418367e-01\n",
            "\n",
            "[92 rows x 4 columns]\n",
            "95 per intervals\n",
            "    LowerBound  UpperBound\n",
            "0      23.3368     49.4448\n",
            "1       4.4294     69.3374\n",
            "2       3.4596     61.8436\n",
            "3     -21.9750     20.2330\n",
            "4       0.9141      2.8381\n",
            "..         ...         ...\n",
            "87     -6.1473      6.1327\n",
            "88     -4.5874      1.2166\n",
            "89     -1.0886      1.5634\n",
            "90     -0.8618      0.9822\n",
            "91     -0.9380      0.1420\n",
            "\n",
            "[92 rows x 2 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "IgiBPQyOZTii",
        "outputId": "3626ca7e-f20a-421f-9a04-cdc46ac51d82"
      },
      "source": [
        "#Residual Plot  \n",
        "plt.scatter(y_predict, y - y_predict )"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f4f10627c10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        },
        {
          "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": "code",
      "metadata": {
        "id": "b8-RCyB7Z_X_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        },
        "outputId": "ef74dd7f-4834-43a3-8160-f5d4badf0c8d"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>crim</th>\n",
              "      <th>zn</th>\n",
              "      <th>indus</th>\n",
              "      <th>chas</th>\n",
              "      <th>nox</th>\n",
              "      <th>rm</th>\n",
              "      <th>age</th>\n",
              "      <th>dis</th>\n",
              "      <th>rad</th>\n",
              "      <th>tax</th>\n",
              "      <th>ptratio</th>\n",
              "      <th>black</th>\n",
              "      <th>lstat</th>\n",
              "      <th>medv</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1</td>\n",
              "      <td>296</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2</td>\n",
              "      <td>242</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3</td>\n",
              "      <td>222</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      crim    zn  indus  chas    nox  ...  tax  ptratio   black  lstat  medv\n",
              "0  0.00632  18.0   2.31     0  0.538  ...  296     15.3  396.90   4.98  24.0\n",
              "1  0.02731   0.0   7.07     0  0.469  ...  242     17.8  396.90   9.14  21.6\n",
              "2  0.02729   0.0   7.07     0  0.469  ...  242     17.8  392.83   4.03  34.7\n",
              "3  0.03237   0.0   2.18     0  0.458  ...  222     18.7  394.63   2.94  33.4\n",
              "4  0.06905   0.0   2.18     0  0.458  ...  222     18.7  396.90   5.33  36.2\n",
              "\n",
              "[5 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uRZfw7ELe1Aa"
      },
      "source": [
        "**Question** **15**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rXSPvwWYeXIT"
      },
      "source": [
        "X = df.iloc[:,1:df.shape[1]].values\n",
        "X = X.astype(np.float) \n",
        "y= df.iloc[:,0].values.reshape(-1,1)"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f5_O5suJcflE",
        "outputId": "895b6652-6f65-40e6-c58c-6641a696d3ab"
      },
      "source": [
        "single_wts = np.zeros((X.shape[1],1))\n",
        "single_wts.shape"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(13, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9igh42P_ep17",
        "outputId": "3abb186a-2787-42e9-96ea-4cc7f4e95f23"
      },
      "source": [
        "for i in range(X.shape[1]):\n",
        "  Xtemp = X[:,i].reshape(-1,1)\n",
        "  lr.fit(Xtemp,y) \n",
        "  y_predict = lr.predict(Xtemp)\n",
        "  summary(Xtemp, y, y_predict, lr) \n",
        "  print('____________________________________________________')\n",
        "  single_wts[i] = lr.coef_[0]"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE =  8.418602620494738\n",
            "R2 Score =  0.04018790803211081\n",
            "Adjusted R2 = 0.038283518960746\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0        4.4537            0.417    10.675       0.000000\n",
            "1       -0.0739            0.016    -4.594       0.000006\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      3.6197      5.2877\n",
            "1     -0.1059     -0.0419\n",
            "____________________________________________________\n",
            "RMSE =  7.850720005720037\n",
            "R2 Score =  0.16531007043075152\n",
            "Adjusted R2 = 0.16365393961811414\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       -2.0637            0.667    -3.093       0.002091\n",
            "1        0.5098            0.051     9.991       0.000000\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     -3.3977     -0.7297\n",
            "1      0.4078      0.6118\n",
            "____________________________________________________\n",
            "RMSE =  8.579609085341941\n",
            "R2 Score =  0.0031238689633057426\n",
            "Adjusted R2 = 0.0011459401318837381\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0        3.7444            0.396     9.453       0.000000\n",
            "1       -1.8928            1.506    -1.257       0.209435\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      2.9524      4.5364\n",
            "1     -4.9048      1.1192\n",
            "____________________________________________________\n",
            "RMSE =  7.794522385795993\n",
            "R2 Score =  0.17721718179269363\n",
            "Adjusted R2 = 0.17558467620101248\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0      -13.7199            1.699    -8.073   5.107026e-15\n",
            "1       31.2485            2.999    10.419   0.000000e+00\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0    -17.1179    -10.3219\n",
            "1     25.2505     37.2465\n",
            "____________________________________________________\n",
            "RMSE =  8.383967962604627\n",
            "R2 Score =  0.048069116716083604\n",
            "Adjusted R2 = 0.04618036496353617\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       20.4818            3.364     6.088   2.272000e-09\n",
            "1       -2.6841            0.532    -5.045   6.346703e-07\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     13.7538     27.2098\n",
            "1     -3.7481     -1.6201\n",
            "____________________________________________________\n",
            "RMSE =  8.04071109524196\n",
            "R2 Score =  0.12442145175894637\n",
            "Adjusted R2 = 0.12268419273465858\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       -3.7779            0.944    -4.002   7.221718e-05\n",
            "1        0.1078            0.013     8.463   2.220446e-16\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     -5.6659     -1.8899\n",
            "1      0.0818      0.1338\n",
            "____________________________________________________\n",
            "RMSE =  7.94961118389392\n",
            "R2 Score =  0.1441493749253987\n",
            "Adjusted R2 = 0.1424512586058062\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0        9.4993            0.730    13.006            0.0\n",
            "1       -1.5509            0.168    -9.213            0.0\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      8.0393     10.9593\n",
            "1     -1.8869     -1.2149\n",
            "____________________________________________________\n",
            "RMSE =  6.704463080224447\n",
            "R2 Score =  0.39125668674998915\n",
            "Adjusted R2 = 0.3900488627157629\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       -2.2872            0.443    -5.157   3.605846e-07\n",
            "1        0.6179            0.034    17.998   0.000000e+00\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     -3.1732     -1.4012\n",
            "1      0.5499      0.6859\n",
            "____________________________________________________\n",
            "RMSE =  6.9830596293175\n",
            "R2 Score =  0.3396142433788122\n",
            "Adjusted R2 = 0.33830395417916703\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       -8.5284            0.816   -10.454            0.0\n",
            "1        0.0297            0.002    16.099            0.0\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0    -10.1604     -6.8964\n",
            "1      0.0257      0.0337\n",
            "____________________________________________________\n",
            "RMSE =  8.223911228666797\n",
            "R2 Score =  0.0840684389437365\n",
            "Adjusted R2 = 0.08225111441783117\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0      -17.6469            3.147    -5.607   3.395255e-08\n",
            "1        1.1520            0.169     6.801   2.942935e-11\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0    -23.9409    -11.3529\n",
            "1      0.8140      1.4900\n",
            "____________________________________________________\n",
            "RMSE =  7.930431041055408\n",
            "R2 Score =  0.1482742394241312\n",
            "Adjusted R2 = 0.14658430735949657\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       16.5535            1.426    11.609            0.0\n",
            "1       -0.0363            0.004    -9.367            0.0\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     13.7015     19.4055\n",
            "1     -0.0443     -0.0283\n",
            "____________________________________________________\n",
            "RMSE =  7.6492986961900336\n",
            "R2 Score =  0.2075909325343357\n",
            "Adjusted R2 = 0.20601869232111014\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       -3.3305            0.694    -4.801       0.000002\n",
            "1        0.5488            0.048    11.491       0.000000\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     -4.7185     -1.9425\n",
            "1      0.4528      0.6448\n",
            "____________________________________________________\n",
            "RMSE =  7.918754674819499\n",
            "R2 Score =  0.15078046904975706\n",
            "Adjusted R2 = 0.14909550966295104\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       11.7965            0.934    12.628            0.0\n",
            "1       -0.3632            0.038    -9.460            0.0\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      9.9285     13.6645\n",
            "1     -0.4392     -0.2872\n",
            "____________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A_KVmYSUfsj-"
      },
      "source": [
        "import seaborn as sns \n",
        "sns.pairplot(df, )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_eTWQrnJiGy4",
        "outputId": "86ee00c1-41e1-4a3c-b62b-de1b892ea31a"
      },
      "source": [
        "lr.fit(X,y)\n",
        "y_predict = lr.predict(X) \n",
        "summary(X,y, y_predict, lr)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE =  6.349493616836943\n",
            "R2 Score =  0.45401038980421504\n",
            "Adjusted R2 = 0.4395838350632695\n",
            "    Coefficients  Standard Errors  t values  Probabilities\n",
            "0        17.0332            7.235     2.354   1.894909e-02\n",
            "1         0.0449            0.019     2.394   1.702489e-02\n",
            "2        -0.0639            0.083    -0.766   4.442940e-01\n",
            "3        -0.7491            1.180    -0.635   5.258670e-01\n",
            "4       -10.3135            5.276    -1.955   5.115200e-02\n",
            "5         0.4301            0.613     0.702   4.830888e-01\n",
            "6         0.0015            0.018     0.081   9.354878e-01\n",
            "7        -0.9872            0.282    -3.503   5.022039e-04\n",
            "8         0.5882            0.088     6.680   6.460454e-11\n",
            "9        -0.0038            0.005    -0.733   4.637927e-01\n",
            "10       -0.2711            0.186    -1.454   1.466113e-01\n",
            "11       -0.0075            0.004    -2.052   4.070233e-02\n",
            "12        0.1262            0.076     1.667   9.620842e-02\n",
            "13       -0.1989            0.061    -3.287   1.086810e-03\n",
            "95 per intervals\n",
            "    LowerBound  UpperBound\n",
            "0       2.5632     31.5032\n",
            "1       0.0069      0.0829\n",
            "2      -0.2299      0.1021\n",
            "3      -3.1091      1.6109\n",
            "4     -20.8655      0.2385\n",
            "5      -0.7959      1.6561\n",
            "6      -0.0345      0.0375\n",
            "7      -1.5512     -0.4232\n",
            "8       0.4122      0.7642\n",
            "9      -0.0138      0.0062\n",
            "10     -0.6431      0.1009\n",
            "11     -0.0155      0.0005\n",
            "12     -0.0258      0.2782\n",
            "13     -0.3209     -0.0769\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l-BTTuHSc150"
      },
      "source": [
        "multi_wts = lr.coef_.T"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "OG3hxjswc9or",
        "outputId": "07e1253a-1cb0-4a31-e794-545a504b496f"
      },
      "source": [
        "plt.plot(single_wts, multi_wts)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f4f10538210>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        },
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "7cwkrZjAM3P0",
        "outputId": "3452edf4-8d9e-4091-ce6c-903a7c883e6e"
      },
      "source": [
        "sns.regplot(x=y_predict, y= y_predict - y, lowess=True)"
      ],
      "execution_count": 45,
      "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"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4f10437a90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        },
        {
          "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CmSdgn1LdDCp",
        "outputId": "1f8c5617-77bb-405e-cfc6-be53e7ff6f5a"
      },
      "source": [
        "for i in range(X.shape[1]):\n",
        "  Xtemp = X[:,i].reshape(-1,1)\n",
        "  Xtemp = np.column_stack((Xtemp,Xtemp**2, Xtemp**3))\n",
        "  lr.fit(Xtemp, y) \n",
        "  y_predict = lr.predict(Xtemp) \n",
        "  summary(Xtemp,y,y_predict,lr)   \n",
        "  print('_________________________________________________________')"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "RMSE =  8.12656177134114\n",
            "R2 Score =  0.21770488699021706\n",
            "Adjusted R2 = 0.21302981659374431\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       25.1905            0.435    57.846   0.000000e+00\n",
            "1       -1.1364            0.144    -7.868   2.242651e-14\n",
            "2        0.0238            0.007     3.494   5.184482e-04\n",
            "3       -0.0001            0.000    -2.242   2.541096e-02\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     24.3205     26.0605\n",
            "1     -1.4244     -0.8484\n",
            "2      0.0098      0.0378\n",
            "3     -0.0001     -0.0001\n",
            "_________________________________________________________\n",
            "RMSE =  8.396230969814876\n",
            "R2 Score =  0.16492460149792232\n",
            "Adjusted R2 = 0.15993411106862698\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       20.4486            0.436    46.905   0.000000e+00\n",
            "1        0.6434            0.111     5.819   1.055518e-08\n",
            "2       -0.0168            0.004    -4.313   1.941865e-05\n",
            "3        0.0001            0.000     3.978   7.981118e-05\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     19.5766     21.3206\n",
            "1      0.4214      0.8654\n",
            "2     -0.0248     -0.0088\n",
            "3      0.0001      0.0001\n",
            "_________________________________________________________\n",
            "RMSE =  7.813406655875142\n",
            "R2 Score =  0.2768343456208131\n",
            "Adjusted R2 = 0.2725126385229295\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       37.0802            1.663    22.293   0.000000e+00\n",
            "1       -2.8070            0.509    -5.511   5.713973e-08\n",
            "2        0.1405            0.042     3.380   7.807276e-04\n",
            "3       -0.0024            0.001    -2.373   1.802575e-02\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     33.7542     40.4062\n",
            "1     -3.8250     -1.7890\n",
            "2      0.0565      0.2245\n",
            "3     -0.0044     -0.0004\n",
            "_________________________________________________________\n",
            "RMSE =  9.046178471340925\n",
            "R2 Score =  0.030635214618155215\n",
            "Adjusted R2 = 0.024842197972447022\n",
            "   Coefficients  Standard Errors      t values  Probabilities\n",
            "0  2.207150e+01            0.418  5.274200e+01            0.0\n",
            "1 -6.256356e+13            0.530 -1.179569e+14            0.0\n",
            "2  3.128178e+13            0.530  5.897845e+13            0.0\n",
            "3  3.128178e+13            0.530  5.897845e+13            0.0\n",
            "95 per intervals\n",
            "     LowerBound    UpperBound\n",
            "0  2.123550e+01  2.290750e+01\n",
            "1 -6.256356e+13 -6.256356e+13\n",
            "2  3.128178e+13  3.128178e+13\n",
            "3  3.128178e+13  3.128178e+13\n",
            "_________________________________________________________\n",
            "RMSE =  8.24945262929823\n",
            "R2 Score =  0.19386606869686562\n",
            "Adjusted R2 = 0.1890485352428628\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0      -22.4864           38.520    -0.584       0.559648\n",
            "1      315.0960          195.100     1.615       0.106928\n",
            "2     -615.8267          320.476    -1.922       0.055222\n",
            "3      350.1860          170.923     2.049       0.041002\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0    -99.5264     54.5536\n",
            "1    -75.1040    705.2960\n",
            "2  -1256.7787     25.1253\n",
            "3      8.3400    692.0320\n",
            "_________________________________________________________\n",
            "RMSE =  6.086142435718217\n",
            "R2 Score =  0.561225722635539\n",
            "Adjusted R2 = 0.5586035655994965\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0      241.3108           47.327     5.099   4.853140e-07\n",
            "1     -109.3906           22.969    -4.763   2.505427e-06\n",
            "2       16.4910            3.675     4.487   8.952479e-06\n",
            "3       -0.7404            0.193    -3.827   1.461903e-04\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0    146.6568    335.9648\n",
            "1   -155.3286    -63.4526\n",
            "2      9.1410     23.8410\n",
            "3     -1.1264     -0.3544\n",
            "_________________________________________________________\n",
            "RMSE =  8.438111822458122\n",
            "R2 Score =  0.15657302205435308\n",
            "Adjusted R2 = 0.15153262178774562\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       28.9311            2.992     9.668       0.000000\n",
            "1       -0.1224            0.201    -0.608       0.543576\n",
            "2        0.0024            0.004     0.599       0.549377\n",
            "3       -0.0000            0.000    -1.017       0.309690\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     22.9471     34.9151\n",
            "1     -0.5244      0.2796\n",
            "2     -0.0056      0.0104\n",
            "3     -0.0000      0.0000\n",
            "_________________________________________________________\n",
            "RMSE =  8.69214896699611\n",
            "R2 Score =  0.10502427275633675\n",
            "Adjusted R2 = 0.09967581223496025\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0        7.0379            2.911     2.417       0.015987\n",
            "1        8.5928            2.066     4.158       0.000038\n",
            "2       -1.2495            0.412    -3.030       0.002569\n",
            "3        0.0560            0.024     2.307       0.021463\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      1.2159     12.8599\n",
            "1      4.4608     12.7248\n",
            "2     -2.0735     -0.4255\n",
            "3      0.0080      0.1040\n",
            "_________________________________________________________\n",
            "RMSE =  8.33688534044944\n",
            "R2 Score =  0.17668772089694773\n",
            "Adjusted R2 = 0.17176752799394146\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       30.2513            2.568    11.781       0.000000\n",
            "1       -3.7995            1.307    -2.907       0.003815\n",
            "2        0.6163            0.186     3.313       0.000991\n",
            "3       -0.0201            0.006    -3.514       0.000482\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     25.1153     35.3873\n",
            "1     -6.4135     -1.1855\n",
            "2      0.2443      0.9883\n",
            "3     -0.0321     -0.0081\n",
            "_________________________________________________________\n",
            "RMSE =  8.082816433815776\n",
            "R2 Score =  0.2261044184844263\n",
            "Adjusted R2 = 0.22147954449130536\n",
            "   Coefficients  Standard Errors    t values  Probabilities\n",
            "0       52.2160            0.000  503255.415   0.000000e+00\n",
            "1       -0.1635            0.013     -12.697   0.000000e+00\n",
            "2        0.0003            0.000       5.117   4.426582e-07\n",
            "3       -0.0000            0.000      -3.436   6.384747e-04\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     52.2160     52.2160\n",
            "1     -0.1895     -0.1375\n",
            "2      0.0003      0.0003\n",
            "3     -0.0000      0.0000\n",
            "_________________________________________________________\n",
            "RMSE =  7.867156026778706\n",
            "R2 Score =  0.266850635471385\n",
            "Adjusted R2 = 0.2624692647670307\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0      312.2864          152.487     2.048       0.041084\n",
            "1      -48.6911           26.884    -1.811       0.070718\n",
            "2        2.8400            1.564     1.816       0.070017\n",
            "3       -0.0569            0.030    -1.892       0.059009\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0      7.3124    617.2604\n",
            "1   -102.4591      5.0769\n",
            "2     -0.2880      5.9680\n",
            "3     -0.1169      0.0031\n",
            "_________________________________________________________\n",
            "RMSE =  8.650699743213677\n",
            "R2 Score =  0.1135394515839131\n",
            "Adjusted R2 = 0.10824187858541057\n",
            "   Coefficients  Standard Errors   t values  Probabilities\n",
            "0       12.5981            0.001  17236.907       0.000000\n",
            "1       -0.0170            0.038     -0.447       0.654988\n",
            "2        0.0002            0.000      0.843       0.399370\n",
            "3       -0.0000            0.000     -0.584       0.559761\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     12.5961     12.6001\n",
            "1     -0.0930      0.0590\n",
            "2      0.0002      0.0002\n",
            "3     -0.0000      0.0000\n",
            "_________________________________________________________\n",
            "RMSE =  5.374416277067973\n",
            "R2 Score =  0.6578476405895719\n",
            "Adjusted R2 = 0.6558029053739718\n",
            "   Coefficients  Standard Errors  t values  Probabilities\n",
            "0       48.6496            1.435    33.909   0.000000e+00\n",
            "1       -3.8656            0.329   -11.757   0.000000e+00\n",
            "2        0.1487            0.021     6.983   9.177548e-12\n",
            "3       -0.0020            0.000    -5.013   7.428441e-07\n",
            "95 per intervals\n",
            "   LowerBound  UpperBound\n",
            "0     45.7796     51.5196\n",
            "1     -4.5236     -3.2076\n",
            "2      0.1067      0.1907\n",
            "3     -0.0020     -0.0020\n",
            "_________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x1YLFP0fNYfI"
      },
      "source": [
        "#Q15 solutions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "46JpBMWELfMr"
      },
      "source": [
        "a) In single plots CHAS can be neglected since it has a relatively higher p value, other predictors show both  positive and negative relations with the target \n",
        "\n",
        "b)Null hypothesis can be rejected for zn, dis, rad, black and medv\n",
        "also still some predictors have both +ve and -ve relations but the coefficients have change drastically with even changes in sign from previous result \n",
        "\n",
        "c) There is definitely some non linearity in data as seen from residual vs prediciton plot and also the polynomial fits perform better than linear fits"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bAelyb6Qf5ld"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}