Regression_(Linear_,_Polynomial)_.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "piFX_maitgnE"
      },
      "source": [
        "# WOC 4.0\n",
        ">> ### Machine Learning\n",
        ">>>> ###### IIT(ISM) Dhanabad\n",
        ">>>> ###### Arushika"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHgMrkYJt4Gu"
      },
      "source": [
        "## Linear regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bC0W4PR05VFh"
      },
      "source": [
        ">> ### Training set"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "kcY9B-nlt-pk"
      },
      "outputs": [],
      "source": [
        "# Importing libraries needed for the project\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as pp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "id": "Wb0TtU2HuFWk",
        "outputId": "56a9eb62-153c-4826-c9e2-bdb4e5e8a8ff"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Unnamed: 0          A            B          C          D          E  \\\n",
              "0               0  -9.989516  1564.957586   8.199060  32.508797  19.464400   \n",
              "1               1 -17.591800  1559.053039  12.302737 -36.351098   6.256406   \n",
              "2               2 -28.321695  1305.900952 -35.681049  -9.039358 -45.519426   \n",
              "3               3 -40.471241  1612.746996 -28.980454   2.137719 -34.767491   \n",
              "4               4 -36.525271  1852.275617 -32.744347  -1.439526 -14.061837   \n",
              "...           ...        ...          ...        ...        ...        ...   \n",
              "49995       49995  38.882059  1829.766795  -9.597762  42.286077 -45.676532   \n",
              "49996       49996 -29.570690  1467.757407  -2.581269   8.699766 -32.209400   \n",
              "49997       49997 -26.656483  1081.812179  19.742925 -49.109287  -8.179490   \n",
              "49998       49998  49.470595  1418.823031  14.854524  -6.995360  27.184947   \n",
              "49999       49999 -25.982072  1679.672351 -34.735487 -16.517472   6.606794   \n",
              "\n",
              "                 F          G          H            I  ...           L  \\\n",
              "0      1644.524093  26.100966  34.731954  4378.575414  ...  770.535311   \n",
              "1      1640.834263  12.954212 -43.333128  4833.766813  ...  997.260070   \n",
              "2      2039.003363  -0.154348  18.107957  4162.395297  ...  616.059291   \n",
              "3      2757.469393  23.857472 -48.434183  4340.953927  ...  715.537625   \n",
              "4      2138.422485  44.061988  33.336936  4099.453685  ...  629.221442   \n",
              "...            ...        ...        ...          ...  ...         ...   \n",
              "49995  2340.446842  44.758699 -49.232038  4561.096049  ...  931.215587   \n",
              "49996  2065.685621  13.244693 -27.154067  4922.613361  ...  646.439398   \n",
              "49997  1755.112415 -26.730046 -32.187078  4289.779346  ...  950.109763   \n",
              "49998  1235.231487  34.556613 -33.790945  4119.297411  ...  742.735044   \n",
              "49999  2375.299327  33.975192  -8.225393  4017.898569  ...  888.777601   \n",
              "\n",
              "               M          N          O          P          Q          R  \\\n",
              "0      30.060441 -25.002361  11.892468 -34.329383  37.218423  -4.440530   \n",
              "1      -1.329145  16.022086  42.972484  -7.372877  45.550946  37.576551   \n",
              "2      -6.997085  27.846844  26.511376  19.323152 -35.807513  -5.913019   \n",
              "3     -12.441561  47.883435  36.994884  30.783992  22.162383  16.465836   \n",
              "4      10.992360 -47.143335  -8.296962  -8.086565  39.169726 -49.540056   \n",
              "...          ...        ...        ...        ...        ...        ...   \n",
              "49995 -19.667192  20.825892  18.055764 -40.074521  44.966776  30.681416   \n",
              "49996  45.407497 -41.574684 -41.278010  34.484129  16.631234 -10.488980   \n",
              "49997  -1.341077 -33.268738  32.604813 -17.198521 -29.136001  24.609231   \n",
              "49998 -48.406474  -4.081799  20.777856 -49.422060 -31.251860 -27.546928   \n",
              "49999  33.897617 -25.710304  27.512513  29.199493  29.509718 -47.344110   \n",
              "\n",
              "               S          T         label  \n",
              "0      29.075092  29.107896    311.232491  \n",
              "1      12.926551 -32.565844   6393.112342  \n",
              "2      15.046779 -34.332357   2601.046223  \n",
              "3      41.435425  33.561233  13572.118106  \n",
              "4     -32.518653 -36.320202  -5462.446898  \n",
              "...          ...        ...           ...  \n",
              "49995  38.376682  33.942225   9034.945727  \n",
              "49996 -11.637358 -25.774032  -6345.178110  \n",
              "49997  11.935784 -35.190456   1483.917022  \n",
              "49998  38.121308 -10.588040  10720.139180  \n",
              "49999  -3.357583 -48.462504   2185.127958  \n",
              "\n",
              "[50000 rows x 22 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-2b9bea40-7c20-4300-bd19-be2060f0f964\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>A</th>\n",
              "      <th>B</th>\n",
              "      <th>C</th>\n",
              "      <th>D</th>\n",
              "      <th>E</th>\n",
              "      <th>F</th>\n",
              "      <th>G</th>\n",
              "      <th>H</th>\n",
              "      <th>I</th>\n",
              "      <th>...</th>\n",
              "      <th>L</th>\n",
              "      <th>M</th>\n",
              "      <th>N</th>\n",
              "      <th>O</th>\n",
              "      <th>P</th>\n",
              "      <th>Q</th>\n",
              "      <th>R</th>\n",
              "      <th>S</th>\n",
              "      <th>T</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>-9.989516</td>\n",
              "      <td>1564.957586</td>\n",
              "      <td>8.199060</td>\n",
              "      <td>32.508797</td>\n",
              "      <td>19.464400</td>\n",
              "      <td>1644.524093</td>\n",
              "      <td>26.100966</td>\n",
              "      <td>34.731954</td>\n",
              "      <td>4378.575414</td>\n",
              "      <td>...</td>\n",
              "      <td>770.535311</td>\n",
              "      <td>30.060441</td>\n",
              "      <td>-25.002361</td>\n",
              "      <td>11.892468</td>\n",
              "      <td>-34.329383</td>\n",
              "      <td>37.218423</td>\n",
              "      <td>-4.440530</td>\n",
              "      <td>29.075092</td>\n",
              "      <td>29.107896</td>\n",
              "      <td>311.232491</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>-17.591800</td>\n",
              "      <td>1559.053039</td>\n",
              "      <td>12.302737</td>\n",
              "      <td>-36.351098</td>\n",
              "      <td>6.256406</td>\n",
              "      <td>1640.834263</td>\n",
              "      <td>12.954212</td>\n",
              "      <td>-43.333128</td>\n",
              "      <td>4833.766813</td>\n",
              "      <td>...</td>\n",
              "      <td>997.260070</td>\n",
              "      <td>-1.329145</td>\n",
              "      <td>16.022086</td>\n",
              "      <td>42.972484</td>\n",
              "      <td>-7.372877</td>\n",
              "      <td>45.550946</td>\n",
              "      <td>37.576551</td>\n",
              "      <td>12.926551</td>\n",
              "      <td>-32.565844</td>\n",
              "      <td>6393.112342</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>-28.321695</td>\n",
              "      <td>1305.900952</td>\n",
              "      <td>-35.681049</td>\n",
              "      <td>-9.039358</td>\n",
              "      <td>-45.519426</td>\n",
              "      <td>2039.003363</td>\n",
              "      <td>-0.154348</td>\n",
              "      <td>18.107957</td>\n",
              "      <td>4162.395297</td>\n",
              "      <td>...</td>\n",
              "      <td>616.059291</td>\n",
              "      <td>-6.997085</td>\n",
              "      <td>27.846844</td>\n",
              "      <td>26.511376</td>\n",
              "      <td>19.323152</td>\n",
              "      <td>-35.807513</td>\n",
              "      <td>-5.913019</td>\n",
              "      <td>15.046779</td>\n",
              "      <td>-34.332357</td>\n",
              "      <td>2601.046223</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>-40.471241</td>\n",
              "      <td>1612.746996</td>\n",
              "      <td>-28.980454</td>\n",
              "      <td>2.137719</td>\n",
              "      <td>-34.767491</td>\n",
              "      <td>2757.469393</td>\n",
              "      <td>23.857472</td>\n",
              "      <td>-48.434183</td>\n",
              "      <td>4340.953927</td>\n",
              "      <td>...</td>\n",
              "      <td>715.537625</td>\n",
              "      <td>-12.441561</td>\n",
              "      <td>47.883435</td>\n",
              "      <td>36.994884</td>\n",
              "      <td>30.783992</td>\n",
              "      <td>22.162383</td>\n",
              "      <td>16.465836</td>\n",
              "      <td>41.435425</td>\n",
              "      <td>33.561233</td>\n",
              "      <td>13572.118106</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>-36.525271</td>\n",
              "      <td>1852.275617</td>\n",
              "      <td>-32.744347</td>\n",
              "      <td>-1.439526</td>\n",
              "      <td>-14.061837</td>\n",
              "      <td>2138.422485</td>\n",
              "      <td>44.061988</td>\n",
              "      <td>33.336936</td>\n",
              "      <td>4099.453685</td>\n",
              "      <td>...</td>\n",
              "      <td>629.221442</td>\n",
              "      <td>10.992360</td>\n",
              "      <td>-47.143335</td>\n",
              "      <td>-8.296962</td>\n",
              "      <td>-8.086565</td>\n",
              "      <td>39.169726</td>\n",
              "      <td>-49.540056</td>\n",
              "      <td>-32.518653</td>\n",
              "      <td>-36.320202</td>\n",
              "      <td>-5462.446898</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>49995</td>\n",
              "      <td>38.882059</td>\n",
              "      <td>1829.766795</td>\n",
              "      <td>-9.597762</td>\n",
              "      <td>42.286077</td>\n",
              "      <td>-45.676532</td>\n",
              "      <td>2340.446842</td>\n",
              "      <td>44.758699</td>\n",
              "      <td>-49.232038</td>\n",
              "      <td>4561.096049</td>\n",
              "      <td>...</td>\n",
              "      <td>931.215587</td>\n",
              "      <td>-19.667192</td>\n",
              "      <td>20.825892</td>\n",
              "      <td>18.055764</td>\n",
              "      <td>-40.074521</td>\n",
              "      <td>44.966776</td>\n",
              "      <td>30.681416</td>\n",
              "      <td>38.376682</td>\n",
              "      <td>33.942225</td>\n",
              "      <td>9034.945727</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49996</th>\n",
              "      <td>49996</td>\n",
              "      <td>-29.570690</td>\n",
              "      <td>1467.757407</td>\n",
              "      <td>-2.581269</td>\n",
              "      <td>8.699766</td>\n",
              "      <td>-32.209400</td>\n",
              "      <td>2065.685621</td>\n",
              "      <td>13.244693</td>\n",
              "      <td>-27.154067</td>\n",
              "      <td>4922.613361</td>\n",
              "      <td>...</td>\n",
              "      <td>646.439398</td>\n",
              "      <td>45.407497</td>\n",
              "      <td>-41.574684</td>\n",
              "      <td>-41.278010</td>\n",
              "      <td>34.484129</td>\n",
              "      <td>16.631234</td>\n",
              "      <td>-10.488980</td>\n",
              "      <td>-11.637358</td>\n",
              "      <td>-25.774032</td>\n",
              "      <td>-6345.178110</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49997</th>\n",
              "      <td>49997</td>\n",
              "      <td>-26.656483</td>\n",
              "      <td>1081.812179</td>\n",
              "      <td>19.742925</td>\n",
              "      <td>-49.109287</td>\n",
              "      <td>-8.179490</td>\n",
              "      <td>1755.112415</td>\n",
              "      <td>-26.730046</td>\n",
              "      <td>-32.187078</td>\n",
              "      <td>4289.779346</td>\n",
              "      <td>...</td>\n",
              "      <td>950.109763</td>\n",
              "      <td>-1.341077</td>\n",
              "      <td>-33.268738</td>\n",
              "      <td>32.604813</td>\n",
              "      <td>-17.198521</td>\n",
              "      <td>-29.136001</td>\n",
              "      <td>24.609231</td>\n",
              "      <td>11.935784</td>\n",
              "      <td>-35.190456</td>\n",
              "      <td>1483.917022</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49998</th>\n",
              "      <td>49998</td>\n",
              "      <td>49.470595</td>\n",
              "      <td>1418.823031</td>\n",
              "      <td>14.854524</td>\n",
              "      <td>-6.995360</td>\n",
              "      <td>27.184947</td>\n",
              "      <td>1235.231487</td>\n",
              "      <td>34.556613</td>\n",
              "      <td>-33.790945</td>\n",
              "      <td>4119.297411</td>\n",
              "      <td>...</td>\n",
              "      <td>742.735044</td>\n",
              "      <td>-48.406474</td>\n",
              "      <td>-4.081799</td>\n",
              "      <td>20.777856</td>\n",
              "      <td>-49.422060</td>\n",
              "      <td>-31.251860</td>\n",
              "      <td>-27.546928</td>\n",
              "      <td>38.121308</td>\n",
              "      <td>-10.588040</td>\n",
              "      <td>10720.139180</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49999</th>\n",
              "      <td>49999</td>\n",
              "      <td>-25.982072</td>\n",
              "      <td>1679.672351</td>\n",
              "      <td>-34.735487</td>\n",
              "      <td>-16.517472</td>\n",
              "      <td>6.606794</td>\n",
              "      <td>2375.299327</td>\n",
              "      <td>33.975192</td>\n",
              "      <td>-8.225393</td>\n",
              "      <td>4017.898569</td>\n",
              "      <td>...</td>\n",
              "      <td>888.777601</td>\n",
              "      <td>33.897617</td>\n",
              "      <td>-25.710304</td>\n",
              "      <td>27.512513</td>\n",
              "      <td>29.199493</td>\n",
              "      <td>29.509718</td>\n",
              "      <td>-47.344110</td>\n",
              "      <td>-3.357583</td>\n",
              "      <td>-48.462504</td>\n",
              "      <td>2185.127958</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>50000 rows × 22 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2b9bea40-7c20-4300-bd19-be2060f0f964')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-2b9bea40-7c20-4300-bd19-be2060f0f964 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-2b9bea40-7c20-4300-bd19-be2060f0f964');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "# Loading dataset \n",
        "data = pd.read_csv('Linear_train.csv')\n",
        "data"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = (data- data.mean())/ data.std()\n",
        "data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "id": "xsYuy8DuUJUA",
        "outputId": "19ac8586-bf9d-4b2a-f52c-a0e091fc63bb"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Unnamed: 0         A         B         C         D         E         F  \\\n",
              "0       -1.731999 -0.347991  0.220312  0.285110  1.133715  0.678330 -0.610903   \n",
              "1       -1.731930 -0.611140  0.199847  0.427126 -1.254843  0.220549 -0.617274   \n",
              "2       -1.731860 -0.982550 -0.677569 -1.233452 -0.307475 -1.573969  0.070213   \n",
              "3       -1.731791 -1.403101  0.385949 -1.001564  0.080227 -1.201313  1.310732   \n",
              "4       -1.731722 -1.266513  1.216147 -1.131821 -0.043858 -0.483668  0.241872   \n",
              "...           ...       ...       ...       ...       ...       ...       ...   \n",
              "49995    1.731722  1.343676  1.138132 -0.330786  1.472862 -1.579414  0.590692   \n",
              "49996    1.731791 -1.025784 -0.116580 -0.087966  0.307846 -1.112651  0.116283   \n",
              "49997    1.731860 -0.924910 -1.454253  0.684609 -1.697389 -0.279790 -0.419959   \n",
              "49998    1.731930  1.710193 -0.286185  0.515436 -0.236574  0.945919 -1.317596   \n",
              "49999    1.731999 -0.901565  0.617910 -1.200728 -0.566870  0.232693  0.650869   \n",
              "\n",
              "              G         H         I  ...         L         M         N  \\\n",
              "0      0.898280  1.199218 -0.424613  ...  0.138291  1.028725 -0.863910   \n",
              "1      0.443115 -1.502330  1.151147  ...  1.707571 -0.056831  0.558906   \n",
              "2     -0.010727  0.623922 -1.172975  ... -0.930919 -0.252847  0.969013   \n",
              "3      0.820607 -1.678859 -0.554849  ... -0.242377 -0.441135  1.663925   \n",
              "4      1.520124  1.150941 -1.390864  ... -0.839817  0.369288 -1.631806   \n",
              "...         ...       ...       ...  ...       ...       ...       ...   \n",
              "49995  1.544246 -1.706470  0.207228  ...  1.250443 -0.691021  0.725512   \n",
              "49996  0.453172 -0.942432  1.458712  ... -0.720642  1.559477 -1.438673   \n",
              "49997 -0.930827 -1.116606 -0.732003  ...  1.381219 -0.057243 -1.150605   \n",
              "49998  1.191031 -1.172110 -1.322170  ... -0.054130 -1.684921 -0.138340   \n",
              "49999  1.170901 -0.287380 -1.673187  ...  0.956707  1.161427 -0.888463   \n",
              "\n",
              "              O         P         Q         R         S         T     label  \n",
              "0      0.423651 -1.184218  1.284498 -0.155822  1.005271  1.008755 -0.248061  \n",
              "1      1.497778 -0.253123  1.572980  1.294387  0.446828 -1.123392  0.982331  \n",
              "2      0.928881  0.668976 -1.243750 -0.206644  0.520149 -1.184463  0.215179  \n",
              "3      1.291192  1.064841  0.763239  0.565756  1.432712  1.162713  2.434678  \n",
              "4     -0.274098 -0.277774  1.352054 -1.712420 -1.124743 -1.253185 -1.416104  \n",
              "...         ...       ...       ...       ...       ...       ...       ...  \n",
              "49995  0.636655 -1.382659  1.552755  1.056403  1.326936  1.175884  1.516787  \n",
              "49996 -1.413925  1.192646  0.571744 -0.364582 -0.402633 -0.888590 -1.594684  \n",
              "49997  1.139471 -0.592507 -1.012774  0.846823  0.412565 -1.214129 -0.010822  \n",
              "49998  0.730730 -1.705529 -1.086028 -0.953333  1.318105 -0.363589  1.857709  \n",
              "49999  0.963481  1.010112  1.017613 -1.636628 -0.116305 -1.672962  0.131037  \n",
              "\n",
              "[50000 rows x 22 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-237265f2-1c85-4746-8864-a3d4153843ce\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>A</th>\n",
              "      <th>B</th>\n",
              "      <th>C</th>\n",
              "      <th>D</th>\n",
              "      <th>E</th>\n",
              "      <th>F</th>\n",
              "      <th>G</th>\n",
              "      <th>H</th>\n",
              "      <th>I</th>\n",
              "      <th>...</th>\n",
              "      <th>L</th>\n",
              "      <th>M</th>\n",
              "      <th>N</th>\n",
              "      <th>O</th>\n",
              "      <th>P</th>\n",
              "      <th>Q</th>\n",
              "      <th>R</th>\n",
              "      <th>S</th>\n",
              "      <th>T</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.731999</td>\n",
              "      <td>-0.347991</td>\n",
              "      <td>0.220312</td>\n",
              "      <td>0.285110</td>\n",
              "      <td>1.133715</td>\n",
              "      <td>0.678330</td>\n",
              "      <td>-0.610903</td>\n",
              "      <td>0.898280</td>\n",
              "      <td>1.199218</td>\n",
              "      <td>-0.424613</td>\n",
              "      <td>...</td>\n",
              "      <td>0.138291</td>\n",
              "      <td>1.028725</td>\n",
              "      <td>-0.863910</td>\n",
              "      <td>0.423651</td>\n",
              "      <td>-1.184218</td>\n",
              "      <td>1.284498</td>\n",
              "      <td>-0.155822</td>\n",
              "      <td>1.005271</td>\n",
              "      <td>1.008755</td>\n",
              "      <td>-0.248061</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.731930</td>\n",
              "      <td>-0.611140</td>\n",
              "      <td>0.199847</td>\n",
              "      <td>0.427126</td>\n",
              "      <td>-1.254843</td>\n",
              "      <td>0.220549</td>\n",
              "      <td>-0.617274</td>\n",
              "      <td>0.443115</td>\n",
              "      <td>-1.502330</td>\n",
              "      <td>1.151147</td>\n",
              "      <td>...</td>\n",
              "      <td>1.707571</td>\n",
              "      <td>-0.056831</td>\n",
              "      <td>0.558906</td>\n",
              "      <td>1.497778</td>\n",
              "      <td>-0.253123</td>\n",
              "      <td>1.572980</td>\n",
              "      <td>1.294387</td>\n",
              "      <td>0.446828</td>\n",
              "      <td>-1.123392</td>\n",
              "      <td>0.982331</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.731860</td>\n",
              "      <td>-0.982550</td>\n",
              "      <td>-0.677569</td>\n",
              "      <td>-1.233452</td>\n",
              "      <td>-0.307475</td>\n",
              "      <td>-1.573969</td>\n",
              "      <td>0.070213</td>\n",
              "      <td>-0.010727</td>\n",
              "      <td>0.623922</td>\n",
              "      <td>-1.172975</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.930919</td>\n",
              "      <td>-0.252847</td>\n",
              "      <td>0.969013</td>\n",
              "      <td>0.928881</td>\n",
              "      <td>0.668976</td>\n",
              "      <td>-1.243750</td>\n",
              "      <td>-0.206644</td>\n",
              "      <td>0.520149</td>\n",
              "      <td>-1.184463</td>\n",
              "      <td>0.215179</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.731791</td>\n",
              "      <td>-1.403101</td>\n",
              "      <td>0.385949</td>\n",
              "      <td>-1.001564</td>\n",
              "      <td>0.080227</td>\n",
              "      <td>-1.201313</td>\n",
              "      <td>1.310732</td>\n",
              "      <td>0.820607</td>\n",
              "      <td>-1.678859</td>\n",
              "      <td>-0.554849</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.242377</td>\n",
              "      <td>-0.441135</td>\n",
              "      <td>1.663925</td>\n",
              "      <td>1.291192</td>\n",
              "      <td>1.064841</td>\n",
              "      <td>0.763239</td>\n",
              "      <td>0.565756</td>\n",
              "      <td>1.432712</td>\n",
              "      <td>1.162713</td>\n",
              "      <td>2.434678</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.731722</td>\n",
              "      <td>-1.266513</td>\n",
              "      <td>1.216147</td>\n",
              "      <td>-1.131821</td>\n",
              "      <td>-0.043858</td>\n",
              "      <td>-0.483668</td>\n",
              "      <td>0.241872</td>\n",
              "      <td>1.520124</td>\n",
              "      <td>1.150941</td>\n",
              "      <td>-1.390864</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.839817</td>\n",
              "      <td>0.369288</td>\n",
              "      <td>-1.631806</td>\n",
              "      <td>-0.274098</td>\n",
              "      <td>-0.277774</td>\n",
              "      <td>1.352054</td>\n",
              "      <td>-1.712420</td>\n",
              "      <td>-1.124743</td>\n",
              "      <td>-1.253185</td>\n",
              "      <td>-1.416104</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>1.731722</td>\n",
              "      <td>1.343676</td>\n",
              "      <td>1.138132</td>\n",
              "      <td>-0.330786</td>\n",
              "      <td>1.472862</td>\n",
              "      <td>-1.579414</td>\n",
              "      <td>0.590692</td>\n",
              "      <td>1.544246</td>\n",
              "      <td>-1.706470</td>\n",
              "      <td>0.207228</td>\n",
              "      <td>...</td>\n",
              "      <td>1.250443</td>\n",
              "      <td>-0.691021</td>\n",
              "      <td>0.725512</td>\n",
              "      <td>0.636655</td>\n",
              "      <td>-1.382659</td>\n",
              "      <td>1.552755</td>\n",
              "      <td>1.056403</td>\n",
              "      <td>1.326936</td>\n",
              "      <td>1.175884</td>\n",
              "      <td>1.516787</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49996</th>\n",
              "      <td>1.731791</td>\n",
              "      <td>-1.025784</td>\n",
              "      <td>-0.116580</td>\n",
              "      <td>-0.087966</td>\n",
              "      <td>0.307846</td>\n",
              "      <td>-1.112651</td>\n",
              "      <td>0.116283</td>\n",
              "      <td>0.453172</td>\n",
              "      <td>-0.942432</td>\n",
              "      <td>1.458712</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.720642</td>\n",
              "      <td>1.559477</td>\n",
              "      <td>-1.438673</td>\n",
              "      <td>-1.413925</td>\n",
              "      <td>1.192646</td>\n",
              "      <td>0.571744</td>\n",
              "      <td>-0.364582</td>\n",
              "      <td>-0.402633</td>\n",
              "      <td>-0.888590</td>\n",
              "      <td>-1.594684</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49997</th>\n",
              "      <td>1.731860</td>\n",
              "      <td>-0.924910</td>\n",
              "      <td>-1.454253</td>\n",
              "      <td>0.684609</td>\n",
              "      <td>-1.697389</td>\n",
              "      <td>-0.279790</td>\n",
              "      <td>-0.419959</td>\n",
              "      <td>-0.930827</td>\n",
              "      <td>-1.116606</td>\n",
              "      <td>-0.732003</td>\n",
              "      <td>...</td>\n",
              "      <td>1.381219</td>\n",
              "      <td>-0.057243</td>\n",
              "      <td>-1.150605</td>\n",
              "      <td>1.139471</td>\n",
              "      <td>-0.592507</td>\n",
              "      <td>-1.012774</td>\n",
              "      <td>0.846823</td>\n",
              "      <td>0.412565</td>\n",
              "      <td>-1.214129</td>\n",
              "      <td>-0.010822</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49998</th>\n",
              "      <td>1.731930</td>\n",
              "      <td>1.710193</td>\n",
              "      <td>-0.286185</td>\n",
              "      <td>0.515436</td>\n",
              "      <td>-0.236574</td>\n",
              "      <td>0.945919</td>\n",
              "      <td>-1.317596</td>\n",
              "      <td>1.191031</td>\n",
              "      <td>-1.172110</td>\n",
              "      <td>-1.322170</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.054130</td>\n",
              "      <td>-1.684921</td>\n",
              "      <td>-0.138340</td>\n",
              "      <td>0.730730</td>\n",
              "      <td>-1.705529</td>\n",
              "      <td>-1.086028</td>\n",
              "      <td>-0.953333</td>\n",
              "      <td>1.318105</td>\n",
              "      <td>-0.363589</td>\n",
              "      <td>1.857709</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49999</th>\n",
              "      <td>1.731999</td>\n",
              "      <td>-0.901565</td>\n",
              "      <td>0.617910</td>\n",
              "      <td>-1.200728</td>\n",
              "      <td>-0.566870</td>\n",
              "      <td>0.232693</td>\n",
              "      <td>0.650869</td>\n",
              "      <td>1.170901</td>\n",
              "      <td>-0.287380</td>\n",
              "      <td>-1.673187</td>\n",
              "      <td>...</td>\n",
              "      <td>0.956707</td>\n",
              "      <td>1.161427</td>\n",
              "      <td>-0.888463</td>\n",
              "      <td>0.963481</td>\n",
              "      <td>1.010112</td>\n",
              "      <td>1.017613</td>\n",
              "      <td>-1.636628</td>\n",
              "      <td>-0.116305</td>\n",
              "      <td>-1.672962</td>\n",
              "      <td>0.131037</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>50000 rows × 22 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-237265f2-1c85-4746-8864-a3d4153843ce')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-237265f2-1c85-4746-8864-a3d4153843ce 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-237265f2-1c85-4746-8864-a3d4153843ce');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "0XsM6uhSu3yl"
      },
      "outputs": [],
      "source": [
        "# From the dataset seperating x and y \n",
        "\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "X_1 = data.iloc[:,1:21] # for m x n dimensional \n",
        "ones = np.ones([X_1.shape[0],1]) #This is done because for convinience X_0 is considered to have entering of only 1(for simplicity)\n",
        "X_1 = np.concatenate ((ones , X_1) , axis=1)\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "y_1 = data.iloc[:,21:22].values\n",
        " \n",
        "# Matrice of theta(coefficient of the features in hypothesis function) is supposed to a 1 x (n+1) dimensional matrice\n",
        "theta = np.zeros([1,21])\n",
        "\n",
        "X_2 = data.iloc[:,0:1].values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "9tC4Z8DAyoAG",
        "outputId": "890bbe40-87cb-4635-fe8b-1d6de7c9d90d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f045c0c2f90>"
            ]
          },
          "metadata": {},
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "pp.scatter(X_2,y_1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Setting Hyperparameters\n",
        "#@title Setting Hypermeters:\n",
        "Alpha = 0.01#@param {type:\"slider\", min:0, max:1, step:0.0000001}\n",
        "iters = 1000 #@param {type:\"slider\", min:200, max:3000, step:100}\n",
        "alpha= Alpha"
      ],
      "metadata": {
        "id": "YLhxzhNbc3z5"
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vtX-r6WxyKMl"
      },
      "source": [
        "`Hypothesis` is:\n",
        "</br></br>\n",
        "<b> h(theta)= (theta.T)*X \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y3OKtyFB0J7O"
      },
      "source": [
        "To predict matrice of theta, we minimise the `cost function` which is basically minimising the `L2 loss`. \n",
        "Which in turn says, the hypothesis closely passes through the output. Hence, Giving us a perfect ground to predict the values further through regression."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "Y4LKsyOczgyH"
      },
      "outputs": [],
      "source": [
        "#Defining Cost function\n",
        "def computeCost(X,y,theta):\n",
        "    tobesummed = np.power(((X @ theta.T)-y),2)\n",
        "    return np.sum(tobesummed)/(2 * len(X))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i8ZxBbND08H3"
      },
      "source": [
        "To minimise the cost we use some algorithms. The most basic of all the algorithms but still one of the most important algorithm is that of `Gradient Descent`.This method is somewhat like hit and trial. Here we minimise the value of theta in each iteration. Till the cost funtion stops minimising or the cost funtion's value becomes static. </br>\n",
        "This minimising of cost function depends on `alpha` which is called the learning rate. There can be different scenerios based on the value of alpha:\n",
        "* if alpha is very large then the value can overshoot \n",
        "* if alpha is very small then it will take infinite no. of iteration to reach the lowest value "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "49q76tk83O63"
      },
      "outputs": [],
      "source": [
        "#Defining gradient descent\n",
        "def gradientDescent(X,y,theta,iters,alpha):\n",
        "    cost = np.zeros(iters)\n",
        "    for i in range(iters):\n",
        "        theta = theta - (alpha/len(X)) * np.sum(X * (X @ theta.T - y), axis=0)\n",
        "        cost[i] = computeCost(X, y, theta)\n",
        "    \n",
        "    return theta,cost"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#running the gd and cost function\n",
        "g,cost = gradientDescent(X_1,y_1,theta,iters,alpha)\n",
        "print(g)\n",
        "\n",
        "finalCost = computeCost(X_1,y_1,g)\n",
        "print(finalCost)"
      ],
      "metadata": {
        "id": "IJHUQK9pg-Bt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ce30e165-a637-4587-c8d9-9a54c26c7d2d"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1.55125041e-16  7.58325949e-02  1.16645110e-02 -1.57927815e-01\n",
            "   4.67049756e-02  2.16064015e-01  1.76425703e-02  1.11008273e-01\n",
            "  -1.69457068e-01  7.01370034e-03  1.34030001e-01  1.81342626e-01\n",
            "   1.74943441e-02 -5.32310935e-01  1.98373216e-01  2.63286594e-01\n",
            "   2.98792027e-01  1.40281498e-01 -5.91835542e-03  5.55548484e-01\n",
            "   1.46337653e-01]]\n",
            "7.805232023070867e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "htYq-VIX44Un",
        "outputId": "5f52a189-5fd8-4b60-b723-3a50687acf59"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 62
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#plot the cost\n",
        "fig, ax = pp.subplots()  \n",
        "ax.plot(np.arange(iters), cost, 'r')  \n",
        "ax.set_xlabel('Iterations')  \n",
        "ax.set_ylabel('Cost')  \n",
        "ax.set_title('Error vs. Training Epoch')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n0L0tkxS5jun"
      },
      "source": [
        ">> ### Test set"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EYRwZZT55r-P"
      },
      "source": [
        "**Now applying the above obtained coefficients and value of alpha, We plot a graph for the test data set to see if the hypothesis is correct.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "id": "6oU49CUv5-f-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "outputId": "c879bc0f-ad5a-4c74-a99f-b961dbea2d40"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0          A            B          C          D          E  \\\n",
              "0              0  40.790740  1187.897579 -28.941991  43.498302  14.157983   \n",
              "1              1  47.968749  1498.588679  24.922821 -38.979082  16.405452   \n",
              "2              2   9.762564  1316.354415   1.170771  10.365178 -11.993156   \n",
              "3              3   6.414629  1895.586749  44.496934 -49.677800 -24.825833   \n",
              "4              4  -4.112012  1130.920162  19.103960  -8.741503 -28.589701   \n",
              "...          ...        ...          ...        ...        ...        ...   \n",
              "9995        9995 -37.802773  1204.712095  30.916166 -32.185868  -1.860028   \n",
              "9996        9996  21.841410  1067.350891  -9.598592  13.545191   2.910106   \n",
              "9997        9997 -34.734278  1630.673420  27.359399  -0.718695 -24.225154   \n",
              "9998        9998 -30.752354  1610.117693 -37.652326 -46.959112  18.151935   \n",
              "9999        9999  39.757972  1360.988948  -7.480509  27.155692  43.509194   \n",
              "\n",
              "                F          G          H            I  ...           L  \\\n",
              "0     2536.000797 -34.181638 -14.940211  4746.739893  ...  707.727094   \n",
              "1     1798.950305 -23.660484 -34.792328  4076.982013  ...  737.135391   \n",
              "2     2714.382200  26.382837  27.442924  4178.719984  ...  940.732329   \n",
              "3     2327.316373   1.406644  44.103008  4586.697737  ...  925.441952   \n",
              "4     1299.418975  42.946135   4.758032  4809.536369  ...  797.953813   \n",
              "...           ...        ...        ...          ...  ...         ...   \n",
              "9995  1515.265232 -43.103776  12.911176  4865.716464  ...  877.773521   \n",
              "9996  1286.431551 -49.542330  27.868152  4513.212740  ...  518.544504   \n",
              "9997  1309.956055  36.839488 -40.966273  4747.087919  ...  948.924788   \n",
              "9998  2489.587758 -33.802220 -11.550250  4912.443446  ...  656.905027   \n",
              "9999  1700.776478   4.496912  42.373176  4579.120167  ...  582.145397   \n",
              "\n",
              "              M          N          O          P          Q          R  \\\n",
              "0     21.030812 -44.606156  -9.625546  42.276162 -11.000471 -19.830564   \n",
              "1    -17.860346  42.274026 -19.886483  16.337922   9.025313  27.760845   \n",
              "2    -35.879432  23.837924   3.729191  33.564390  12.848880 -45.837834   \n",
              "3    -19.409771  25.346975  -7.729920 -42.813516 -17.666168  35.506064   \n",
              "4    -46.788081  43.876292  34.009303  34.061089 -30.182903 -41.188733   \n",
              "...         ...        ...        ...        ...        ...        ...   \n",
              "9995 -14.401216  -1.152501   9.371124 -16.953167   5.590761  27.769178   \n",
              "9996  -4.202304  -6.779170   2.384596  20.661830  -7.804846  -3.170458   \n",
              "9997 -31.628023  -5.662373 -45.441406 -33.063193 -23.153715  -7.089845   \n",
              "9998 -48.696117 -20.709813 -27.404294  14.174336  40.169075  37.329627   \n",
              "9999  28.458183 -47.300191 -19.032777 -15.959350 -10.118301  38.306081   \n",
              "\n",
              "              S          T         label  \n",
              "0     -5.529430 -28.154864   -163.522723  \n",
              "1     21.484409 -24.206545   6484.664510  \n",
              "2    -49.592176  36.688611   2393.818082  \n",
              "3    -49.048652 -34.048583  -9397.072355  \n",
              "4     26.828040 -22.476663  10487.323575  \n",
              "...         ...        ...           ...  \n",
              "9995 -42.025878 -46.347044  -7526.092452  \n",
              "9996  39.886812 -17.630468   6133.716734  \n",
              "9997 -25.366712  47.034834  -1404.204034  \n",
              "9998 -27.968720 -18.475040   1972.371711  \n",
              "9999  -2.826688 -38.647683  -6120.248772  \n",
              "\n",
              "[10000 rows x 22 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c9626836-25e0-41dc-86cb-7609dff9c9b0\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>A</th>\n",
              "      <th>B</th>\n",
              "      <th>C</th>\n",
              "      <th>D</th>\n",
              "      <th>E</th>\n",
              "      <th>F</th>\n",
              "      <th>G</th>\n",
              "      <th>H</th>\n",
              "      <th>I</th>\n",
              "      <th>...</th>\n",
              "      <th>L</th>\n",
              "      <th>M</th>\n",
              "      <th>N</th>\n",
              "      <th>O</th>\n",
              "      <th>P</th>\n",
              "      <th>Q</th>\n",
              "      <th>R</th>\n",
              "      <th>S</th>\n",
              "      <th>T</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>40.790740</td>\n",
              "      <td>1187.897579</td>\n",
              "      <td>-28.941991</td>\n",
              "      <td>43.498302</td>\n",
              "      <td>14.157983</td>\n",
              "      <td>2536.000797</td>\n",
              "      <td>-34.181638</td>\n",
              "      <td>-14.940211</td>\n",
              "      <td>4746.739893</td>\n",
              "      <td>...</td>\n",
              "      <td>707.727094</td>\n",
              "      <td>21.030812</td>\n",
              "      <td>-44.606156</td>\n",
              "      <td>-9.625546</td>\n",
              "      <td>42.276162</td>\n",
              "      <td>-11.000471</td>\n",
              "      <td>-19.830564</td>\n",
              "      <td>-5.529430</td>\n",
              "      <td>-28.154864</td>\n",
              "      <td>-163.522723</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>47.968749</td>\n",
              "      <td>1498.588679</td>\n",
              "      <td>24.922821</td>\n",
              "      <td>-38.979082</td>\n",
              "      <td>16.405452</td>\n",
              "      <td>1798.950305</td>\n",
              "      <td>-23.660484</td>\n",
              "      <td>-34.792328</td>\n",
              "      <td>4076.982013</td>\n",
              "      <td>...</td>\n",
              "      <td>737.135391</td>\n",
              "      <td>-17.860346</td>\n",
              "      <td>42.274026</td>\n",
              "      <td>-19.886483</td>\n",
              "      <td>16.337922</td>\n",
              "      <td>9.025313</td>\n",
              "      <td>27.760845</td>\n",
              "      <td>21.484409</td>\n",
              "      <td>-24.206545</td>\n",
              "      <td>6484.664510</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>9.762564</td>\n",
              "      <td>1316.354415</td>\n",
              "      <td>1.170771</td>\n",
              "      <td>10.365178</td>\n",
              "      <td>-11.993156</td>\n",
              "      <td>2714.382200</td>\n",
              "      <td>26.382837</td>\n",
              "      <td>27.442924</td>\n",
              "      <td>4178.719984</td>\n",
              "      <td>...</td>\n",
              "      <td>940.732329</td>\n",
              "      <td>-35.879432</td>\n",
              "      <td>23.837924</td>\n",
              "      <td>3.729191</td>\n",
              "      <td>33.564390</td>\n",
              "      <td>12.848880</td>\n",
              "      <td>-45.837834</td>\n",
              "      <td>-49.592176</td>\n",
              "      <td>36.688611</td>\n",
              "      <td>2393.818082</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>6.414629</td>\n",
              "      <td>1895.586749</td>\n",
              "      <td>44.496934</td>\n",
              "      <td>-49.677800</td>\n",
              "      <td>-24.825833</td>\n",
              "      <td>2327.316373</td>\n",
              "      <td>1.406644</td>\n",
              "      <td>44.103008</td>\n",
              "      <td>4586.697737</td>\n",
              "      <td>...</td>\n",
              "      <td>925.441952</td>\n",
              "      <td>-19.409771</td>\n",
              "      <td>25.346975</td>\n",
              "      <td>-7.729920</td>\n",
              "      <td>-42.813516</td>\n",
              "      <td>-17.666168</td>\n",
              "      <td>35.506064</td>\n",
              "      <td>-49.048652</td>\n",
              "      <td>-34.048583</td>\n",
              "      <td>-9397.072355</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>-4.112012</td>\n",
              "      <td>1130.920162</td>\n",
              "      <td>19.103960</td>\n",
              "      <td>-8.741503</td>\n",
              "      <td>-28.589701</td>\n",
              "      <td>1299.418975</td>\n",
              "      <td>42.946135</td>\n",
              "      <td>4.758032</td>\n",
              "      <td>4809.536369</td>\n",
              "      <td>...</td>\n",
              "      <td>797.953813</td>\n",
              "      <td>-46.788081</td>\n",
              "      <td>43.876292</td>\n",
              "      <td>34.009303</td>\n",
              "      <td>34.061089</td>\n",
              "      <td>-30.182903</td>\n",
              "      <td>-41.188733</td>\n",
              "      <td>26.828040</td>\n",
              "      <td>-22.476663</td>\n",
              "      <td>10487.323575</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>9995</td>\n",
              "      <td>-37.802773</td>\n",
              "      <td>1204.712095</td>\n",
              "      <td>30.916166</td>\n",
              "      <td>-32.185868</td>\n",
              "      <td>-1.860028</td>\n",
              "      <td>1515.265232</td>\n",
              "      <td>-43.103776</td>\n",
              "      <td>12.911176</td>\n",
              "      <td>4865.716464</td>\n",
              "      <td>...</td>\n",
              "      <td>877.773521</td>\n",
              "      <td>-14.401216</td>\n",
              "      <td>-1.152501</td>\n",
              "      <td>9.371124</td>\n",
              "      <td>-16.953167</td>\n",
              "      <td>5.590761</td>\n",
              "      <td>27.769178</td>\n",
              "      <td>-42.025878</td>\n",
              "      <td>-46.347044</td>\n",
              "      <td>-7526.092452</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>9996</td>\n",
              "      <td>21.841410</td>\n",
              "      <td>1067.350891</td>\n",
              "      <td>-9.598592</td>\n",
              "      <td>13.545191</td>\n",
              "      <td>2.910106</td>\n",
              "      <td>1286.431551</td>\n",
              "      <td>-49.542330</td>\n",
              "      <td>27.868152</td>\n",
              "      <td>4513.212740</td>\n",
              "      <td>...</td>\n",
              "      <td>518.544504</td>\n",
              "      <td>-4.202304</td>\n",
              "      <td>-6.779170</td>\n",
              "      <td>2.384596</td>\n",
              "      <td>20.661830</td>\n",
              "      <td>-7.804846</td>\n",
              "      <td>-3.170458</td>\n",
              "      <td>39.886812</td>\n",
              "      <td>-17.630468</td>\n",
              "      <td>6133.716734</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>9997</td>\n",
              "      <td>-34.734278</td>\n",
              "      <td>1630.673420</td>\n",
              "      <td>27.359399</td>\n",
              "      <td>-0.718695</td>\n",
              "      <td>-24.225154</td>\n",
              "      <td>1309.956055</td>\n",
              "      <td>36.839488</td>\n",
              "      <td>-40.966273</td>\n",
              "      <td>4747.087919</td>\n",
              "      <td>...</td>\n",
              "      <td>948.924788</td>\n",
              "      <td>-31.628023</td>\n",
              "      <td>-5.662373</td>\n",
              "      <td>-45.441406</td>\n",
              "      <td>-33.063193</td>\n",
              "      <td>-23.153715</td>\n",
              "      <td>-7.089845</td>\n",
              "      <td>-25.366712</td>\n",
              "      <td>47.034834</td>\n",
              "      <td>-1404.204034</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>9998</td>\n",
              "      <td>-30.752354</td>\n",
              "      <td>1610.117693</td>\n",
              "      <td>-37.652326</td>\n",
              "      <td>-46.959112</td>\n",
              "      <td>18.151935</td>\n",
              "      <td>2489.587758</td>\n",
              "      <td>-33.802220</td>\n",
              "      <td>-11.550250</td>\n",
              "      <td>4912.443446</td>\n",
              "      <td>...</td>\n",
              "      <td>656.905027</td>\n",
              "      <td>-48.696117</td>\n",
              "      <td>-20.709813</td>\n",
              "      <td>-27.404294</td>\n",
              "      <td>14.174336</td>\n",
              "      <td>40.169075</td>\n",
              "      <td>37.329627</td>\n",
              "      <td>-27.968720</td>\n",
              "      <td>-18.475040</td>\n",
              "      <td>1972.371711</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>9999</td>\n",
              "      <td>39.757972</td>\n",
              "      <td>1360.988948</td>\n",
              "      <td>-7.480509</td>\n",
              "      <td>27.155692</td>\n",
              "      <td>43.509194</td>\n",
              "      <td>1700.776478</td>\n",
              "      <td>4.496912</td>\n",
              "      <td>42.373176</td>\n",
              "      <td>4579.120167</td>\n",
              "      <td>...</td>\n",
              "      <td>582.145397</td>\n",
              "      <td>28.458183</td>\n",
              "      <td>-47.300191</td>\n",
              "      <td>-19.032777</td>\n",
              "      <td>-15.959350</td>\n",
              "      <td>-10.118301</td>\n",
              "      <td>38.306081</td>\n",
              "      <td>-2.826688</td>\n",
              "      <td>-38.647683</td>\n",
              "      <td>-6120.248772</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 22 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c9626836-25e0-41dc-86cb-7609dff9c9b0')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-c9626836-25e0-41dc-86cb-7609dff9c9b0 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-c9626836-25e0-41dc-86cb-7609dff9c9b0');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ],
      "source": [
        "# Loading test data\n",
        "data_2 = pd.read_csv ('Linear_test.csv')\n",
        "data_2\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data_2 = (data_2- data_2.mean())/ data_2.std()\n",
        "data_2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "id": "6f-JNo-NVPTX",
        "outputId": "2b5c6f56-b76a-46a6-c7bd-78adf19c2ad4"
      },
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0         A         B         C         D         E         F  \\\n",
              "0      -1.731791  1.418929 -1.103767 -1.015922  1.506075  0.505696  0.918187   \n",
              "1      -1.731445  1.667086 -0.025907  0.855964 -1.355878  0.583768 -0.359069   \n",
              "2      -1.731098  0.346227 -0.658120  0.030543  0.356360 -0.402730  1.227310   \n",
              "3      -1.730752  0.230482  1.351373  1.536195 -1.727122 -0.848506  0.556552   \n",
              "4      -1.730405 -0.133443 -1.301435  0.653749 -0.306639 -0.979253 -1.224722   \n",
              "...          ...       ...       ...       ...       ...       ...       ...   \n",
              "9995    1.730405 -1.298196 -1.045433  1.064242 -1.120155 -0.050730 -0.850676   \n",
              "9996    1.730752  0.763815 -1.521971 -0.343709  0.466706  0.114972 -1.247228   \n",
              "9997    1.731098 -1.192113  0.432326  0.940639 -0.028249 -0.827640 -1.206462   \n",
              "9998    1.731445 -1.054450  0.361014 -1.318619 -1.632784  0.644436  0.837757   \n",
              "9999    1.731791  1.383224 -0.503272 -0.270102  0.938989  1.525285 -0.529198   \n",
              "\n",
              "             G         H         I  ...         L         M         N  \\\n",
              "0    -1.198187 -0.526236  0.845059  ... -0.295410  0.727729 -1.543727   \n",
              "1    -0.832853 -1.210736 -1.481209  ... -0.090823 -0.623225  1.464723   \n",
              "2     0.904838  0.935132 -1.127843  ...  1.325556 -1.249150  0.826325   \n",
              "3     0.037571  1.509571  0.289185  ...  1.219185 -0.677047  0.878580   \n",
              "4     1.479978  0.152958  1.063170  ...  0.332278 -1.628082  1.520205   \n",
              "...        ...       ...       ...  ...       ...       ...       ...   \n",
              "9995 -1.507997  0.434078  1.258300  ...  0.887566 -0.503066 -0.039033   \n",
              "9996 -1.731568  0.949794  0.033950  ... -1.611512 -0.148788 -0.233870   \n",
              "9997  1.267932 -1.423614  0.846268  ...  1.382549 -1.101470 -0.195198   \n",
              "9998 -1.185012 -0.409351  1.420597  ... -0.648968 -1.694361 -0.716255   \n",
              "9999  0.144877  1.449927  0.262866  ... -1.169054  0.985732 -1.637015   \n",
              "\n",
              "             O         P         Q         R         S         T     label  \n",
              "0    -0.353886  1.462431 -0.384335 -0.695139 -0.194884 -0.976481 -0.360210  \n",
              "1    -0.709703  0.562143  0.307757  0.960890  0.745346 -0.839881  0.991163  \n",
              "2     0.109213  1.160055  0.439899 -1.600108 -1.728508  1.266911  0.159619  \n",
              "3    -0.288152 -1.490939 -0.614702  1.230399 -1.709591 -1.180386 -2.237108  \n",
              "4     1.159231  1.177294 -1.047281 -1.438335  0.931334 -0.780032  1.804781  \n",
              "...        ...       ...       ...       ...       ...       ...       ...  \n",
              "9995  0.304857 -0.593354  0.189058  0.961180 -1.465160 -1.605876 -1.856795  \n",
              "9996  0.062587  0.712221 -0.273894 -0.115420  1.385850 -0.612368  0.919826  \n",
              "9997 -1.595866 -1.152516 -0.804352 -0.251802 -0.885330  1.624859 -0.612402  \n",
              "9998 -0.970397  0.487047  1.384086  1.293853 -0.975894 -0.641588  0.073952  \n",
              "9999 -0.680099 -0.558860 -0.353848  1.327830 -0.100813 -1.339501 -1.571030  \n",
              "\n",
              "[10000 rows x 22 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a00b3fbc-7120-4b7f-80ce-c1ecda215a4c\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>A</th>\n",
              "      <th>B</th>\n",
              "      <th>C</th>\n",
              "      <th>D</th>\n",
              "      <th>E</th>\n",
              "      <th>F</th>\n",
              "      <th>G</th>\n",
              "      <th>H</th>\n",
              "      <th>I</th>\n",
              "      <th>...</th>\n",
              "      <th>L</th>\n",
              "      <th>M</th>\n",
              "      <th>N</th>\n",
              "      <th>O</th>\n",
              "      <th>P</th>\n",
              "      <th>Q</th>\n",
              "      <th>R</th>\n",
              "      <th>S</th>\n",
              "      <th>T</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.731791</td>\n",
              "      <td>1.418929</td>\n",
              "      <td>-1.103767</td>\n",
              "      <td>-1.015922</td>\n",
              "      <td>1.506075</td>\n",
              "      <td>0.505696</td>\n",
              "      <td>0.918187</td>\n",
              "      <td>-1.198187</td>\n",
              "      <td>-0.526236</td>\n",
              "      <td>0.845059</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.295410</td>\n",
              "      <td>0.727729</td>\n",
              "      <td>-1.543727</td>\n",
              "      <td>-0.353886</td>\n",
              "      <td>1.462431</td>\n",
              "      <td>-0.384335</td>\n",
              "      <td>-0.695139</td>\n",
              "      <td>-0.194884</td>\n",
              "      <td>-0.976481</td>\n",
              "      <td>-0.360210</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.731445</td>\n",
              "      <td>1.667086</td>\n",
              "      <td>-0.025907</td>\n",
              "      <td>0.855964</td>\n",
              "      <td>-1.355878</td>\n",
              "      <td>0.583768</td>\n",
              "      <td>-0.359069</td>\n",
              "      <td>-0.832853</td>\n",
              "      <td>-1.210736</td>\n",
              "      <td>-1.481209</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.090823</td>\n",
              "      <td>-0.623225</td>\n",
              "      <td>1.464723</td>\n",
              "      <td>-0.709703</td>\n",
              "      <td>0.562143</td>\n",
              "      <td>0.307757</td>\n",
              "      <td>0.960890</td>\n",
              "      <td>0.745346</td>\n",
              "      <td>-0.839881</td>\n",
              "      <td>0.991163</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.731098</td>\n",
              "      <td>0.346227</td>\n",
              "      <td>-0.658120</td>\n",
              "      <td>0.030543</td>\n",
              "      <td>0.356360</td>\n",
              "      <td>-0.402730</td>\n",
              "      <td>1.227310</td>\n",
              "      <td>0.904838</td>\n",
              "      <td>0.935132</td>\n",
              "      <td>-1.127843</td>\n",
              "      <td>...</td>\n",
              "      <td>1.325556</td>\n",
              "      <td>-1.249150</td>\n",
              "      <td>0.826325</td>\n",
              "      <td>0.109213</td>\n",
              "      <td>1.160055</td>\n",
              "      <td>0.439899</td>\n",
              "      <td>-1.600108</td>\n",
              "      <td>-1.728508</td>\n",
              "      <td>1.266911</td>\n",
              "      <td>0.159619</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.730752</td>\n",
              "      <td>0.230482</td>\n",
              "      <td>1.351373</td>\n",
              "      <td>1.536195</td>\n",
              "      <td>-1.727122</td>\n",
              "      <td>-0.848506</td>\n",
              "      <td>0.556552</td>\n",
              "      <td>0.037571</td>\n",
              "      <td>1.509571</td>\n",
              "      <td>0.289185</td>\n",
              "      <td>...</td>\n",
              "      <td>1.219185</td>\n",
              "      <td>-0.677047</td>\n",
              "      <td>0.878580</td>\n",
              "      <td>-0.288152</td>\n",
              "      <td>-1.490939</td>\n",
              "      <td>-0.614702</td>\n",
              "      <td>1.230399</td>\n",
              "      <td>-1.709591</td>\n",
              "      <td>-1.180386</td>\n",
              "      <td>-2.237108</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.730405</td>\n",
              "      <td>-0.133443</td>\n",
              "      <td>-1.301435</td>\n",
              "      <td>0.653749</td>\n",
              "      <td>-0.306639</td>\n",
              "      <td>-0.979253</td>\n",
              "      <td>-1.224722</td>\n",
              "      <td>1.479978</td>\n",
              "      <td>0.152958</td>\n",
              "      <td>1.063170</td>\n",
              "      <td>...</td>\n",
              "      <td>0.332278</td>\n",
              "      <td>-1.628082</td>\n",
              "      <td>1.520205</td>\n",
              "      <td>1.159231</td>\n",
              "      <td>1.177294</td>\n",
              "      <td>-1.047281</td>\n",
              "      <td>-1.438335</td>\n",
              "      <td>0.931334</td>\n",
              "      <td>-0.780032</td>\n",
              "      <td>1.804781</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>1.730405</td>\n",
              "      <td>-1.298196</td>\n",
              "      <td>-1.045433</td>\n",
              "      <td>1.064242</td>\n",
              "      <td>-1.120155</td>\n",
              "      <td>-0.050730</td>\n",
              "      <td>-0.850676</td>\n",
              "      <td>-1.507997</td>\n",
              "      <td>0.434078</td>\n",
              "      <td>1.258300</td>\n",
              "      <td>...</td>\n",
              "      <td>0.887566</td>\n",
              "      <td>-0.503066</td>\n",
              "      <td>-0.039033</td>\n",
              "      <td>0.304857</td>\n",
              "      <td>-0.593354</td>\n",
              "      <td>0.189058</td>\n",
              "      <td>0.961180</td>\n",
              "      <td>-1.465160</td>\n",
              "      <td>-1.605876</td>\n",
              "      <td>-1.856795</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>1.730752</td>\n",
              "      <td>0.763815</td>\n",
              "      <td>-1.521971</td>\n",
              "      <td>-0.343709</td>\n",
              "      <td>0.466706</td>\n",
              "      <td>0.114972</td>\n",
              "      <td>-1.247228</td>\n",
              "      <td>-1.731568</td>\n",
              "      <td>0.949794</td>\n",
              "      <td>0.033950</td>\n",
              "      <td>...</td>\n",
              "      <td>-1.611512</td>\n",
              "      <td>-0.148788</td>\n",
              "      <td>-0.233870</td>\n",
              "      <td>0.062587</td>\n",
              "      <td>0.712221</td>\n",
              "      <td>-0.273894</td>\n",
              "      <td>-0.115420</td>\n",
              "      <td>1.385850</td>\n",
              "      <td>-0.612368</td>\n",
              "      <td>0.919826</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>1.731098</td>\n",
              "      <td>-1.192113</td>\n",
              "      <td>0.432326</td>\n",
              "      <td>0.940639</td>\n",
              "      <td>-0.028249</td>\n",
              "      <td>-0.827640</td>\n",
              "      <td>-1.206462</td>\n",
              "      <td>1.267932</td>\n",
              "      <td>-1.423614</td>\n",
              "      <td>0.846268</td>\n",
              "      <td>...</td>\n",
              "      <td>1.382549</td>\n",
              "      <td>-1.101470</td>\n",
              "      <td>-0.195198</td>\n",
              "      <td>-1.595866</td>\n",
              "      <td>-1.152516</td>\n",
              "      <td>-0.804352</td>\n",
              "      <td>-0.251802</td>\n",
              "      <td>-0.885330</td>\n",
              "      <td>1.624859</td>\n",
              "      <td>-0.612402</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>1.731445</td>\n",
              "      <td>-1.054450</td>\n",
              "      <td>0.361014</td>\n",
              "      <td>-1.318619</td>\n",
              "      <td>-1.632784</td>\n",
              "      <td>0.644436</td>\n",
              "      <td>0.837757</td>\n",
              "      <td>-1.185012</td>\n",
              "      <td>-0.409351</td>\n",
              "      <td>1.420597</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.648968</td>\n",
              "      <td>-1.694361</td>\n",
              "      <td>-0.716255</td>\n",
              "      <td>-0.970397</td>\n",
              "      <td>0.487047</td>\n",
              "      <td>1.384086</td>\n",
              "      <td>1.293853</td>\n",
              "      <td>-0.975894</td>\n",
              "      <td>-0.641588</td>\n",
              "      <td>0.073952</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>1.731791</td>\n",
              "      <td>1.383224</td>\n",
              "      <td>-0.503272</td>\n",
              "      <td>-0.270102</td>\n",
              "      <td>0.938989</td>\n",
              "      <td>1.525285</td>\n",
              "      <td>-0.529198</td>\n",
              "      <td>0.144877</td>\n",
              "      <td>1.449927</td>\n",
              "      <td>0.262866</td>\n",
              "      <td>...</td>\n",
              "      <td>-1.169054</td>\n",
              "      <td>0.985732</td>\n",
              "      <td>-1.637015</td>\n",
              "      <td>-0.680099</td>\n",
              "      <td>-0.558860</td>\n",
              "      <td>-0.353848</td>\n",
              "      <td>1.327830</td>\n",
              "      <td>-0.100813</td>\n",
              "      <td>-1.339501</td>\n",
              "      <td>-1.571030</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 22 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a00b3fbc-7120-4b7f-80ce-c1ecda215a4c')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-a00b3fbc-7120-4b7f-80ce-c1ecda215a4c 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-a00b3fbc-7120-4b7f-80ce-c1ecda215a4c');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "id": "pGFDZWixDUww"
      },
      "outputs": [],
      "source": [
        "# Seperating the x and y matrices\n",
        "# Like in the training set\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "X_3 = data_2.iloc[:,1:21] # for m x n dimensional \n",
        "ones = np.ones([X_3.shape[0],1]) #This is done because for convinience X_0 is considered to have entering of only 1(for simplicity)\n",
        "X_3 = np.concatenate ((ones , X_3) , axis=1)\n",
        "\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "y_2 = data_2.iloc[:,21:22].values\n",
        " \n",
        "# Matrice of theta(Coefficient of features in hypothesis function) of the dimension (n+1) * 1\n",
        "theta= np.array(g)\n",
        "\n",
        "# Set hyperparameters\n",
        "alpha_2 = Alpha\n",
        "iters_2 = iters\n",
        "\n",
        "X_4 = data_2.iloc[:,0:1]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "X8wjrqN-Ki3b",
        "outputId": "220dff3f-8751-4542-cb8a-4334b2efa66f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f045bcf9b10>"
            ]
          },
          "metadata": {},
          "execution_count": 66
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "pp.scatter(X_4,y_2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4RcEbFKSEZvT"
      },
      "source": [
        "For training and test dataset the value of coefficient and final cost value came out to be the same. Hence, Linear regression fits the data well."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zgvxy0VXcQWD",
        "outputId": "089d5864-19f0-43a9-9627-a65f278b73e5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.35826985]\n",
            " [ 0.98827079]\n",
            " [ 0.15887224]\n",
            " ...\n",
            " [-0.61417458]\n",
            " [ 0.07496795]\n",
            " [-1.56555332]]\n"
          ]
        }
      ],
      "source": [
        "# Y values (or Labels) can be found by multiplying the arrays of x and theta which is g(gradient)\n",
        "y_3 = X_3.dot(g.T)\n",
        "print(y_3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k2R_xdQXfusc",
        "outputId": "81ab8eb4-9bad-4824-fea0-a4fa3c0eaea6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.36020969]\n",
            " [ 0.99116316]\n",
            " [ 0.15961937]\n",
            " ...\n",
            " [-0.61240221]\n",
            " [ 0.07395223]\n",
            " [-1.57102966]]\n"
          ]
        }
      ],
      "source": [
        "print(y_2)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculating the value of RMSE\n",
        "np.sqrt(np.sum(((y_2-y_3)**2).mean()))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J4g2LYaoyteQ",
        "outputId": "1cdbdf6b-2a4d-4871-f646-76ccfb4d8350"
      },
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0027827950941184372"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "What is a good RMSE value?\n",
        "\n",
        "The short answer: `**It depends**.`\n",
        "<br><br>\n",
        "The lower the RMSE, the better a given model is able to “fit” a dataset. However, the range of the dataset you’re working with is important in determining whether or not a given RMSE value is “low” or not.\n",
        "<br><br>\n",
        "Going by this logic as the value of y_test is small and the rmse is very very small so it shows the model is working well and fits the data well."
      ],
      "metadata": {
        "id": "N2_Uk_QOVxpf"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jl9jsJw-gPl0"
      },
      "source": [
        "As the results of y predicted by the hypothesis function is same as that of the labels given in the dataset. Hence, proved that the linear regression is the perfect choice for the dataset provided."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "5-Ol-hhlErBy",
        "outputId": "9da58aa9-27d5-4cc4-e84f-b723a77f9157"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 70
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#plot the cost\n",
        "fig, ax = pp.subplots()  \n",
        "ax.plot(np.arange(iters), cost, 'r')  \n",
        "ax.set_xlabel('Iterations')  \n",
        "ax.set_ylabel('Cost')  \n",
        "ax.set_title('Error vs. Training Epoch')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BlsCLuvDE4LD"
      },
      "source": [
        "Here too the cost function is static after 300-400 iteration. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RDJ3BnZoFGmj"
      },
      "source": [
        "# <b> Plotting (Linear Regression)\n",
        "ploting the datasets training and test \n",
        "and then them together."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        },
        "id": "klPJa16jO08N",
        "outputId": "1ea248ee-504f-4466-bcd4-5e1370a4a63d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig = pp.figure()\n",
        "ax1 = fig.add_subplot(111)\n",
        "ax1.scatter(X_2, y_1, s = 10, c = 'b', label = 'training set')\n",
        "ax1.scatter(X_4, y_2, s = 10, c = 'r', label = 'test set')\n",
        "pp.legend(loc='upper right');\n",
        "pp.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFURaDI4FPKJ"
      },
      "source": [
        "# Polynomial Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yuthU9YaFUTQ"
      },
      "source": [
        "The Algorithm\n",
        "* Modify the hypothesis function of Linear Regression according to the data you have.\n",
        "* Add new higher (whichever) degree features you want to the input.\n",
        "* Do the Gradient Descent/mini-batch Gradient Descent to the modified input to find the parameters — weights and bias.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ycpoq1r5B9-6"
      },
      "source": [
        "### Training Set"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 103,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "eAhhHPi3GslW",
        "outputId": "f1c87c47-b7eb-4564-94d0-3b115cda7fae"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Unnamed: 0         X         Y         Z        label\n",
              "0               0  0.643715 -9.866550 -5.836019   307.972927\n",
              "1               1 -1.366446 -3.761945 -8.756162   136.398375\n",
              "2               2 -4.090270 -1.836218 -1.846066  -310.724813\n",
              "3               3 -8.730478 -1.923651  3.892972     1.755447\n",
              "4               4  5.367169  0.358357  6.703989  -343.582590\n",
              "...           ...       ...       ...       ...          ...\n",
              "49995       49995  2.693877 -1.362685 -7.392968   683.405727\n",
              "49996       49996 -9.270188 -5.456920 -2.343480 -1874.385403\n",
              "49997       49997  6.616753 -2.847288 -0.504040   663.873655\n",
              "49998       49998  3.558199  4.507526 -4.823674  -421.004005\n",
              "49999       49999  0.623431  8.863234 -3.231040  -699.718682\n",
              "\n",
              "[50000 rows x 5 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-67b767ba-6197-48a4-9ef5-74bbcdb3e347\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>X</th>\n",
              "      <th>Y</th>\n",
              "      <th>Z</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.643715</td>\n",
              "      <td>-9.866550</td>\n",
              "      <td>-5.836019</td>\n",
              "      <td>307.972927</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>-1.366446</td>\n",
              "      <td>-3.761945</td>\n",
              "      <td>-8.756162</td>\n",
              "      <td>136.398375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>-4.090270</td>\n",
              "      <td>-1.836218</td>\n",
              "      <td>-1.846066</td>\n",
              "      <td>-310.724813</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>-8.730478</td>\n",
              "      <td>-1.923651</td>\n",
              "      <td>3.892972</td>\n",
              "      <td>1.755447</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>5.367169</td>\n",
              "      <td>0.358357</td>\n",
              "      <td>6.703989</td>\n",
              "      <td>-343.582590</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\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>49995</td>\n",
              "      <td>2.693877</td>\n",
              "      <td>-1.362685</td>\n",
              "      <td>-7.392968</td>\n",
              "      <td>683.405727</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49996</th>\n",
              "      <td>49996</td>\n",
              "      <td>-9.270188</td>\n",
              "      <td>-5.456920</td>\n",
              "      <td>-2.343480</td>\n",
              "      <td>-1874.385403</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49997</th>\n",
              "      <td>49997</td>\n",
              "      <td>6.616753</td>\n",
              "      <td>-2.847288</td>\n",
              "      <td>-0.504040</td>\n",
              "      <td>663.873655</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49998</th>\n",
              "      <td>49998</td>\n",
              "      <td>3.558199</td>\n",
              "      <td>4.507526</td>\n",
              "      <td>-4.823674</td>\n",
              "      <td>-421.004005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49999</th>\n",
              "      <td>49999</td>\n",
              "      <td>0.623431</td>\n",
              "      <td>8.863234</td>\n",
              "      <td>-3.231040</td>\n",
              "      <td>-699.718682</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>50000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-67b767ba-6197-48a4-9ef5-74bbcdb3e347')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-67b767ba-6197-48a4-9ef5-74bbcdb3e347 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-67b767ba-6197-48a4-9ef5-74bbcdb3e347');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ],
      "source": [
        "data_3 = pd.read_csv('Polynomial_train.csv')\n",
        "data_3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VcWnnLOmxtaq"
      },
      "source": [
        "Normalizing the values of dataset to speed up the gradient descent process."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "5FE14POaJSjN",
        "outputId": "d8c2f434-57fd-42e9-a40b-4acf4696f04c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Unnamed: 0         X         Y         Z     label\n",
              "0       -1.731999  0.105753 -1.697386 -1.010452  0.244413\n",
              "1       -1.731930 -0.242734 -0.643264 -1.515023  0.102123\n",
              "2       -1.731860 -0.714943 -0.310736 -0.321029 -0.268685\n",
              "3       -1.731791 -1.519383 -0.325833  0.670617 -0.009539\n",
              "4       -1.731722  0.924624  0.068216  1.156332 -0.295934\n",
              "...           ...       ...       ...       ...       ...\n",
              "49995    1.731722  0.461175 -0.228968 -1.279477  0.555767\n",
              "49996    1.731791 -1.612949 -0.935946 -0.406977 -1.565458\n",
              "49997    1.731860  1.141256 -0.485324 -0.089141  0.539568\n",
              "49998    1.731930  0.611016  0.784680 -0.835529 -0.360141\n",
              "49999    1.731999  0.102237  1.536809 -0.560339 -0.591285\n",
              "\n",
              "[50000 rows x 5 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-176af266-fcc9-4f18-9a71-04764588c2d8\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>X</th>\n",
              "      <th>Y</th>\n",
              "      <th>Z</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.731999</td>\n",
              "      <td>0.105753</td>\n",
              "      <td>-1.697386</td>\n",
              "      <td>-1.010452</td>\n",
              "      <td>0.244413</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.731930</td>\n",
              "      <td>-0.242734</td>\n",
              "      <td>-0.643264</td>\n",
              "      <td>-1.515023</td>\n",
              "      <td>0.102123</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.731860</td>\n",
              "      <td>-0.714943</td>\n",
              "      <td>-0.310736</td>\n",
              "      <td>-0.321029</td>\n",
              "      <td>-0.268685</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.731791</td>\n",
              "      <td>-1.519383</td>\n",
              "      <td>-0.325833</td>\n",
              "      <td>0.670617</td>\n",
              "      <td>-0.009539</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.731722</td>\n",
              "      <td>0.924624</td>\n",
              "      <td>0.068216</td>\n",
              "      <td>1.156332</td>\n",
              "      <td>-0.295934</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\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>1.731722</td>\n",
              "      <td>0.461175</td>\n",
              "      <td>-0.228968</td>\n",
              "      <td>-1.279477</td>\n",
              "      <td>0.555767</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49996</th>\n",
              "      <td>1.731791</td>\n",
              "      <td>-1.612949</td>\n",
              "      <td>-0.935946</td>\n",
              "      <td>-0.406977</td>\n",
              "      <td>-1.565458</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49997</th>\n",
              "      <td>1.731860</td>\n",
              "      <td>1.141256</td>\n",
              "      <td>-0.485324</td>\n",
              "      <td>-0.089141</td>\n",
              "      <td>0.539568</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49998</th>\n",
              "      <td>1.731930</td>\n",
              "      <td>0.611016</td>\n",
              "      <td>0.784680</td>\n",
              "      <td>-0.835529</td>\n",
              "      <td>-0.360141</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49999</th>\n",
              "      <td>1.731999</td>\n",
              "      <td>0.102237</td>\n",
              "      <td>1.536809</td>\n",
              "      <td>-0.560339</td>\n",
              "      <td>-0.591285</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>50000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-176af266-fcc9-4f18-9a71-04764588c2d8')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-176af266-fcc9-4f18-9a71-04764588c2d8 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-176af266-fcc9-4f18-9a71-04764588c2d8');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ],
      "source": [
        "data_3 = (data_3 - data_3.mean())/ data_3.std()\n",
        "data_3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 105,
      "metadata": {
        "id": "GeUcz8B-Hb-k"
      },
      "outputs": [],
      "source": [
        "# Seperating the x and y matrices\n",
        "\n",
        "# Like in the training set\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "x= data_3.iloc[:,1:2].values # for m x 1 dimensional \n",
        "\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "Y = data_3.iloc[:,2:3].values\n",
        "\n",
        "# z-matrice is supposed to be a m x 1 dimensional matrice\n",
        "Z = data_3.iloc[:,3:4].values\n",
        " \n",
        "# Label matrices is supposed to a m x 1 dimensional matrice\n",
        "Label_1 = data_3.iloc[:,4:5].values"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(Z.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "POJHkY5I8M-T",
        "outputId": "0d6adebe-495d-4e8d-ca00-4030de6f14da"
      },
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(50000, 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 107,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "zKddtCIqIrB2",
        "outputId": "b92e9789-8a3e-4be3-c234-54c7b3421e3d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f0459cef4d0>"
            ]
          },
          "metadata": {},
          "execution_count": 107
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "pp.scatter(x,Label_1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mwNFbIfDJYI5"
      },
      "source": [
        "A three degree function clearly seems to be the best choice for the hypothesis curve. Hence the highest degree of each term in the hypothesis can be 3."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wgbrJQR8yHu5"
      },
      "source": [
        "` Hypothesis function` for polynomial regression will seem like this:\n",
        "\n",
        "<b> h_theta (x,y,z) = theta_0 + theta_1 * x + theta_2 * y + theta_3 * z + theta_4 * x^2 + theta_5 * y^2 + theta_6 * z^2 + theta_7 * xy + theta_8 * yz + theta_9 * zx + theta_10 * x^3 + theta_11 * y^3 + theta_12 * z^3 + theta_13 * x^2(y) + theta_14 * x^2(z) + theta_15 * y^2(z) + theta_16 * y^2(x) + theta_17 * z^2(x) + theta_18 * z^2(y)+ theta_19 * xyz"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 143,
      "metadata": {
        "id": "_CH2qYuN2FRF"
      },
      "outputs": [],
      "source": [
        "# Here we will construct the features matrix(X_5). \n",
        "# First we will create the individual columns and then append them together.\n",
        "\n",
        "# x_0 for simplicity is considered to be 1 matrices.\n",
        "ones = np.ones([x.shape[0],1]) #Dimension is m x 1\n",
        "x_0 = ones\n",
        "\n",
        "# x_1 is simply the x feature given in the dataset\n",
        "x_1 = x\n",
        "\n",
        "# x_2 is simply the y feature given in the dataset\n",
        "x_2 = Y\n",
        "\n",
        "# x_3 is simply the z feature given in the dataset\n",
        "x_3 = Z\n",
        "\n",
        "# x_4 is square of the x feature given in the dataset\n",
        "x_4 = x**2\n",
        "\n",
        "# x_5 is square of the y feature given in the dataset \n",
        "x_5 = Y**2\n",
        "\n",
        "# x_6 is square of the z feature given in the dataset \n",
        "x_6 = Z**2\n",
        "\n",
        "# x_7 is the multiplycation of x and y matrice \n",
        "x_7 = x*(Y)\n",
        "\n",
        "# x_8 is the multiplication of y and z matrice \n",
        "x_8 = Y*(Z)\n",
        "\n",
        "# x_9 is the multiplication of z and x matrice\n",
        "x_9 = Z*(x)\n",
        "\n",
        "# x_10 is the cube of the x feature given in the dataset\n",
        "x_10 = x**3\n",
        "\n",
        "# x_11 is the cube of the y feature given in the dataset\n",
        "x_11 = Y**3\n",
        "\n",
        "# x_12 is the cube of the z feature given in the dataset\n",
        "x_12 = Z**3\n",
        "\n",
        "# x_13 is the multiplication of square of x and y matrice\n",
        "x_13 = (x**2)*Y\n",
        "\n",
        "# x_14 is the multiplication of square of x and z matrice\n",
        "x_14 = (x**2)*Z\n",
        "\n",
        "# x_15 is the multplication of square of y and x matrice\n",
        "x_15 = (Y**2)*x\n",
        "\n",
        "# x_16 is the multiplication of square of y and z matrice\n",
        "x_16 = (Y**2)*Z\n",
        "\n",
        "# x_17 is the multiplication of square of z and x matrice\n",
        "x_17 = (Z**2)*x\n",
        "\n",
        "# x_18 is the multiplication of square of z and y matrice \n",
        "x_18 = (Z**2)*Y\n",
        "\n",
        "# x_19 is the multiplcation of all three features givven in the dataset x,y and z\n",
        "x_19 = (x*Y)*Z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 144,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b3NaRih6-kLx",
        "outputId": "a05f3ffd-1a43-4c84-ce63-3d4569f40f4f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1.          0.1057533  -1.69738613 ...  0.10797556 -1.73305432\n",
            "   0.1813804 ]\n",
            " [ 1.         -0.2427338  -0.64326391 ... -0.55714537 -1.47647961\n",
            "  -0.23655851]\n",
            " [ 1.         -0.71494348 -0.31073582 ... -0.07368195 -0.03202438\n",
            "  -0.07131941]\n",
            " ...\n",
            " [ 1.          1.1412558  -0.48532404 ...  0.00906858 -0.00385646\n",
            "   0.0493734 ]\n",
            " [ 1.          0.61101634  0.78468006 ...  0.42655612  0.54779235\n",
            "  -0.40059647]\n",
            " [ 1.          0.10223675  1.53680881 ...  0.03210022  0.48252616\n",
            "  -0.08803946]]\n"
          ]
        }
      ],
      "source": [
        "# Appending the featueres together\n",
        "X_5 = np.concatenate((x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_10,x_11,x_12,x_13,x_14,x_15,x_16,x_17,x_18,x_19),axis=1)\n",
        "X_5 = np.asarray(X_5)\n",
        "print(X_5)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X_5.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TTHA_1a0apul",
        "outputId": "494b4321-27cf-4aaa-b433-2d137de2e3fb"
      },
      "execution_count": 145,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 20)"
            ]
          },
          "metadata": {},
          "execution_count": 145
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 146,
      "metadata": {
        "id": "VaVEsmkaAe3I"
      },
      "outputs": [],
      "source": [
        "# Matrice of theta(coefficient of the features in hypothesis function) is supposed to a 1 x (n+1) dimensional matrice\n",
        "theta = np.zeros([1,20])"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Setting Hyperparameters\n",
        "Alpha = 0.01 #@param {type:\"slider\", min:0, max:1, step:0.01}\n",
        "iters = 1000 #@param {type:\"slider\", min:100, max:3000, step:100}\n",
        "alpha_3 = Alpha\n",
        "iters_3 = iters"
      ],
      "metadata": {
        "id": "HnK0ohbkii1l"
      },
      "execution_count": 147,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 148,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BteM8a_HAYOO",
        "outputId": "306c8561-9174-4e26-9f54-aab6ce9ce078"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-1.02924437e-02 -1.69292464e-03 -2.69648691e-03 -2.95285309e-03\n",
            "   2.79547706e-02 -1.39395077e-01  1.10662986e-01 -8.86373525e-01\n",
            "   1.94524577e-01 -3.87654946e-01  4.45668665e-03 -4.20096320e-04\n",
            "   2.08186229e-04  6.24350352e-04 -6.11516413e-04 -3.78593517e-04\n",
            "   7.93289452e-05 -4.41822750e-04 -9.46198495e-05 -1.45516679e-04]]\n",
            "2.5754531047527503e-05\n"
          ]
        }
      ],
      "source": [
        "#running the gd and cost function\n",
        "g,cost = gradientDescent(X_5,Label_1,theta,iters_3,alpha_3)\n",
        "print(g)\n",
        "\n",
        "finalCost = computeCost(X_5,Label_1,g)\n",
        "print(finalCost)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 149,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "_KkWVjtUBZZo",
        "outputId": "067b374a-f0fa-4253-97dd-a27c16796a92"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 149
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#plot the cost\n",
        "fig, ax = pp.subplots()  \n",
        "ax.plot(np.arange(iters), cost, 'r')  \n",
        "ax.set_xlabel('Iterations')  \n",
        "ax.set_ylabel('Cost')  \n",
        "ax.set_title('Error vs. Training Epoch')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ufFiHB2KBze8"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pQLlTaKxB0Yp"
      },
      "source": [
        "### Test Set"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 150,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "YE74MQ2kCFKO",
        "outputId": "cca11429-02fa-49d5-aa8f-526406ceda9b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0         X         Y         Z        label\n",
              "0              0  9.322078  0.413096  5.984731  -657.669309\n",
              "1              1  2.811964  6.142752  6.419237  -545.362524\n",
              "2              2 -2.669784  7.775091 -6.931907   -75.044187\n",
              "3              3 -6.992156 -9.205548  0.852580 -2403.124902\n",
              "4              4  1.574294 -2.213266  6.029188     8.595325\n",
              "...          ...       ...       ...       ...          ...\n",
              "9995        9995 -0.992449 -7.853677  7.748156  -635.006038\n",
              "9996        9996  8.574451  6.271919 -5.734962 -1275.855209\n",
              "9997        9997  6.640997  6.864877  4.511685 -1771.640694\n",
              "9998        9998 -6.262414  1.323203 -3.917748   -22.746921\n",
              "9999        9999  8.289792 -0.371541  2.099039   -64.853446\n",
              "\n",
              "[10000 rows x 5 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a134f9a2-5e0b-4ed0-ad88-983180abf440\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>X</th>\n",
              "      <th>Y</th>\n",
              "      <th>Z</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>9.322078</td>\n",
              "      <td>0.413096</td>\n",
              "      <td>5.984731</td>\n",
              "      <td>-657.669309</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>2.811964</td>\n",
              "      <td>6.142752</td>\n",
              "      <td>6.419237</td>\n",
              "      <td>-545.362524</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>-2.669784</td>\n",
              "      <td>7.775091</td>\n",
              "      <td>-6.931907</td>\n",
              "      <td>-75.044187</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>-6.992156</td>\n",
              "      <td>-9.205548</td>\n",
              "      <td>0.852580</td>\n",
              "      <td>-2403.124902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1.574294</td>\n",
              "      <td>-2.213266</td>\n",
              "      <td>6.029188</td>\n",
              "      <td>8.595325</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\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>9995</td>\n",
              "      <td>-0.992449</td>\n",
              "      <td>-7.853677</td>\n",
              "      <td>7.748156</td>\n",
              "      <td>-635.006038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>9996</td>\n",
              "      <td>8.574451</td>\n",
              "      <td>6.271919</td>\n",
              "      <td>-5.734962</td>\n",
              "      <td>-1275.855209</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>9997</td>\n",
              "      <td>6.640997</td>\n",
              "      <td>6.864877</td>\n",
              "      <td>4.511685</td>\n",
              "      <td>-1771.640694</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>9998</td>\n",
              "      <td>-6.262414</td>\n",
              "      <td>1.323203</td>\n",
              "      <td>-3.917748</td>\n",
              "      <td>-22.746921</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>9999</td>\n",
              "      <td>8.289792</td>\n",
              "      <td>-0.371541</td>\n",
              "      <td>2.099039</td>\n",
              "      <td>-64.853446</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a134f9a2-5e0b-4ed0-ad88-983180abf440')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-a134f9a2-5e0b-4ed0-ad88-983180abf440 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-a134f9a2-5e0b-4ed0-ad88-983180abf440');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 150
        }
      ],
      "source": [
        "data_4 = pd.read_csv('Polynomial_test.csv')\n",
        "data_4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vSFcZ1KmChcp"
      },
      "source": [
        "Normalizing the dataset "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 151,
      "metadata": {
        "id": "RXTQCobCCgU2"
      },
      "outputs": [],
      "source": [
        "# Seperating the columns provided in the dataset.\n",
        "\n",
        "# Like in the training set\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "x_test= data_3.iloc[:,1:2] # for m x 1 dimensional \n",
        "\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "Y_test = data_3.iloc[:,2:3].values\n",
        "\n",
        "# z-matrice is supposed to be a m x 1 dimensional matrice\n",
        "Z_test = data_3.iloc[:,3:4].values\n",
        " \n",
        "# Label matrices is supposed to a m x 1 dimensional matrice\n",
        "Label_2 = data_3.iloc[:,4:5].values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 152,
      "metadata": {
        "id": "k6CTKy_VDXqH"
      },
      "outputs": [],
      "source": [
        "# Here we will construct the features matrix(X_6). \n",
        "# First we will create the individual columns and then append them together.\n",
        "\n",
        "# x_0 for simplicity is considered to be 1 matrices.\n",
        "ones = np.ones([x_test.shape[0],1]) #Dimension is m x 1\n",
        "x_0 = ones\n",
        "\n",
        "# x_1 is simply the x feature given in the dataset\n",
        "x_1 = x_test\n",
        "\n",
        "# x_2 is simply the y feature given in the dataset\n",
        "x_2 = Y_test\n",
        "\n",
        "# x_3 is simply the z feature given in the dataset\n",
        "x_3 = Z_test\n",
        "\n",
        "# x_4 is square of the x feature given in the dataset\n",
        "x_4 = x_test**2\n",
        "\n",
        "# x_5 is square of the y feature given in the dataset \n",
        "x_5 = Y_test**2\n",
        "\n",
        "# x_6 is square of the z feature given in the dataset \n",
        "x_6 = Z_test**2\n",
        "\n",
        "# x_7 is the multiplycation of x and y matrice \n",
        "x_7 = x_test*(Y_test)\n",
        "\n",
        "# x_8 is the multiplication of y and z matrice \n",
        "x_8 = Y_test*(Z_test)\n",
        "\n",
        "# x_9 is the multiplication of z and x matrice\n",
        "x_9 = Z_test*(x_test)\n",
        "\n",
        "# x_10 is the cube of the x feature given in the dataset\n",
        "x_10 = x_test**3\n",
        "\n",
        "# x_11 is the cube of the y feature given in the dataset\n",
        "x_11 = Y_test**3\n",
        "\n",
        "# x_12 is the cube of the z feature given in the dataset\n",
        "x_12 = Z_test**3\n",
        "\n",
        "# x_13 is the multiplication of square of x and y matrice\n",
        "x_13 = (x_test**2)*Y_test\n",
        "\n",
        "# x_14 is the multiplication of square of x and z matrice\n",
        "x_14 = (x_test**2)*Z_test\n",
        "\n",
        "# x_15 is the multplication of square of y and x matrice\n",
        "x_15 = (Y_test**2)*x_test\n",
        "\n",
        "# x_16 is the multiplication of square of y and z matrice\n",
        "x_16 = (Y_test**2)*Z_test\n",
        "\n",
        "# x_17 is the multiplication of square of z and x matrice\n",
        "x_17 = (Z_test**2)*x_test\n",
        "\n",
        "# x_18 is the multiplication of square of z and y matrice \n",
        "x_18 = (Z_test**2)*Y_test\n",
        "\n",
        "# x_19 is the multiplcation of all three features givven in the dataset x,y and z\n",
        "x_19 = (x_test*Y_test)*Z_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 153,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nEv1xKCLEG1l",
        "outputId": "5a1f56af-e1b2-4422-9054-b6712ae8803f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1.          0.1057533  -1.69738613 ...  0.10797556 -1.73305432\n",
            "   0.1813804 ]\n",
            " [ 1.         -0.2427338  -0.64326391 ... -0.55714537 -1.47647961\n",
            "  -0.23655851]\n",
            " [ 1.         -0.71494348 -0.31073582 ... -0.07368195 -0.03202438\n",
            "  -0.07131941]\n",
            " ...\n",
            " [ 1.          1.1412558  -0.48532404 ...  0.00906858 -0.00385646\n",
            "   0.0493734 ]\n",
            " [ 1.          0.61101634  0.78468006 ...  0.42655612  0.54779235\n",
            "  -0.40059647]\n",
            " [ 1.          0.10223675  1.53680881 ...  0.03210022  0.48252616\n",
            "  -0.08803946]]\n"
          ]
        }
      ],
      "source": [
        "X_6= np.concatenate((x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_10,x_11,x_12,x_13,x_14,x_15,x_16,x_17,x_18,x_19),axis=1)\n",
        "X_6 = np.asarray(X_6)\n",
        "print(X_6)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 154,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "Kp9v5FIECkY9",
        "outputId": "7ae1fa20-f748-426e-c426-aca42fb8e11e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0         X         Y         Z     label\n",
              "0      -1.731791  1.602895  0.057199  1.034578 -0.563902\n",
              "1      -1.731445  0.474656  1.049657  1.109700 -0.470760\n",
              "2      -1.731098 -0.475360  1.332401 -1.198596 -0.080700\n",
              "3      -1.730752 -1.224451 -1.608887  0.147274 -2.011504\n",
              "4      -1.730405  0.260161 -0.397724  1.042264 -0.011333\n",
              "...          ...       ...       ...       ...       ...\n",
              "9995    1.730405 -0.184669 -1.374724  1.339458 -0.545107\n",
              "9996    1.730752  1.473327  1.072031 -0.991655 -1.076598\n",
              "9997    1.731098  1.138249  1.174739  0.779901 -1.487780\n",
              "9998    1.731445 -1.097983  0.214842 -0.677474 -0.037327\n",
              "9999    1.731791  1.423994 -0.078711  0.362776 -0.072248\n",
              "\n",
              "[10000 rows x 5 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-3bad6f1b-d227-4865-910f-3fc9082231dc\">\n",
              "    <div 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>Unnamed: 0</th>\n",
              "      <th>X</th>\n",
              "      <th>Y</th>\n",
              "      <th>Z</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.731791</td>\n",
              "      <td>1.602895</td>\n",
              "      <td>0.057199</td>\n",
              "      <td>1.034578</td>\n",
              "      <td>-0.563902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.731445</td>\n",
              "      <td>0.474656</td>\n",
              "      <td>1.049657</td>\n",
              "      <td>1.109700</td>\n",
              "      <td>-0.470760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.731098</td>\n",
              "      <td>-0.475360</td>\n",
              "      <td>1.332401</td>\n",
              "      <td>-1.198596</td>\n",
              "      <td>-0.080700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.730752</td>\n",
              "      <td>-1.224451</td>\n",
              "      <td>-1.608887</td>\n",
              "      <td>0.147274</td>\n",
              "      <td>-2.011504</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.730405</td>\n",
              "      <td>0.260161</td>\n",
              "      <td>-0.397724</td>\n",
              "      <td>1.042264</td>\n",
              "      <td>-0.011333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\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>1.730405</td>\n",
              "      <td>-0.184669</td>\n",
              "      <td>-1.374724</td>\n",
              "      <td>1.339458</td>\n",
              "      <td>-0.545107</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>1.730752</td>\n",
              "      <td>1.473327</td>\n",
              "      <td>1.072031</td>\n",
              "      <td>-0.991655</td>\n",
              "      <td>-1.076598</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>1.731098</td>\n",
              "      <td>1.138249</td>\n",
              "      <td>1.174739</td>\n",
              "      <td>0.779901</td>\n",
              "      <td>-1.487780</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>1.731445</td>\n",
              "      <td>-1.097983</td>\n",
              "      <td>0.214842</td>\n",
              "      <td>-0.677474</td>\n",
              "      <td>-0.037327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>1.731791</td>\n",
              "      <td>1.423994</td>\n",
              "      <td>-0.078711</td>\n",
              "      <td>0.362776</td>\n",
              "      <td>-0.072248</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3bad6f1b-d227-4865-910f-3fc9082231dc')\"\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 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-3bad6f1b-d227-4865-910f-3fc9082231dc 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-3bad6f1b-d227-4865-910f-3fc9082231dc');\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",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 154
        }
      ],
      "source": [
        "data_4 = (data_4 - data_4.mean())/data_4.std()\n",
        "data_4"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 155,
      "metadata": {
        "id": "QA6kjcqTD_M2"
      },
      "outputs": [],
      "source": [
        "# Matrice of theta(coefficient of the features in hypothesis function) is supposed to a 1 x (n+1) dimensional matrice\n",
        "theta = np.array(g)\n",
        "\n",
        "# Setting hyperparameters \n",
        "alpha = alpha_3\n",
        "iters = iters_3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 156,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cBL3iYOQERh1",
        "outputId": "1c575dce-2a68-4620-be8f-afcc1f36f7a3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(50000, 20)\n",
            "(1, 20)\n",
            "(20, 1)\n"
          ]
        }
      ],
      "source": [
        "print(X_6.shape)\n",
        "print(theta.shape)\n",
        "print(theta.T.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 157,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "heVKYBGXFqX0",
        "outputId": "69c1e1fa-1897-4f11-ec48-41da32367e57"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 0.24452644]\n",
            " [ 0.10267807]\n",
            " [-0.26309839]\n",
            " ...\n",
            " [ 0.53883478]\n",
            " [-0.36301437]\n",
            " [-0.59349343]]\n"
          ]
        }
      ],
      "source": [
        "# Y values (or Labels) can be found by multiplying the arrays of x and theta which is g(gradient)\n",
        "y_4 = X_6.dot(theta.T)\n",
        "print(y_4) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 158,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5EoHiLkoLkC4",
        "outputId": "5622ef82-11eb-4a55-d07a-83d9dabec37a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 0.24441308]\n",
            " [ 0.10212305]\n",
            " [-0.26868471]\n",
            " ...\n",
            " [ 0.53956832]\n",
            " [-0.36014133]\n",
            " [-0.59128471]]\n"
          ]
        }
      ],
      "source": [
        "print(Label_2)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#combined rmse value\n",
        "rss=((Label_2-y_4)**2).sum()\n",
        "mse=np.mean((Label_2-y_4)**2)\n",
        "print(\"Final rmse value is =\",np.sqrt(np.mean((Label_2-y_4)**2)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RhFm7soo4naF",
        "outputId": "14833802-0aa8-4303-fe22-04d91d6740d3"
      },
      "execution_count": 159,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final rmse value is = 0.007176981405511304\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cHl942CHLwlb"
      },
      "source": [
        "# Plotting (Polynomial Regression)\n",
        "Plotting traing dataset and test dataset together"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 160,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "emTrrKGIL95w",
        "outputId": "67c40a08-6b50-4a59-8d2f-89ae1574aede"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig = pp.figure()\n",
        "ax1 = fig.add_subplot(111)\n",
        "ax1.scatter(x, Label_1, s = 10, c = 'b', label = 'training set')\n",
        "ax1.scatter(x_test, Label_2, s = 10, c = 'r', label = 'test set')\n",
        "pp.legend(loc='upper right');\n",
        "pp.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Regression (Linear , Polynomial) .ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}