Project_Linear_Regression_Gradient_Descent.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J4iM2Um01x2M"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def normalize_features(X):\n",
        "  #Normalize features to have zero and unit variance\n",
        "  mean=np.mean(X,axis=0)\n",
        "  std=np.std(X,axis=0)\n",
        "  X_normalized=(X-mean)/std\n",
        "  return X_normalized,mean,std"
      ],
      "metadata": {
        "id": "8wo8f-do17e5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def compute_cost(X,y,theta):\n",
        "  #Computing the mean squared error\n",
        "  m=len(y)\n",
        "  predictions=np.dot(X,theta)\n",
        "  cost=np.sum((predictions-y)**2)/(2*m)\n",
        "  return cost"
      ],
      "metadata": {
        "id": "5-dZRDUj2ahd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def gradient_descent(X,y,theta,learning_rate,num_iterations,print_cost_interval=100):\n",
        "  #Perform gradient descent to optimize theta\n",
        "  m=len(y)\n",
        "  cost_history=[]\n",
        "  for i in range(num_iterations):\n",
        "    predictions=np.dot(X,theta)\n",
        "    errors=predictions-y\n",
        "    theta-=(learning_rate/m)*np.dot(X.T,errors)\n",
        "    cost=compute_cost(X,y,theta)\n",
        "    cost_history.append(cost)\n",
        "    if i % print_cost_interval==0:\n",
        "      print(f\"Iteration {i},Cost: {cost}\")\n",
        "  return theta,cost_history"
      ],
      "metadata": {
        "id": "UxponPQa22ru"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def r_sqaured(y_true,y_pred):\n",
        "  #Compute R-sqaured score\n",
        "  ss_total=np.sum((y_true-np.mean(y_true))**2)\n",
        "  ss_residual=np.sum((y_true-y_pred)**2)\n",
        "  r2=1-(ss_residual/ss_total)\n",
        "  return r2"
      ],
      "metadata": {
        "id": "E0oQD8FM4CNH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df=pd.read_csv('/content/sample_data/Lineardata_train.csv')\n",
        "df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "5X9X2xMT8Ny6",
        "outputId": "9343a3aa-4d5d-4cab-9026-ffaf8af4d80d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "             target  feature 1  feature 2  feature 3  feature 4  feature 5  \\\n",
              "0      -5928.102746  -0.900470   0.850978  -2.069526   0.573887  -6.878165   \n",
              "1       -738.890855  -0.266567   2.865496  -6.396780   1.517906  -0.339633   \n",
              "2     -20186.841587  -0.058919   0.635366  -3.563216   1.848845  -4.255648   \n",
              "3      30145.771674  -0.892483  -0.287881  -1.643086   0.630195  -2.989874   \n",
              "4      -3469.553888  -1.568419   1.535581  -4.562323  -1.953245  -3.505171   \n",
              "...             ...        ...        ...        ...        ...        ...   \n",
              "49995  -7567.227845   2.029910  -0.928164  -2.463563   5.312071   2.070290   \n",
              "49996  -9973.851789  -0.223475   0.341542  -4.423256  -0.104668   4.384320   \n",
              "49997  -8246.697221  -0.321085   1.608386 -11.177100  -1.140550 -10.832891   \n",
              "49998  -9101.101377  -2.383432   1.214911   0.925113   0.017874   2.022561   \n",
              "49999   3420.729860   1.396534   1.044984   6.974686  -2.503387  -6.951460   \n",
              "\n",
              "       feature 6  feature 7  feature 8  feature 9  ...  feature 11  \\\n",
              "0       1.533172  -6.163896 -18.134398  17.040815  ...  -12.524825   \n",
              "1      -2.173984  -7.100097  30.940664  -1.158169  ...    5.686297   \n",
              "2      -6.495151  14.768858  20.968617  10.851276  ...   16.819230   \n",
              "3      -6.706778   1.035763  42.115932   4.530884  ...  -13.998268   \n",
              "4       2.970568  11.589140  32.642438  -6.865592  ...   10.057674   \n",
              "...          ...        ...        ...        ...  ...         ...   \n",
              "49995   0.835355  -4.421930  18.292309 -10.357047  ...   -2.827488   \n",
              "49996  -2.290826   4.612476  29.667901  -9.675776  ...  -17.744738   \n",
              "49997  -8.625981 -27.740091 -14.166217   9.169728  ...    3.841781   \n",
              "49998   1.209647   5.006908 -12.043059  -5.756141  ...    5.308136   \n",
              "49999  -7.683350 -15.804647  -5.326198  11.574373  ...    5.594694   \n",
              "\n",
              "       feature 12  feature 13  feature 14  feature 15  feature 16  feature 17  \\\n",
              "0        3.376208  -19.266370  -24.347122  -21.504898  -83.231616   23.086856   \n",
              "1       -6.862812    7.168795  -17.873042  -51.859538    9.262772   19.648597   \n",
              "2       -8.112394    7.120777    4.301635  -36.838036 -408.786938   14.054136   \n",
              "3       -1.071906   40.051813    4.392608  -31.311818  534.588309  -20.380642   \n",
              "4       -3.719569  -52.342557  -13.150729    0.922421   -6.818339   -9.958228   \n",
              "...           ...         ...         ...         ...         ...         ...   \n",
              "49995   17.940836   25.724137  -29.713820    0.625372 -183.410260   19.439815   \n",
              "49996   -0.708422   15.907878   10.865072  -31.280568 -354.186800    6.363459   \n",
              "49997  -17.941987   -2.167623   11.336067   -2.542123  -98.327808  -13.690353   \n",
              "49998   12.387029   20.220357   -1.359887   83.958829 -314.127483   -2.550699   \n",
              "49999   -2.408064    6.790581  -12.917546   -5.899725  -24.414767  -37.180535   \n",
              "\n",
              "       feature 18  feature 19  feature 20  \n",
              "0       -9.684523   18.211899  -16.848424  \n",
              "1        6.529141   -4.577279   28.080530  \n",
              "2       -6.451438  -17.080408  -13.500953  \n",
              "3       -1.092364   28.453693   14.643806  \n",
              "4       12.798234    0.804627    1.271561  \n",
              "...           ...         ...         ...  \n",
              "49995    6.640099  -41.093484   -1.010290  \n",
              "49996    0.370644   35.952861    3.752642  \n",
              "49997   -4.299753   16.053032   14.812715  \n",
              "49998   -5.082801    7.514089   30.150485  \n",
              "49999   -2.134946   90.429367  -36.412232  \n",
              "\n",
              "[50000 rows x 21 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-3efa6afa-9f8b-4b3a-9b80-980876a12085\" class=\"colab-df-container\">\n",
              "    <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>target</th>\n",
              "      <th>feature 1</th>\n",
              "      <th>feature 2</th>\n",
              "      <th>feature 3</th>\n",
              "      <th>feature 4</th>\n",
              "      <th>feature 5</th>\n",
              "      <th>feature 6</th>\n",
              "      <th>feature 7</th>\n",
              "      <th>feature 8</th>\n",
              "      <th>feature 9</th>\n",
              "      <th>...</th>\n",
              "      <th>feature 11</th>\n",
              "      <th>feature 12</th>\n",
              "      <th>feature 13</th>\n",
              "      <th>feature 14</th>\n",
              "      <th>feature 15</th>\n",
              "      <th>feature 16</th>\n",
              "      <th>feature 17</th>\n",
              "      <th>feature 18</th>\n",
              "      <th>feature 19</th>\n",
              "      <th>feature 20</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-5928.102746</td>\n",
              "      <td>-0.900470</td>\n",
              "      <td>0.850978</td>\n",
              "      <td>-2.069526</td>\n",
              "      <td>0.573887</td>\n",
              "      <td>-6.878165</td>\n",
              "      <td>1.533172</td>\n",
              "      <td>-6.163896</td>\n",
              "      <td>-18.134398</td>\n",
              "      <td>17.040815</td>\n",
              "      <td>...</td>\n",
              "      <td>-12.524825</td>\n",
              "      <td>3.376208</td>\n",
              "      <td>-19.266370</td>\n",
              "      <td>-24.347122</td>\n",
              "      <td>-21.504898</td>\n",
              "      <td>-83.231616</td>\n",
              "      <td>23.086856</td>\n",
              "      <td>-9.684523</td>\n",
              "      <td>18.211899</td>\n",
              "      <td>-16.848424</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-738.890855</td>\n",
              "      <td>-0.266567</td>\n",
              "      <td>2.865496</td>\n",
              "      <td>-6.396780</td>\n",
              "      <td>1.517906</td>\n",
              "      <td>-0.339633</td>\n",
              "      <td>-2.173984</td>\n",
              "      <td>-7.100097</td>\n",
              "      <td>30.940664</td>\n",
              "      <td>-1.158169</td>\n",
              "      <td>...</td>\n",
              "      <td>5.686297</td>\n",
              "      <td>-6.862812</td>\n",
              "      <td>7.168795</td>\n",
              "      <td>-17.873042</td>\n",
              "      <td>-51.859538</td>\n",
              "      <td>9.262772</td>\n",
              "      <td>19.648597</td>\n",
              "      <td>6.529141</td>\n",
              "      <td>-4.577279</td>\n",
              "      <td>28.080530</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-20186.841587</td>\n",
              "      <td>-0.058919</td>\n",
              "      <td>0.635366</td>\n",
              "      <td>-3.563216</td>\n",
              "      <td>1.848845</td>\n",
              "      <td>-4.255648</td>\n",
              "      <td>-6.495151</td>\n",
              "      <td>14.768858</td>\n",
              "      <td>20.968617</td>\n",
              "      <td>10.851276</td>\n",
              "      <td>...</td>\n",
              "      <td>16.819230</td>\n",
              "      <td>-8.112394</td>\n",
              "      <td>7.120777</td>\n",
              "      <td>4.301635</td>\n",
              "      <td>-36.838036</td>\n",
              "      <td>-408.786938</td>\n",
              "      <td>14.054136</td>\n",
              "      <td>-6.451438</td>\n",
              "      <td>-17.080408</td>\n",
              "      <td>-13.500953</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>30145.771674</td>\n",
              "      <td>-0.892483</td>\n",
              "      <td>-0.287881</td>\n",
              "      <td>-1.643086</td>\n",
              "      <td>0.630195</td>\n",
              "      <td>-2.989874</td>\n",
              "      <td>-6.706778</td>\n",
              "      <td>1.035763</td>\n",
              "      <td>42.115932</td>\n",
              "      <td>4.530884</td>\n",
              "      <td>...</td>\n",
              "      <td>-13.998268</td>\n",
              "      <td>-1.071906</td>\n",
              "      <td>40.051813</td>\n",
              "      <td>4.392608</td>\n",
              "      <td>-31.311818</td>\n",
              "      <td>534.588309</td>\n",
              "      <td>-20.380642</td>\n",
              "      <td>-1.092364</td>\n",
              "      <td>28.453693</td>\n",
              "      <td>14.643806</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-3469.553888</td>\n",
              "      <td>-1.568419</td>\n",
              "      <td>1.535581</td>\n",
              "      <td>-4.562323</td>\n",
              "      <td>-1.953245</td>\n",
              "      <td>-3.505171</td>\n",
              "      <td>2.970568</td>\n",
              "      <td>11.589140</td>\n",
              "      <td>32.642438</td>\n",
              "      <td>-6.865592</td>\n",
              "      <td>...</td>\n",
              "      <td>10.057674</td>\n",
              "      <td>-3.719569</td>\n",
              "      <td>-52.342557</td>\n",
              "      <td>-13.150729</td>\n",
              "      <td>0.922421</td>\n",
              "      <td>-6.818339</td>\n",
              "      <td>-9.958228</td>\n",
              "      <td>12.798234</td>\n",
              "      <td>0.804627</td>\n",
              "      <td>1.271561</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49995</th>\n",
              "      <td>-7567.227845</td>\n",
              "      <td>2.029910</td>\n",
              "      <td>-0.928164</td>\n",
              "      <td>-2.463563</td>\n",
              "      <td>5.312071</td>\n",
              "      <td>2.070290</td>\n",
              "      <td>0.835355</td>\n",
              "      <td>-4.421930</td>\n",
              "      <td>18.292309</td>\n",
              "      <td>-10.357047</td>\n",
              "      <td>...</td>\n",
              "      <td>-2.827488</td>\n",
              "      <td>17.940836</td>\n",
              "      <td>25.724137</td>\n",
              "      <td>-29.713820</td>\n",
              "      <td>0.625372</td>\n",
              "      <td>-183.410260</td>\n",
              "      <td>19.439815</td>\n",
              "      <td>6.640099</td>\n",
              "      <td>-41.093484</td>\n",
              "      <td>-1.010290</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49996</th>\n",
              "      <td>-9973.851789</td>\n",
              "      <td>-0.223475</td>\n",
              "      <td>0.341542</td>\n",
              "      <td>-4.423256</td>\n",
              "      <td>-0.104668</td>\n",
              "      <td>4.384320</td>\n",
              "      <td>-2.290826</td>\n",
              "      <td>4.612476</td>\n",
              "      <td>29.667901</td>\n",
              "      <td>-9.675776</td>\n",
              "      <td>...</td>\n",
              "      <td>-17.744738</td>\n",
              "      <td>-0.708422</td>\n",
              "      <td>15.907878</td>\n",
              "      <td>10.865072</td>\n",
              "      <td>-31.280568</td>\n",
              "      <td>-354.186800</td>\n",
              "      <td>6.363459</td>\n",
              "      <td>0.370644</td>\n",
              "      <td>35.952861</td>\n",
              "      <td>3.752642</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49997</th>\n",
              "      <td>-8246.697221</td>\n",
              "      <td>-0.321085</td>\n",
              "      <td>1.608386</td>\n",
              "      <td>-11.177100</td>\n",
              "      <td>-1.140550</td>\n",
              "      <td>-10.832891</td>\n",
              "      <td>-8.625981</td>\n",
              "      <td>-27.740091</td>\n",
              "      <td>-14.166217</td>\n",
              "      <td>9.169728</td>\n",
              "      <td>...</td>\n",
              "      <td>3.841781</td>\n",
              "      <td>-17.941987</td>\n",
              "      <td>-2.167623</td>\n",
              "      <td>11.336067</td>\n",
              "      <td>-2.542123</td>\n",
              "      <td>-98.327808</td>\n",
              "      <td>-13.690353</td>\n",
              "      <td>-4.299753</td>\n",
              "      <td>16.053032</td>\n",
              "      <td>14.812715</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49998</th>\n",
              "      <td>-9101.101377</td>\n",
              "      <td>-2.383432</td>\n",
              "      <td>1.214911</td>\n",
              "      <td>0.925113</td>\n",
              "      <td>0.017874</td>\n",
              "      <td>2.022561</td>\n",
              "      <td>1.209647</td>\n",
              "      <td>5.006908</td>\n",
              "      <td>-12.043059</td>\n",
              "      <td>-5.756141</td>\n",
              "      <td>...</td>\n",
              "      <td>5.308136</td>\n",
              "      <td>12.387029</td>\n",
              "      <td>20.220357</td>\n",
              "      <td>-1.359887</td>\n",
              "      <td>83.958829</td>\n",
              "      <td>-314.127483</td>\n",
              "      <td>-2.550699</td>\n",
              "      <td>-5.082801</td>\n",
              "      <td>7.514089</td>\n",
              "      <td>30.150485</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49999</th>\n",
              "      <td>3420.729860</td>\n",
              "      <td>1.396534</td>\n",
              "      <td>1.044984</td>\n",
              "      <td>6.974686</td>\n",
              "      <td>-2.503387</td>\n",
              "      <td>-6.951460</td>\n",
              "      <td>-7.683350</td>\n",
              "      <td>-15.804647</td>\n",
              "      <td>-5.326198</td>\n",
              "      <td>11.574373</td>\n",
              "      <td>...</td>\n",
              "      <td>5.594694</td>\n",
              "      <td>-2.408064</td>\n",
              "      <td>6.790581</td>\n",
              "      <td>-12.917546</td>\n",
              "      <td>-5.899725</td>\n",
              "      <td>-24.414767</td>\n",
              "      <td>-37.180535</td>\n",
              "      <td>-2.134946</td>\n",
              "      <td>90.429367</td>\n",
              "      <td>-36.412232</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>50000 rows × 21 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3efa6afa-9f8b-4b3a-9b80-980876a12085')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-3efa6afa-9f8b-4b3a-9b80-980876a12085 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-3efa6afa-9f8b-4b3a-9b80-980876a12085');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-36f442d9-074a-4e89-b7fa-8625148e7d41\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-36f442d9-074a-4e89-b7fa-8625148e7d41')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-36f442d9-074a-4e89-b7fa-8625148e7d41 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_51bc8ace-4a0b-4bcb-8ac0-265305745e8b\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('df')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_51bc8ace-4a0b-4bcb-8ac0-265305745e8b button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('df');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df_np=df.to_numpy()\n",
        "df_np.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BCFI_6KtAftx",
        "outputId": "41226391-f2fc-47a6-b470-8625606477e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 21)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X,y=df_np[:,1:],df_np[:,0:1]\n",
        "X.shape,y.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L7-wU6Og5Dgb",
        "outputId": "a97c6322-0d3c-4a05-c0de-04980adcf29f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((50000, 20), (50000, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qPzPT6il5Gba",
        "outputId": "ae4d474e-2be3-4324-a5dd-f353e1e9b722"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ -5928.10274562],\n",
              "       [  -738.89085527],\n",
              "       [-20186.84158668],\n",
              "       ...,\n",
              "       [ -8246.69722146],\n",
              "       [ -9101.10137698],\n",
              "       [  3420.72986003]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def train_test_split(X,y,test_ratio=0.2,random_seed=None):\n",
        "  if random_seed is not None:\n",
        "    np.random.seed(random_seed)\n",
        "  #Shuffle indices\n",
        "  indices=np.arange(X.shape[0])\n",
        "  np.random.shuffle(indices)\n",
        "  #Calculate the number of samples for testing\n",
        "  test_size=int(X.shape[0]*test_ratio)\n",
        "  #Split the data\n",
        "  test_indices=indices[:test_size]\n",
        "  train_indices=indices[test_size:]\n",
        "  X_train,X_test=X[train_indices],X[test_indices]\n",
        "  y_train,y_test=y[train_indices],y[test_indices]\n",
        "  return X_train,X_test,y_train,y_test"
      ],
      "metadata": {
        "id": "YJTaSOpO92MO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Split the data into training and testing sets\n",
        "X_train,X_test,y_train,y_test=train_test_split(X,y,test_ratio=0.2,random_seed=42)"
      ],
      "metadata": {
        "id": "4Pe9f4Ac_PM9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_train.shape,X_test.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZMSdACbRA3KE",
        "outputId": "de59774c-4e5c-4f15-849c-65d2b04b5bc6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((40000, 20), (10000, 20))"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_train.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6hJhkRv0A56m",
        "outputId": "83ef747d-858f-4df6-d04c-7962e2a4769a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(40000, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Normalize features\n",
        "X_normalized,mean,std=normalize_features(X_train)"
      ],
      "metadata": {
        "id": "edyj1chB5IGH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_normalized"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2mgm93_D5P8X",
        "outputId": "852d3a5e-0657-4aa3-8768-656eeaebc3a2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.45775205, -0.48757813,  1.08269692, ..., -1.16065271,\n",
              "        -0.90891443,  0.98677163],\n",
              "       [-0.33240745,  0.43686615, -0.67175291, ...,  2.01739815,\n",
              "        -0.15981407, -0.10383174],\n",
              "       [-0.74925428,  0.48095683, -0.54168024, ..., -0.37290956,\n",
              "         1.21023425,  0.7553406 ],\n",
              "       ...,\n",
              "       [ 1.74080701, -0.52089606,  0.09435555, ..., -0.82256806,\n",
              "        -0.43292423,  0.26915817],\n",
              "       [-1.38438685, -1.30408921, -0.08026594, ..., -0.30972753,\n",
              "         1.4668701 ,  1.7918175 ],\n",
              "       [ 1.28782662, -0.60347955, -0.8443776 , ..., -0.12723843,\n",
              "         0.79892582, -0.95683495]])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Add bias therm to the features\n",
        "X_normalized_b=np.c_[np.ones((X_normalized.shape[0],1)),X_normalized]"
      ],
      "metadata": {
        "id": "9lEIbbNT5TfQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Initialize the weights\n",
        "theta=np.random.randn(X_normalized_b.shape[1],1)"
      ],
      "metadata": {
        "id": "YTy1xreQ5imi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Set hyperparameters\n",
        "learning_rate=0.01\n",
        "num_iterations=1000"
      ],
      "metadata": {
        "id": "2hXujabi5wUR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Perform gradient descent\n",
        "theta,cost_history=gradient_descent(X_normalized_b,y_train,theta,learning_rate,num_iterations)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L9wHhdJg5_0h",
        "outputId": "fd15a4ce-40d1-4fdd-b99e-72f2966806b9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0,Cost: 63931001.22195706\n",
            "Iteration 100,Cost: 8604849.547788186\n",
            "Iteration 200,Cost: 1159609.4399933873\n",
            "Iteration 300,Cost: 156465.08524298744\n",
            "Iteration 400,Cost: 21137.84113280586\n",
            "Iteration 500,Cost: 2859.180766622486\n",
            "Iteration 600,Cost: 387.22507727882595\n",
            "Iteration 700,Cost: 52.51123148756628\n",
            "Iteration 800,Cost: 7.13353581900828\n",
            "Iteration 900,Cost: 0.9740332888061018\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Make predictions\n",
        "X_test_normalized=(X_test-mean)/std\n",
        "X_test_normalized_b=np.c_[np.ones((X_test_normalized.shape[0],1)),X_test_normalized]\n",
        "predictions=np.dot(X_test_normalized_b,theta)"
      ],
      "metadata": {
        "id": "53VARAPu6TVg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Compute R-squared score\n",
        "r2=r_sqaured(y_test,predictions)"
      ],
      "metadata": {
        "id": "mclt66CC63tZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Plot cost history\n",
        "plt.plot(cost_history)\n",
        "plt.xlabel('Iterations')\n",
        "plt.ylabel('Cost')\n",
        "plt.title('Gradient Descent Cost History')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "Ji_xgKVj7Aw2",
        "outputId": "b1f89d3f-dfd9-4dc6-a0f1-80a6b8792123"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Theta (weights):\",theta)\n",
        "print(\"Predictions for X_test:\",predictions)\n",
        "print(\"R-sqaured score:\",r2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2AWJ-K2d7T_w",
        "outputId": "2b1ab16d-73dc-4470-81ea-ebb5db6bd1c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Theta (weights): [[4.77181723e+01]\n",
            " [2.20174978e+01]\n",
            " [3.30799054e+01]\n",
            " [9.93022143e+00]\n",
            " [6.03820733e+00]\n",
            " [1.75687581e+02]\n",
            " [3.28524896e+02]\n",
            " [2.53313500e+02]\n",
            " [9.01033415e+02]\n",
            " [4.35629433e+02]\n",
            " [8.37967293e+01]\n",
            " [1.20994216e+02]\n",
            " [1.60878733e+03]\n",
            " [1.67729932e+03]\n",
            " [1.31393215e+03]\n",
            " [5.98664680e+02]\n",
            " [1.05469382e+04]\n",
            " [5.04253293e+02]\n",
            " [6.78789845e+02]\n",
            " [3.16337452e+03]\n",
            " [2.30368095e+02]]\n",
            "Predictions for X_test: [[  5052.47080807]\n",
            " [ -3879.37770314]\n",
            " [  1797.34650158]\n",
            " ...\n",
            " [-27101.96550725]\n",
            " [-11309.99561889]\n",
            " [   623.30654986]]\n",
            "R-sqaured score: 0.9999999978525291\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "On the test dataset"
      ],
      "metadata": {
        "id": "J1jhqcpgf094"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pf=pd.read_csv('/content/sample_data/Lineardata_test.csv')\n",
        "pf"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "i4UfyrWJZwzZ",
        "outputId": "6fd81f07-e14f-4aa6-8d6f-137d7a50f242"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         ID  feature 1  feature 2  feature 3  feature 4  feature 5  feature 6  \\\n",
              "0     14189   0.634260  -0.771727   4.297694  -2.022710   0.487001   2.316767   \n",
              "1     14742   0.456128   3.154433   0.182006  -0.730634  -5.759530   1.448589   \n",
              "2     13905   0.390815  -5.278284   1.625943  -1.775914  -2.461865   1.439888   \n",
              "3     10072   1.067949   4.851061   3.909243   2.005500   2.880720   1.054944   \n",
              "4     14879  -0.589611  -3.533016  -1.705736   2.063013  -0.738696   2.475443   \n",
              "...     ...        ...        ...        ...        ...        ...        ...   \n",
              "9995  19851   1.967136  -6.819440   3.597360  -0.482508   4.679231   0.861442   \n",
              "9996  11818  -0.656285  -3.294604  12.222256  -0.184108   8.286414  -6.437312   \n",
              "9997  15552  -0.349932   4.611955  -2.814735   1.851754  -2.354195   6.639817   \n",
              "9998  12161   0.295833   1.825552  -8.824731   2.119270  -4.629213  -2.354794   \n",
              "9999  14055  -0.555837  -0.111039  -0.477407  -4.750409   1.870868   0.971285   \n",
              "\n",
              "      feature 7  feature 8  feature 9  ...  feature 11  feature 12  \\\n",
              "0     11.626397 -10.657142   9.254734  ...   -8.728623    7.035966   \n",
              "1    -10.292540  20.441249   9.943525  ...   -4.899841   20.762134   \n",
              "2      6.213269 -17.212310 -17.308743  ...    8.239316    6.588928   \n",
              "3     -1.652801  -4.267849   3.860784  ...   -4.580152    5.748974   \n",
              "4     -4.982819 -19.693204   0.660739  ...    2.222820  -11.731821   \n",
              "...         ...        ...        ...  ...         ...         ...   \n",
              "9995   8.810749 -20.384415  20.427585  ...    1.489196   12.767614   \n",
              "9996 -19.611691 -13.487207  23.986240  ...    9.897794  -15.720693   \n",
              "9997 -25.299515  -3.145723 -41.248652  ...   19.601819   -3.216492   \n",
              "9998   0.919091  52.204003   7.350877  ...   10.640964   11.686231   \n",
              "9999 -15.576291 -26.872691   9.271291  ...    1.993274  -28.686598   \n",
              "\n",
              "      feature 13  feature 14  feature 15  feature 16  feature 17  feature 18  \\\n",
              "0       5.828558    8.596358  -16.510202 -132.396813   12.213839   21.383123   \n",
              "1      -4.117988  -12.677107  -40.923007  367.557009   21.607952   -1.207279   \n",
              "2      27.017658   -1.806317  -18.574372  -39.807081  -18.389553    7.466803   \n",
              "3       6.949329   -2.369054   -6.953435   23.932892   -1.575264  -34.352606   \n",
              "4      -8.069874   -5.881325  -26.060090  244.017215  -23.257490    9.819982   \n",
              "...          ...         ...         ...         ...         ...         ...   \n",
              "9995   52.530303   20.517596  -42.428871   35.227784   -9.244004  -18.759314   \n",
              "9996   26.401396   11.421553 -104.558180 -318.607244   -7.446830   -6.457686   \n",
              "9997  -17.299449   -8.975811   59.531358  244.333157   28.656620   11.294024   \n",
              "9998    7.259193    7.733906   54.680591 -472.335102  -24.281308  -16.099344   \n",
              "9999   36.927375   19.368287  -49.919033   68.711582   12.463516   -9.315026   \n",
              "\n",
              "      feature 19  feature 20  \n",
              "0     -37.841857   18.892385  \n",
              "1     -28.154185   -3.603744  \n",
              "2      49.904659   46.990062  \n",
              "3      16.941476    5.104177  \n",
              "4     -34.672912    9.324556  \n",
              "...          ...         ...  \n",
              "9995  -42.260514   -2.261597  \n",
              "9996   12.002813  -20.317446  \n",
              "9997    1.441938    4.395482  \n",
              "9998   10.744757    6.578695  \n",
              "9999  -10.490830   13.288540  \n",
              "\n",
              "[10000 rows x 21 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-63e2eb37-2686-4b31-aba3-581664daacaf\" class=\"colab-df-container\">\n",
              "    <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>ID</th>\n",
              "      <th>feature 1</th>\n",
              "      <th>feature 2</th>\n",
              "      <th>feature 3</th>\n",
              "      <th>feature 4</th>\n",
              "      <th>feature 5</th>\n",
              "      <th>feature 6</th>\n",
              "      <th>feature 7</th>\n",
              "      <th>feature 8</th>\n",
              "      <th>feature 9</th>\n",
              "      <th>...</th>\n",
              "      <th>feature 11</th>\n",
              "      <th>feature 12</th>\n",
              "      <th>feature 13</th>\n",
              "      <th>feature 14</th>\n",
              "      <th>feature 15</th>\n",
              "      <th>feature 16</th>\n",
              "      <th>feature 17</th>\n",
              "      <th>feature 18</th>\n",
              "      <th>feature 19</th>\n",
              "      <th>feature 20</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>14189</td>\n",
              "      <td>0.634260</td>\n",
              "      <td>-0.771727</td>\n",
              "      <td>4.297694</td>\n",
              "      <td>-2.022710</td>\n",
              "      <td>0.487001</td>\n",
              "      <td>2.316767</td>\n",
              "      <td>11.626397</td>\n",
              "      <td>-10.657142</td>\n",
              "      <td>9.254734</td>\n",
              "      <td>...</td>\n",
              "      <td>-8.728623</td>\n",
              "      <td>7.035966</td>\n",
              "      <td>5.828558</td>\n",
              "      <td>8.596358</td>\n",
              "      <td>-16.510202</td>\n",
              "      <td>-132.396813</td>\n",
              "      <td>12.213839</td>\n",
              "      <td>21.383123</td>\n",
              "      <td>-37.841857</td>\n",
              "      <td>18.892385</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>14742</td>\n",
              "      <td>0.456128</td>\n",
              "      <td>3.154433</td>\n",
              "      <td>0.182006</td>\n",
              "      <td>-0.730634</td>\n",
              "      <td>-5.759530</td>\n",
              "      <td>1.448589</td>\n",
              "      <td>-10.292540</td>\n",
              "      <td>20.441249</td>\n",
              "      <td>9.943525</td>\n",
              "      <td>...</td>\n",
              "      <td>-4.899841</td>\n",
              "      <td>20.762134</td>\n",
              "      <td>-4.117988</td>\n",
              "      <td>-12.677107</td>\n",
              "      <td>-40.923007</td>\n",
              "      <td>367.557009</td>\n",
              "      <td>21.607952</td>\n",
              "      <td>-1.207279</td>\n",
              "      <td>-28.154185</td>\n",
              "      <td>-3.603744</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>13905</td>\n",
              "      <td>0.390815</td>\n",
              "      <td>-5.278284</td>\n",
              "      <td>1.625943</td>\n",
              "      <td>-1.775914</td>\n",
              "      <td>-2.461865</td>\n",
              "      <td>1.439888</td>\n",
              "      <td>6.213269</td>\n",
              "      <td>-17.212310</td>\n",
              "      <td>-17.308743</td>\n",
              "      <td>...</td>\n",
              "      <td>8.239316</td>\n",
              "      <td>6.588928</td>\n",
              "      <td>27.017658</td>\n",
              "      <td>-1.806317</td>\n",
              "      <td>-18.574372</td>\n",
              "      <td>-39.807081</td>\n",
              "      <td>-18.389553</td>\n",
              "      <td>7.466803</td>\n",
              "      <td>49.904659</td>\n",
              "      <td>46.990062</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>10072</td>\n",
              "      <td>1.067949</td>\n",
              "      <td>4.851061</td>\n",
              "      <td>3.909243</td>\n",
              "      <td>2.005500</td>\n",
              "      <td>2.880720</td>\n",
              "      <td>1.054944</td>\n",
              "      <td>-1.652801</td>\n",
              "      <td>-4.267849</td>\n",
              "      <td>3.860784</td>\n",
              "      <td>...</td>\n",
              "      <td>-4.580152</td>\n",
              "      <td>5.748974</td>\n",
              "      <td>6.949329</td>\n",
              "      <td>-2.369054</td>\n",
              "      <td>-6.953435</td>\n",
              "      <td>23.932892</td>\n",
              "      <td>-1.575264</td>\n",
              "      <td>-34.352606</td>\n",
              "      <td>16.941476</td>\n",
              "      <td>5.104177</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>14879</td>\n",
              "      <td>-0.589611</td>\n",
              "      <td>-3.533016</td>\n",
              "      <td>-1.705736</td>\n",
              "      <td>2.063013</td>\n",
              "      <td>-0.738696</td>\n",
              "      <td>2.475443</td>\n",
              "      <td>-4.982819</td>\n",
              "      <td>-19.693204</td>\n",
              "      <td>0.660739</td>\n",
              "      <td>...</td>\n",
              "      <td>2.222820</td>\n",
              "      <td>-11.731821</td>\n",
              "      <td>-8.069874</td>\n",
              "      <td>-5.881325</td>\n",
              "      <td>-26.060090</td>\n",
              "      <td>244.017215</td>\n",
              "      <td>-23.257490</td>\n",
              "      <td>9.819982</td>\n",
              "      <td>-34.672912</td>\n",
              "      <td>9.324556</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9995</th>\n",
              "      <td>19851</td>\n",
              "      <td>1.967136</td>\n",
              "      <td>-6.819440</td>\n",
              "      <td>3.597360</td>\n",
              "      <td>-0.482508</td>\n",
              "      <td>4.679231</td>\n",
              "      <td>0.861442</td>\n",
              "      <td>8.810749</td>\n",
              "      <td>-20.384415</td>\n",
              "      <td>20.427585</td>\n",
              "      <td>...</td>\n",
              "      <td>1.489196</td>\n",
              "      <td>12.767614</td>\n",
              "      <td>52.530303</td>\n",
              "      <td>20.517596</td>\n",
              "      <td>-42.428871</td>\n",
              "      <td>35.227784</td>\n",
              "      <td>-9.244004</td>\n",
              "      <td>-18.759314</td>\n",
              "      <td>-42.260514</td>\n",
              "      <td>-2.261597</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>11818</td>\n",
              "      <td>-0.656285</td>\n",
              "      <td>-3.294604</td>\n",
              "      <td>12.222256</td>\n",
              "      <td>-0.184108</td>\n",
              "      <td>8.286414</td>\n",
              "      <td>-6.437312</td>\n",
              "      <td>-19.611691</td>\n",
              "      <td>-13.487207</td>\n",
              "      <td>23.986240</td>\n",
              "      <td>...</td>\n",
              "      <td>9.897794</td>\n",
              "      <td>-15.720693</td>\n",
              "      <td>26.401396</td>\n",
              "      <td>11.421553</td>\n",
              "      <td>-104.558180</td>\n",
              "      <td>-318.607244</td>\n",
              "      <td>-7.446830</td>\n",
              "      <td>-6.457686</td>\n",
              "      <td>12.002813</td>\n",
              "      <td>-20.317446</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>15552</td>\n",
              "      <td>-0.349932</td>\n",
              "      <td>4.611955</td>\n",
              "      <td>-2.814735</td>\n",
              "      <td>1.851754</td>\n",
              "      <td>-2.354195</td>\n",
              "      <td>6.639817</td>\n",
              "      <td>-25.299515</td>\n",
              "      <td>-3.145723</td>\n",
              "      <td>-41.248652</td>\n",
              "      <td>...</td>\n",
              "      <td>19.601819</td>\n",
              "      <td>-3.216492</td>\n",
              "      <td>-17.299449</td>\n",
              "      <td>-8.975811</td>\n",
              "      <td>59.531358</td>\n",
              "      <td>244.333157</td>\n",
              "      <td>28.656620</td>\n",
              "      <td>11.294024</td>\n",
              "      <td>1.441938</td>\n",
              "      <td>4.395482</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>12161</td>\n",
              "      <td>0.295833</td>\n",
              "      <td>1.825552</td>\n",
              "      <td>-8.824731</td>\n",
              "      <td>2.119270</td>\n",
              "      <td>-4.629213</td>\n",
              "      <td>-2.354794</td>\n",
              "      <td>0.919091</td>\n",
              "      <td>52.204003</td>\n",
              "      <td>7.350877</td>\n",
              "      <td>...</td>\n",
              "      <td>10.640964</td>\n",
              "      <td>11.686231</td>\n",
              "      <td>7.259193</td>\n",
              "      <td>7.733906</td>\n",
              "      <td>54.680591</td>\n",
              "      <td>-472.335102</td>\n",
              "      <td>-24.281308</td>\n",
              "      <td>-16.099344</td>\n",
              "      <td>10.744757</td>\n",
              "      <td>6.578695</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>14055</td>\n",
              "      <td>-0.555837</td>\n",
              "      <td>-0.111039</td>\n",
              "      <td>-0.477407</td>\n",
              "      <td>-4.750409</td>\n",
              "      <td>1.870868</td>\n",
              "      <td>0.971285</td>\n",
              "      <td>-15.576291</td>\n",
              "      <td>-26.872691</td>\n",
              "      <td>9.271291</td>\n",
              "      <td>...</td>\n",
              "      <td>1.993274</td>\n",
              "      <td>-28.686598</td>\n",
              "      <td>36.927375</td>\n",
              "      <td>19.368287</td>\n",
              "      <td>-49.919033</td>\n",
              "      <td>68.711582</td>\n",
              "      <td>12.463516</td>\n",
              "      <td>-9.315026</td>\n",
              "      <td>-10.490830</td>\n",
              "      <td>13.288540</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 21 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-63e2eb37-2686-4b31-aba3-581664daacaf')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-63e2eb37-2686-4b31-aba3-581664daacaf button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-63e2eb37-2686-4b31-aba3-581664daacaf');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-6c334c0b-ebc6-462c-bb3d-40e081d8d0f3\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-6c334c0b-ebc6-462c-bb3d-40e081d8d0f3')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-6c334c0b-ebc6-462c-bb3d-40e081d8d0f3 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_c3bcbf1a-fe0b-4d04-8843-c2d4dfe29ea5\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('pf')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M7,19H8.4L18.45,9,17,7.55,7,17.6ZM5,21V16.75L18.45,3.32a2,2,0,0,1,2.83,0l1.4,1.43a1.91,1.91,0,0,1,.58,1.4,1.91,1.91,0,0,1-.58,1.4L9.25,21ZM18.45,9,17,7.55Zm-12,3A5.31,5.31,0,0,0,4.9,8.1,5.31,5.31,0,0,0,1,6.5,5.31,5.31,0,0,0,4.9,4.9,5.31,5.31,0,0,0,6.5,1,5.31,5.31,0,0,0,8.1,4.9,5.31,5.31,0,0,0,12,6.5,5.46,5.46,0,0,0,6.5,12Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_c3bcbf1a-fe0b-4d04-8843-c2d4dfe29ea5 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('pf');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pf_np=pf.to_numpy()\n",
        "pf_np.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Yoa_a6zgaLMB",
        "outputId": "3b342c36-227f-40e4-e5c1-b9328a66c011"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 21)"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "P_test,q_test=df_np[:,1:],df_np[:,0:1]\n",
        "P_test.shape,q_test.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D-g3-BxmaRF-",
        "outputId": "8009d977-3824-48c9-9d48-a6f6bb9b26c3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((10000, 20), (10000, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Normalize features\n",
        "P_test_normalized,mean,std=normalize_features(P_test)"
      ],
      "metadata": {
        "id": "wbD0SkKlaynW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Add bias therm to the features\n",
        "P_test_normalized_b=np.c_[np.ones((P_test_normalized.shape[0],1)),P_test_normalized]"
      ],
      "metadata": {
        "id": "QvmAbo8pa30A"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Make predictions\n",
        "predictions_test=np.dot(P_test_normalized_b,theta)"
      ],
      "metadata": {
        "id": "Kx-banYSabRN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Compute R-squared score\n",
        "r2=r_sqaured(q_test,predictions_test)"
      ],
      "metadata": {
        "id": "W4QGuV81bNZu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Predictions for X_test:\",predictions)\n",
        "print(\"R-sqaured score:\",r2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pCzqBxqabT0W",
        "outputId": "cc8468ff-f5c6-4944-b4a8-aa6423c54170"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Predictions for X_test: [[  5052.47080807]\n",
            " [ -3879.37770314]\n",
            " [  1797.34650158]\n",
            " ...\n",
            " [-27101.96550725]\n",
            " [-11309.99561889]\n",
            " [   623.30654986]]\n",
            "R-sqaured score: -42.321510333945334\n"
          ]
        }
      ]
    }
  ]
}