14_snp_physical_predictors_with_sumat_PCR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <p style=\"text-align: justify;\"><div class=\"alert alert-info\" role=\"alert\">Multiple Linear Regression with genetic and physical predictors with Sumat predictor as unique fat fold predictor coupled with Principal Components Analysis</div></p>\n",
    "\n",
    "## `Ana González Guerra` \n",
    "\n",
    "### ` Student of the master in Data Science at the University of Cantabria` "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Index<a class=\"anchor\" id=\"index\"></a>\n",
    "* [Loading data](#1)\n",
    "    * [Genetic predictors](#2)\n",
    "    * [Physical predictors](#9)\n",
    "    * [Target variables](#3)\n",
    "* [Train/test partition](#4)\n",
    "* [Multiple Linear Regression coupled with PCA](#5)\n",
    "    * [Training the model](#6)\n",
    "    * [Cross-validation](#7)\n",
    "        * [RMSE error in the test prediction after cross-validation](#8)\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading data <a class=\"anchor\" id =\"1\" ></a>\n",
    "\n",
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Genetic predictors <a class=\"anchor\" id=\"2\"></a>\n",
    "\n",
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use genetic predictors coded based on log-additive model codifying the states of the predictors alphabetically with 1, 2 or 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>rs10034661</th><th scope=col>rs10063949</th><th scope=col>rs1024610</th><th scope=col>rs1024611</th><th scope=col>rs1042713</th><th scope=col>rs1045485</th><th scope=col>rs10491003</th><th scope=col>rs1049305</th><th scope=col>rs1049434</th><th scope=col>rs10497520</th><th scope=col>...</th><th scope=col>rs8111989</th><th scope=col>rs8192678</th><th scope=col>rs824205</th><th scope=col>rs833070</th><th scope=col>rs884736</th><th scope=col>rs921943</th><th scope=col>rs9469199</th><th scope=col>rs970547</th><th scope=col>rs9902453</th><th scope=col>rs9939609</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>3  </td><td>2  </td><td>2  </td><td>3  </td><td>1  </td><td>2  </td><td>3  </td><td>2  </td><td>2  </td><td>2  </td><td>...</td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>1  </td><td>2  </td><td>1  </td></tr>\n",
       "\t<tr><td>3  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>3  </td><td>3  </td><td>3  </td><td>1  </td><td>1  </td><td>...</td><td>2  </td><td>2  </td><td>1  </td><td>2  </td><td>2  </td><td>2  </td><td>3  </td><td>2  </td><td>2  </td><td>3  </td></tr>\n",
       "\t<tr><td>3  </td><td>3  </td><td>2  </td><td>3  </td><td>2  </td><td>3  </td><td>3  </td><td>2  </td><td>1  </td><td>1  </td><td>...</td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>1  </td><td>3  </td><td>2  </td><td>2  </td><td>1  </td></tr>\n",
       "\t<tr><td>3  </td><td>3  </td><td>3  </td><td>2  </td><td>2  </td><td>3  </td><td>3  </td><td>1  </td><td>2  </td><td>1  </td><td>...</td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>2  </td><td>3  </td><td>1  </td><td>1  </td><td>1  </td></tr>\n",
       "\t<tr><td>3  </td><td>2  </td><td>3  </td><td>2  </td><td>3  </td><td>1  </td><td>3  </td><td>2  </td><td>3  </td><td>1  </td><td>...</td><td>2  </td><td>2  </td><td>2  </td><td>3  </td><td>3  </td><td>3  </td><td>3  </td><td>1  </td><td>2  </td><td>2  </td></tr>\n",
       "\t<tr><td>3  </td><td>2  </td><td>3  </td><td>2  </td><td>2  </td><td>3  </td><td>3  </td><td>2  </td><td>2  </td><td>1  </td><td>...</td><td>2  </td><td>2  </td><td>2  </td><td>3  </td><td>2  </td><td>2  </td><td>3  </td><td>2  </td><td>3  </td><td>3  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       " rs10034661 & rs10063949 & rs1024610 & rs1024611 & rs1042713 & rs1045485 & rs10491003 & rs1049305 & rs1049434 & rs10497520 & ... & rs8111989 & rs8192678 & rs824205 & rs833070 & rs884736 & rs921943 & rs9469199 & rs970547 & rs9902453 & rs9939609\\\\\n",
       "\\hline\n",
       "\t 3   & 2   & 2   & 3   & 1   & 2   & 3   & 2   & 2   & 2   & ... & 2   & 2   & 2   & 2   & 2   & 2   & 2   & 1   & 2   & 1  \\\\\n",
       "\t 3   & 2   & 2   & 2   & 2   & 3   & 3   & 3   & 1   & 1   & ... & 2   & 2   & 1   & 2   & 2   & 2   & 3   & 2   & 2   & 3  \\\\\n",
       "\t 3   & 3   & 2   & 3   & 2   & 3   & 3   & 2   & 1   & 1   & ... & 2   & 2   & 2   & 2   & 2   & 1   & 3   & 2   & 2   & 1  \\\\\n",
       "\t 3   & 3   & 3   & 2   & 2   & 3   & 3   & 1   & 2   & 1   & ... & 2   & 2   & 2   & 2   & 2   & 2   & 3   & 1   & 1   & 1  \\\\\n",
       "\t 3   & 2   & 3   & 2   & 3   & 1   & 3   & 2   & 3   & 1   & ... & 2   & 2   & 2   & 3   & 3   & 3   & 3   & 1   & 2   & 2  \\\\\n",
       "\t 3   & 2   & 3   & 2   & 2   & 3   & 3   & 2   & 2   & 1   & ... & 2   & 2   & 2   & 3   & 2   & 2   & 3   & 2   & 3   & 3  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| rs10034661 | rs10063949 | rs1024610 | rs1024611 | rs1042713 | rs1045485 | rs10491003 | rs1049305 | rs1049434 | rs10497520 | ... | rs8111989 | rs8192678 | rs824205 | rs833070 | rs884736 | rs921943 | rs9469199 | rs970547 | rs9902453 | rs9939609 |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 3   | 2   | 2   | 3   | 1   | 2   | 3   | 2   | 2   | 2   | ... | 2   | 2   | 2   | 2   | 2   | 2   | 2   | 1   | 2   | 1   |\n",
       "| 3   | 2   | 2   | 2   | 2   | 3   | 3   | 3   | 1   | 1   | ... | 2   | 2   | 1   | 2   | 2   | 2   | 3   | 2   | 2   | 3   |\n",
       "| 3   | 3   | 2   | 3   | 2   | 3   | 3   | 2   | 1   | 1   | ... | 2   | 2   | 2   | 2   | 2   | 1   | 3   | 2   | 2   | 1   |\n",
       "| 3   | 3   | 3   | 2   | 2   | 3   | 3   | 1   | 2   | 1   | ... | 2   | 2   | 2   | 2   | 2   | 2   | 3   | 1   | 1   | 1   |\n",
       "| 3   | 2   | 3   | 2   | 3   | 1   | 3   | 2   | 3   | 1   | ... | 2   | 2   | 2   | 3   | 3   | 3   | 3   | 1   | 2   | 2   |\n",
       "| 3   | 2   | 3   | 2   | 2   | 3   | 3   | 2   | 2   | 1   | ... | 2   | 2   | 2   | 3   | 2   | 2   | 3   | 2   | 3   | 3   |\n",
       "\n"
      ],
      "text/plain": [
       "  rs10034661 rs10063949 rs1024610 rs1024611 rs1042713 rs1045485 rs10491003\n",
       "1 3          2          2         3         1         2         3         \n",
       "2 3          2          2         2         2         3         3         \n",
       "3 3          3          2         3         2         3         3         \n",
       "4 3          3          3         2         2         3         3         \n",
       "5 3          2          3         2         3         1         3         \n",
       "6 3          2          3         2         2         3         3         \n",
       "  rs1049305 rs1049434 rs10497520 ... rs8111989 rs8192678 rs824205 rs833070\n",
       "1 2         2         2          ... 2         2         2        2       \n",
       "2 3         1         1          ... 2         2         1        2       \n",
       "3 2         1         1          ... 2         2         2        2       \n",
       "4 1         2         1          ... 2         2         2        2       \n",
       "5 2         3         1          ... 2         2         2        3       \n",
       "6 2         2         1          ... 2         2         2        3       \n",
       "  rs884736 rs921943 rs9469199 rs970547 rs9902453 rs9939609\n",
       "1 2        2        2         1        2         1        \n",
       "2 2        2        3         2        2         3        \n",
       "3 2        1        3         2        2         1        \n",
       "4 2        2        3         1        1         1        \n",
       "5 3        3        3         1        2         2        \n",
       "6 2        2        3         2        3         3        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "handle_genetic <-  read.csv('handle_genetic_cod_28_04_20.csv')\n",
    "\n",
    "head(handle_genetic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Physical predictors <a class=\"anchor\" id=\"9\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>W1Fc</th><th scope=col>W1Ox</th><th scope=col>W1Lac</th><th scope=col>W1tFc</th><th scope=col>W1tOx</th><th scope=col>W1tLac</th><th scope=col>W1tBorg</th><th scope=col>W1t5Fc</th><th scope=col>W1t5Ox</th><th scope=col>W1t5Lac</th><th scope=col>...</th><th scope=col>PlieguePec</th><th scope=col>PliegueAx</th><th scope=col>PliegueTri</th><th scope=col>PliegueSub</th><th scope=col>PliegueAbd</th><th scope=col>PliegueSup</th><th scope=col>tpcgrasa1</th><th scope=col>tpcgrasa2</th><th scope=col>PerCue</th><th scope=col>PerCin</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 0.09690101</td><td>-0.3612723 </td><td>-0.2759823 </td><td>-1.45702474</td><td> 0.54870046</td><td>-1.5817296 </td><td>-1.2280957 </td><td>-3.38052307</td><td>-0.7215023 </td><td>-2.7847814 </td><td>...        </td><td>-0.8757439 </td><td>-0.8951047 </td><td> 1.0159821 </td><td>-1.0183111 </td><td>-1.2665456 </td><td>-1.0811267 </td><td> 0.37659536</td><td>0.02830971 </td><td>-2.2056212 </td><td>-1.727334  </td></tr>\n",
       "\t<tr><td>-1.03822515</td><td>-0.6698591 </td><td> 1.5789808 </td><td>-0.61695891</td><td>-1.07606258</td><td> 0.2939295 </td><td>-1.2280957 </td><td>-2.55958657</td><td> 0.2886009 </td><td>-2.1390350 </td><td>...        </td><td>-1.0373448 </td><td>-1.0624242 </td><td>-0.8734794 </td><td>-1.2829706 </td><td>-1.3202312 </td><td>-1.1361661 </td><td>-0.43175736</td><td>0.03866565 </td><td>-0.8281578 </td><td>-1.462643  </td></tr>\n",
       "\t<tr><td> 1.32283727</td><td> 0.5644880 </td><td>-1.0179676 </td><td>-0.01024471</td><td> 0.79866401</td><td>-1.1128148 </td><td> 0.8699011 </td><td> 0.01268113</td><td> 0.2886009 </td><td>-1.0493379 </td><td>...        </td><td>-1.1038863 </td><td>-1.2619206 </td><td>-1.1918942 </td><td>-1.5390928 </td><td>-1.4276024 </td><td>-1.4113634 </td><td>-0.86426995</td><td>0.23888577 </td><td>-2.2056212 </td><td>-1.674395  </td></tr>\n",
       "\t<tr><td> 0.59635652</td><td> 0.4101946 </td><td>-0.3996465 </td><td>-0.66362924</td><td>-1.82595321</td><td> 0.2001465 </td><td>-1.2280957 </td><td> 1.10726313</td><td> 0.4329014 </td><td>-0.7668239 </td><td>...        </td><td>-0.8472261 </td><td>-0.6537784 </td><td> 0.3040546 </td><td>-0.6255905 </td><td>-0.6798385 </td><td>-0.4595045 </td><td> 0.61849286</td><td>1.07832946 </td><td>-0.9659042 </td><td>-1.356766  </td></tr>\n",
       "\t<tr><td>-2.03713617</td><td> 0.4101946 </td><td> 0.8369956 </td><td> 0.36311788</td><td> 0.04877337</td><td> 0.8566272 </td><td>-0.1790973 </td><td>-0.09677707</td><td>-1.0101032 </td><td>-0.3228732 </td><td>...        </td><td> 1.2440796 </td><td> 0.8038323 </td><td> 1.8540739 </td><td> 0.8855301 </td><td> 1.0917868 </td><td> 1.2013922 </td><td> 2.13407275</td><td>1.66913269 </td><td>-1.5168895 </td><td>-1.219127  </td></tr>\n",
       "\t<tr><td>-0.17552926</td><td> 0.7187814 </td><td> 0.3423387 </td><td> 0.45645853</td><td> 0.67368224</td><td>-0.3625512 </td><td> 0.8699011 </td><td>-0.31569347</td><td> 0.5772018 </td><td>-0.9282605 </td><td>...        </td><td>-0.8092024 </td><td>-0.8564925 </td><td> 0.4933012 </td><td>-0.7963386 </td><td>-1.1169928 </td><td>-0.8577312 </td><td>-0.07384767</td><td>0.33604799 </td><td>-1.1036505 </td><td>-1.303828  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllllllllllllllllllllll}\n",
       " W1Fc & W1Ox & W1Lac & W1tFc & W1tOx & W1tLac & W1tBorg & W1t5Fc & W1t5Ox & W1t5Lac & ... & PlieguePec & PliegueAx & PliegueTri & PliegueSub & PliegueAbd & PliegueSup & tpcgrasa1 & tpcgrasa2 & PerCue & PerCin\\\\\n",
       "\\hline\n",
       "\t  0.09690101 & -0.3612723  & -0.2759823  & -1.45702474 &  0.54870046 & -1.5817296  & -1.2280957  & -3.38052307 & -0.7215023  & -2.7847814  & ...         & -0.8757439  & -0.8951047  &  1.0159821  & -1.0183111  & -1.2665456  & -1.0811267  &  0.37659536 & 0.02830971  & -2.2056212  & -1.727334  \\\\\n",
       "\t -1.03822515 & -0.6698591  &  1.5789808  & -0.61695891 & -1.07606258 &  0.2939295  & -1.2280957  & -2.55958657 &  0.2886009  & -2.1390350  & ...         & -1.0373448  & -1.0624242  & -0.8734794  & -1.2829706  & -1.3202312  & -1.1361661  & -0.43175736 & 0.03866565  & -0.8281578  & -1.462643  \\\\\n",
       "\t  1.32283727 &  0.5644880  & -1.0179676  & -0.01024471 &  0.79866401 & -1.1128148  &  0.8699011  &  0.01268113 &  0.2886009  & -1.0493379  & ...         & -1.1038863  & -1.2619206  & -1.1918942  & -1.5390928  & -1.4276024  & -1.4113634  & -0.86426995 & 0.23888577  & -2.2056212  & -1.674395  \\\\\n",
       "\t  0.59635652 &  0.4101946  & -0.3996465  & -0.66362924 & -1.82595321 &  0.2001465  & -1.2280957  &  1.10726313 &  0.4329014  & -0.7668239  & ...         & -0.8472261  & -0.6537784  &  0.3040546  & -0.6255905  & -0.6798385  & -0.4595045  &  0.61849286 & 1.07832946  & -0.9659042  & -1.356766  \\\\\n",
       "\t -2.03713617 &  0.4101946  &  0.8369956  &  0.36311788 &  0.04877337 &  0.8566272  & -0.1790973  & -0.09677707 & -1.0101032  & -0.3228732  & ...         &  1.2440796  &  0.8038323  &  1.8540739  &  0.8855301  &  1.0917868  &  1.2013922  &  2.13407275 & 1.66913269  & -1.5168895  & -1.219127  \\\\\n",
       "\t -0.17552926 &  0.7187814  &  0.3423387  &  0.45645853 &  0.67368224 & -0.3625512  &  0.8699011  & -0.31569347 &  0.5772018  & -0.9282605  & ...         & -0.8092024  & -0.8564925  &  0.4933012  & -0.7963386  & -1.1169928  & -0.8577312  & -0.07384767 & 0.33604799  & -1.1036505  & -1.303828  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| W1Fc | W1Ox | W1Lac | W1tFc | W1tOx | W1tLac | W1tBorg | W1t5Fc | W1t5Ox | W1t5Lac | ... | PlieguePec | PliegueAx | PliegueTri | PliegueSub | PliegueAbd | PliegueSup | tpcgrasa1 | tpcgrasa2 | PerCue | PerCin |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  0.09690101 | -0.3612723  | -0.2759823  | -1.45702474 |  0.54870046 | -1.5817296  | -1.2280957  | -3.38052307 | -0.7215023  | -2.7847814  | ...         | -0.8757439  | -0.8951047  |  1.0159821  | -1.0183111  | -1.2665456  | -1.0811267  |  0.37659536 | 0.02830971  | -2.2056212  | -1.727334   |\n",
       "| -1.03822515 | -0.6698591  |  1.5789808  | -0.61695891 | -1.07606258 |  0.2939295  | -1.2280957  | -2.55958657 |  0.2886009  | -2.1390350  | ...         | -1.0373448  | -1.0624242  | -0.8734794  | -1.2829706  | -1.3202312  | -1.1361661  | -0.43175736 | 0.03866565  | -0.8281578  | -1.462643   |\n",
       "|  1.32283727 |  0.5644880  | -1.0179676  | -0.01024471 |  0.79866401 | -1.1128148  |  0.8699011  |  0.01268113 |  0.2886009  | -1.0493379  | ...         | -1.1038863  | -1.2619206  | -1.1918942  | -1.5390928  | -1.4276024  | -1.4113634  | -0.86426995 | 0.23888577  | -2.2056212  | -1.674395   |\n",
       "|  0.59635652 |  0.4101946  | -0.3996465  | -0.66362924 | -1.82595321 |  0.2001465  | -1.2280957  |  1.10726313 |  0.4329014  | -0.7668239  | ...         | -0.8472261  | -0.6537784  |  0.3040546  | -0.6255905  | -0.6798385  | -0.4595045  |  0.61849286 | 1.07832946  | -0.9659042  | -1.356766   |\n",
       "| -2.03713617 |  0.4101946  |  0.8369956  |  0.36311788 |  0.04877337 |  0.8566272  | -0.1790973  | -0.09677707 | -1.0101032  | -0.3228732  | ...         |  1.2440796  |  0.8038323  |  1.8540739  |  0.8855301  |  1.0917868  |  1.2013922  |  2.13407275 | 1.66913269  | -1.5168895  | -1.219127   |\n",
       "| -0.17552926 |  0.7187814  |  0.3423387  |  0.45645853 |  0.67368224 | -0.3625512  |  0.8699011  | -0.31569347 |  0.5772018  | -0.9282605  | ...         | -0.8092024  | -0.8564925  |  0.4933012  | -0.7963386  | -1.1169928  | -0.8577312  | -0.07384767 | 0.33604799  | -1.1036505  | -1.303828   |\n",
       "\n"
      ],
      "text/plain": [
       "  W1Fc        W1Ox       W1Lac      W1tFc       W1tOx       W1tLac    \n",
       "1  0.09690101 -0.3612723 -0.2759823 -1.45702474  0.54870046 -1.5817296\n",
       "2 -1.03822515 -0.6698591  1.5789808 -0.61695891 -1.07606258  0.2939295\n",
       "3  1.32283727  0.5644880 -1.0179676 -0.01024471  0.79866401 -1.1128148\n",
       "4  0.59635652  0.4101946 -0.3996465 -0.66362924 -1.82595321  0.2001465\n",
       "5 -2.03713617  0.4101946  0.8369956  0.36311788  0.04877337  0.8566272\n",
       "6 -0.17552926  0.7187814  0.3423387  0.45645853  0.67368224 -0.3625512\n",
       "  W1tBorg    W1t5Fc      W1t5Ox     W1t5Lac    ... PlieguePec PliegueAx \n",
       "1 -1.2280957 -3.38052307 -0.7215023 -2.7847814 ... -0.8757439 -0.8951047\n",
       "2 -1.2280957 -2.55958657  0.2886009 -2.1390350 ... -1.0373448 -1.0624242\n",
       "3  0.8699011  0.01268113  0.2886009 -1.0493379 ... -1.1038863 -1.2619206\n",
       "4 -1.2280957  1.10726313  0.4329014 -0.7668239 ... -0.8472261 -0.6537784\n",
       "5 -0.1790973 -0.09677707 -1.0101032 -0.3228732 ...  1.2440796  0.8038323\n",
       "6  0.8699011 -0.31569347  0.5772018 -0.9282605 ... -0.8092024 -0.8564925\n",
       "  PliegueTri PliegueSub PliegueAbd PliegueSup tpcgrasa1   tpcgrasa2  PerCue    \n",
       "1  1.0159821 -1.0183111 -1.2665456 -1.0811267  0.37659536 0.02830971 -2.2056212\n",
       "2 -0.8734794 -1.2829706 -1.3202312 -1.1361661 -0.43175736 0.03866565 -0.8281578\n",
       "3 -1.1918942 -1.5390928 -1.4276024 -1.4113634 -0.86426995 0.23888577 -2.2056212\n",
       "4  0.3040546 -0.6255905 -0.6798385 -0.4595045  0.61849286 1.07832946 -0.9659042\n",
       "5  1.8540739  0.8855301  1.0917868  1.2013922  2.13407275 1.66913269 -1.5168895\n",
       "6  0.4933012 -0.7963386 -1.1169928 -0.8577312 -0.07384767 0.33604799 -1.1036505\n",
       "  PerCin   \n",
       "1 -1.727334\n",
       "2 -1.462643\n",
       "3 -1.674395\n",
       "4 -1.356766\n",
       "5 -1.219127\n",
       "6 -1.303828"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'W1Fc'</li>\n",
       "\t<li>'W1Ox'</li>\n",
       "\t<li>'W1Lac'</li>\n",
       "\t<li>'W1tFc'</li>\n",
       "\t<li>'W1tOx'</li>\n",
       "\t<li>'W1tLac'</li>\n",
       "\t<li>'W1tBorg'</li>\n",
       "\t<li>'W1t5Fc'</li>\n",
       "\t<li>'W1t5Ox'</li>\n",
       "\t<li>'W1t5Lac'</li>\n",
       "\t<li>'W2tFc'</li>\n",
       "\t<li>'W2tOx'</li>\n",
       "\t<li>'W2tLac'</li>\n",
       "\t<li>'W2tBorg'</li>\n",
       "\t<li>'W2t5Fc'</li>\n",
       "\t<li>'W2t5Ox'</li>\n",
       "\t<li>'W2t5Lac'</li>\n",
       "\t<li>'W2t10Fc'</li>\n",
       "\t<li>'W2t10Ox'</li>\n",
       "\t<li>'W2t10Lac'</li>\n",
       "\t<li>'Sumat'</li>\n",
       "\t<li>'Peso'</li>\n",
       "\t<li>'Edad'</li>\n",
       "\t<li>'Altura'</li>\n",
       "\t<li>'PlieguePec'</li>\n",
       "\t<li>'PliegueAx'</li>\n",
       "\t<li>'PliegueTri'</li>\n",
       "\t<li>'PliegueSub'</li>\n",
       "\t<li>'PliegueAbd'</li>\n",
       "\t<li>'PliegueSup'</li>\n",
       "\t<li>'tpcgrasa1'</li>\n",
       "\t<li>'tpcgrasa2'</li>\n",
       "\t<li>'PerCue'</li>\n",
       "\t<li>'PerCin'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'W1Fc'\n",
       "\\item 'W1Ox'\n",
       "\\item 'W1Lac'\n",
       "\\item 'W1tFc'\n",
       "\\item 'W1tOx'\n",
       "\\item 'W1tLac'\n",
       "\\item 'W1tBorg'\n",
       "\\item 'W1t5Fc'\n",
       "\\item 'W1t5Ox'\n",
       "\\item 'W1t5Lac'\n",
       "\\item 'W2tFc'\n",
       "\\item 'W2tOx'\n",
       "\\item 'W2tLac'\n",
       "\\item 'W2tBorg'\n",
       "\\item 'W2t5Fc'\n",
       "\\item 'W2t5Ox'\n",
       "\\item 'W2t5Lac'\n",
       "\\item 'W2t10Fc'\n",
       "\\item 'W2t10Ox'\n",
       "\\item 'W2t10Lac'\n",
       "\\item 'Sumat'\n",
       "\\item 'Peso'\n",
       "\\item 'Edad'\n",
       "\\item 'Altura'\n",
       "\\item 'PlieguePec'\n",
       "\\item 'PliegueAx'\n",
       "\\item 'PliegueTri'\n",
       "\\item 'PliegueSub'\n",
       "\\item 'PliegueAbd'\n",
       "\\item 'PliegueSup'\n",
       "\\item 'tpcgrasa1'\n",
       "\\item 'tpcgrasa2'\n",
       "\\item 'PerCue'\n",
       "\\item 'PerCin'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'W1Fc'\n",
       "2. 'W1Ox'\n",
       "3. 'W1Lac'\n",
       "4. 'W1tFc'\n",
       "5. 'W1tOx'\n",
       "6. 'W1tLac'\n",
       "7. 'W1tBorg'\n",
       "8. 'W1t5Fc'\n",
       "9. 'W1t5Ox'\n",
       "10. 'W1t5Lac'\n",
       "11. 'W2tFc'\n",
       "12. 'W2tOx'\n",
       "13. 'W2tLac'\n",
       "14. 'W2tBorg'\n",
       "15. 'W2t5Fc'\n",
       "16. 'W2t5Ox'\n",
       "17. 'W2t5Lac'\n",
       "18. 'W2t10Fc'\n",
       "19. 'W2t10Ox'\n",
       "20. 'W2t10Lac'\n",
       "21. 'Sumat'\n",
       "22. 'Peso'\n",
       "23. 'Edad'\n",
       "24. 'Altura'\n",
       "25. 'PlieguePec'\n",
       "26. 'PliegueAx'\n",
       "27. 'PliegueTri'\n",
       "28. 'PliegueSub'\n",
       "29. 'PliegueAbd'\n",
       "30. 'PliegueSup'\n",
       "31. 'tpcgrasa1'\n",
       "32. 'tpcgrasa2'\n",
       "33. 'PerCue'\n",
       "34. 'PerCin'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"W1Fc\"       \"W1Ox\"       \"W1Lac\"      \"W1tFc\"      \"W1tOx\"     \n",
       " [6] \"W1tLac\"     \"W1tBorg\"    \"W1t5Fc\"     \"W1t5Ox\"     \"W1t5Lac\"   \n",
       "[11] \"W2tFc\"      \"W2tOx\"      \"W2tLac\"     \"W2tBorg\"    \"W2t5Fc\"    \n",
       "[16] \"W2t5Ox\"     \"W2t5Lac\"    \"W2t10Fc\"    \"W2t10Ox\"    \"W2t10Lac\"  \n",
       "[21] \"Sumat\"      \"Peso\"       \"Edad\"       \"Altura\"     \"PlieguePec\"\n",
       "[26] \"PliegueAx\"  \"PliegueTri\" \"PliegueSub\" \"PliegueAbd\" \"PliegueSup\"\n",
       "[31] \"tpcgrasa1\"  \"tpcgrasa2\"  \"PerCue\"     \"PerCin\"    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "handle_physical <- read.csv('handle_physical_transformed_for_multiple_linear_regression.csv')\n",
    "head(handle_physical)\n",
    "names(handle_physical)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid interference with the predictors related to FFM1 and similars, we eliminated the predictors that in their name contain the FM substring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "handle_physical <- handle_physical[!grepl('FM',names(handle_physical))] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We delete all the fat fold predictors that are not Sumat:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'W1Fc'</li>\n",
       "\t<li>'W1Ox'</li>\n",
       "\t<li>'W1Lac'</li>\n",
       "\t<li>'W1tFc'</li>\n",
       "\t<li>'W1tOx'</li>\n",
       "\t<li>'W1tLac'</li>\n",
       "\t<li>'W1tBorg'</li>\n",
       "\t<li>'W1t5Fc'</li>\n",
       "\t<li>'W1t5Ox'</li>\n",
       "\t<li>'W1t5Lac'</li>\n",
       "\t<li>'W2tFc'</li>\n",
       "\t<li>'W2tOx'</li>\n",
       "\t<li>'W2tLac'</li>\n",
       "\t<li>'W2tBorg'</li>\n",
       "\t<li>'W2t5Fc'</li>\n",
       "\t<li>'W2t5Ox'</li>\n",
       "\t<li>'W2t5Lac'</li>\n",
       "\t<li>'W2t10Fc'</li>\n",
       "\t<li>'W2t10Ox'</li>\n",
       "\t<li>'W2t10Lac'</li>\n",
       "\t<li>'Sumat'</li>\n",
       "\t<li>'Peso'</li>\n",
       "\t<li>'Edad'</li>\n",
       "\t<li>'Altura'</li>\n",
       "\t<li>'tpcgrasa1'</li>\n",
       "\t<li>'tpcgrasa2'</li>\n",
       "\t<li>'PerCue'</li>\n",
       "\t<li>'PerCin'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'W1Fc'\n",
       "\\item 'W1Ox'\n",
       "\\item 'W1Lac'\n",
       "\\item 'W1tFc'\n",
       "\\item 'W1tOx'\n",
       "\\item 'W1tLac'\n",
       "\\item 'W1tBorg'\n",
       "\\item 'W1t5Fc'\n",
       "\\item 'W1t5Ox'\n",
       "\\item 'W1t5Lac'\n",
       "\\item 'W2tFc'\n",
       "\\item 'W2tOx'\n",
       "\\item 'W2tLac'\n",
       "\\item 'W2tBorg'\n",
       "\\item 'W2t5Fc'\n",
       "\\item 'W2t5Ox'\n",
       "\\item 'W2t5Lac'\n",
       "\\item 'W2t10Fc'\n",
       "\\item 'W2t10Ox'\n",
       "\\item 'W2t10Lac'\n",
       "\\item 'Sumat'\n",
       "\\item 'Peso'\n",
       "\\item 'Edad'\n",
       "\\item 'Altura'\n",
       "\\item 'tpcgrasa1'\n",
       "\\item 'tpcgrasa2'\n",
       "\\item 'PerCue'\n",
       "\\item 'PerCin'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'W1Fc'\n",
       "2. 'W1Ox'\n",
       "3. 'W1Lac'\n",
       "4. 'W1tFc'\n",
       "5. 'W1tOx'\n",
       "6. 'W1tLac'\n",
       "7. 'W1tBorg'\n",
       "8. 'W1t5Fc'\n",
       "9. 'W1t5Ox'\n",
       "10. 'W1t5Lac'\n",
       "11. 'W2tFc'\n",
       "12. 'W2tOx'\n",
       "13. 'W2tLac'\n",
       "14. 'W2tBorg'\n",
       "15. 'W2t5Fc'\n",
       "16. 'W2t5Ox'\n",
       "17. 'W2t5Lac'\n",
       "18. 'W2t10Fc'\n",
       "19. 'W2t10Ox'\n",
       "20. 'W2t10Lac'\n",
       "21. 'Sumat'\n",
       "22. 'Peso'\n",
       "23. 'Edad'\n",
       "24. 'Altura'\n",
       "25. 'tpcgrasa1'\n",
       "26. 'tpcgrasa2'\n",
       "27. 'PerCue'\n",
       "28. 'PerCin'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"W1Fc\"      \"W1Ox\"      \"W1Lac\"     \"W1tFc\"     \"W1tOx\"     \"W1tLac\"   \n",
       " [7] \"W1tBorg\"   \"W1t5Fc\"    \"W1t5Ox\"    \"W1t5Lac\"   \"W2tFc\"     \"W2tOx\"    \n",
       "[13] \"W2tLac\"    \"W2tBorg\"   \"W2t5Fc\"    \"W2t5Ox\"    \"W2t5Lac\"   \"W2t10Fc\"  \n",
       "[19] \"W2t10Ox\"   \"W2t10Lac\"  \"Sumat\"     \"Peso\"      \"Edad\"      \"Altura\"   \n",
       "[25] \"tpcgrasa1\" \"tpcgrasa2\" \"PerCue\"    \"PerCin\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "handle_physical <- handle_physical[!grepl('Pliegue',names(handle_physical))] \n",
    "\n",
    "names(handle_physical)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Target variables <a class=\"anchor\" id=\"3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>W1MaxWAbs</th><th scope=col>W1MaxWRel</th><th scope=col>W1maxRPM</th><th scope=col>W1MedWAbs</th><th scope=col>W1MedWRel</th><th scope=col>W1medRPM</th><th scope=col>W2MaxWAbs</th><th scope=col>W2MaxWRel</th><th scope=col>W2maxRPM</th><th scope=col>W2MedWAbs</th><th scope=col>...</th><th scope=col>W2DifWRelFFM1</th><th scope=col>W2DifWRelFFM2</th><th scope=col>W1.2MaxDifWAbs</th><th scope=col>W1.2MaxDifWRel</th><th scope=col>W1.2MaxDifWRelFFM1</th><th scope=col>W1.2MaxDifWRelFFM2</th><th scope=col>W1.2MedDifWAbs</th><th scope=col>W1.2MedDifWRel</th><th scope=col>W1.2MedDifWRelFFM1</th><th scope=col>W1.2MedDifWRelFFM2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>0</th><td>398        </td><td> 8.747253  </td><td>122        </td><td>206        </td><td>4.527473   </td><td>100        </td><td>397        </td><td>8.725275   </td><td>122        </td><td>224        </td><td>...        </td><td> 4.479981  </td><td> 4.544592  </td><td>  1        </td><td> 0.02197802</td><td> 0.02589585</td><td> 0.02626932</td><td>-18        </td><td>-0.39560440</td><td>-0.46612522</td><td>-0.47284774</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>511        </td><td> 8.964912  </td><td>128        </td><td>294        </td><td>5.157895   </td><td>109        </td><td>523        </td><td>9.175439   </td><td>122        </td><td>295        </td><td>...        </td><td> 4.552187  </td><td> 4.889881  </td><td>-12        </td><td>-0.21052632</td><td>-0.23958880</td><td>-0.25736216</td><td> -1        </td><td>-0.01754386</td><td>-0.01996573</td><td>-0.02144685</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>524        </td><td>10.174757  </td><td>130        </td><td>262        </td><td>5.087379   </td><td>107        </td><td>476        </td><td>9.242718   </td><td>125        </td><td>245        </td><td>...        </td><td> 4.958966  </td><td> 5.566747  </td><td> 48        </td><td> 0.93203883</td><td> 1.03043453</td><td> 1.15672661</td><td> 17        </td><td> 0.33009709</td><td> 0.36494556</td><td> 0.40967401</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>541        </td><td> 8.868852  </td><td>128        </td><td>351        </td><td>5.754098   </td><td>118        </td><td>472        </td><td>7.737705   </td><td>130        </td><td>333        </td><td>...        </td><td> 2.792441  </td><td> 3.020719  </td><td> 69        </td><td> 1.13114754</td><td> 1.38617564</td><td> 1.49949379</td><td> 18        </td><td> 0.29508197</td><td> 0.36161104</td><td> 0.39117229</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>547        </td><td> 9.596491  </td><td>143        </td><td>291        </td><td>5.105263   </td><td>116        </td><td>169        </td><td>2.964912   </td><td>130        </td><td>302        </td><td>...        </td><td>-3.215855  </td><td>-3.248973  </td><td>378        </td><td> 6.63157895</td><td> 9.13979775</td><td> 9.23392354</td><td>-11        </td><td>-0.19298246</td><td>-0.26597295</td><td>-0.26871206</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>553        </td><td> 9.701754  </td><td>133        </td><td>365        </td><td>6.403509   </td><td>121        </td><td>556        </td><td>9.754386   </td><td>136        </td><td>355        </td><td>...        </td><td> 4.113095  </td><td> 4.408965  </td><td> -3        </td><td>-0.05263158</td><td>-0.06138948</td><td>-0.06580544</td><td> 10        </td><td> 0.17543860</td><td> 0.20463161</td><td> 0.21935148</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllllllllllllllllllllllll}\n",
       "  & W1MaxWAbs & W1MaxWRel & W1maxRPM & W1MedWAbs & W1MedWRel & W1medRPM & W2MaxWAbs & W2MaxWRel & W2maxRPM & W2MedWAbs & ... & W2DifWRelFFM1 & W2DifWRelFFM2 & W1.2MaxDifWAbs & W1.2MaxDifWRel & W1.2MaxDifWRelFFM1 & W1.2MaxDifWRelFFM2 & W1.2MedDifWAbs & W1.2MedDifWRel & W1.2MedDifWRelFFM1 & W1.2MedDifWRelFFM2\\\\\n",
       "\\hline\n",
       "\t0 & 398         &  8.747253   & 122         & 206         & 4.527473    & 100         & 397         & 8.725275    & 122         & 224         & ...         &  4.479981   &  4.544592   &   1         &  0.02197802 &  0.02589585 &  0.02626932 & -18         & -0.39560440 & -0.46612522 & -0.47284774\\\\\n",
       "\t4 & 511         &  8.964912   & 128         & 294         & 5.157895    & 109         & 523         & 9.175439    & 122         & 295         & ...         &  4.552187   &  4.889881   & -12         & -0.21052632 & -0.23958880 & -0.25736216 &  -1         & -0.01754386 & -0.01996573 & -0.02144685\\\\\n",
       "\t7 & 524         & 10.174757   & 130         & 262         & 5.087379    & 107         & 476         & 9.242718    & 125         & 245         & ...         &  4.958966   &  5.566747   &  48         &  0.93203883 &  1.03043453 &  1.15672661 &  17         &  0.33009709 &  0.36494556 &  0.40967401\\\\\n",
       "\t8 & 541         &  8.868852   & 128         & 351         & 5.754098    & 118         & 472         & 7.737705    & 130         & 333         & ...         &  2.792441   &  3.020719   &  69         &  1.13114754 &  1.38617564 &  1.49949379 &  18         &  0.29508197 &  0.36161104 &  0.39117229\\\\\n",
       "\t9 & 547         &  9.596491   & 143         & 291         & 5.105263    & 116         & 169         & 2.964912    & 130         & 302         & ...         & -3.215855   & -3.248973   & 378         &  6.63157895 &  9.13979775 &  9.23392354 & -11         & -0.19298246 & -0.26597295 & -0.26871206\\\\\n",
       "\t11 & 553         &  9.701754   & 133         & 365         & 6.403509    & 121         & 556         & 9.754386    & 136         & 355         & ...         &  4.113095   &  4.408965   &  -3         & -0.05263158 & -0.06138948 & -0.06580544 &  10         &  0.17543860 &  0.20463161 &  0.21935148\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | W1MaxWAbs | W1MaxWRel | W1maxRPM | W1MedWAbs | W1MedWRel | W1medRPM | W2MaxWAbs | W2MaxWRel | W2maxRPM | W2MedWAbs | ... | W2DifWRelFFM1 | W2DifWRelFFM2 | W1.2MaxDifWAbs | W1.2MaxDifWRel | W1.2MaxDifWRelFFM1 | W1.2MaxDifWRelFFM2 | W1.2MedDifWAbs | W1.2MedDifWRel | W1.2MedDifWRelFFM1 | W1.2MedDifWRelFFM2 |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0 | 398         |  8.747253   | 122         | 206         | 4.527473    | 100         | 397         | 8.725275    | 122         | 224         | ...         |  4.479981   |  4.544592   |   1         |  0.02197802 |  0.02589585 |  0.02626932 | -18         | -0.39560440 | -0.46612522 | -0.47284774 |\n",
       "| 4 | 511         |  8.964912   | 128         | 294         | 5.157895    | 109         | 523         | 9.175439    | 122         | 295         | ...         |  4.552187   |  4.889881   | -12         | -0.21052632 | -0.23958880 | -0.25736216 |  -1         | -0.01754386 | -0.01996573 | -0.02144685 |\n",
       "| 7 | 524         | 10.174757   | 130         | 262         | 5.087379    | 107         | 476         | 9.242718    | 125         | 245         | ...         |  4.958966   |  5.566747   |  48         |  0.93203883 |  1.03043453 |  1.15672661 |  17         |  0.33009709 |  0.36494556 |  0.40967401 |\n",
       "| 8 | 541         |  8.868852   | 128         | 351         | 5.754098    | 118         | 472         | 7.737705    | 130         | 333         | ...         |  2.792441   |  3.020719   |  69         |  1.13114754 |  1.38617564 |  1.49949379 |  18         |  0.29508197 |  0.36161104 |  0.39117229 |\n",
       "| 9 | 547         |  9.596491   | 143         | 291         | 5.105263    | 116         | 169         | 2.964912    | 130         | 302         | ...         | -3.215855   | -3.248973   | 378         |  6.63157895 |  9.13979775 |  9.23392354 | -11         | -0.19298246 | -0.26597295 | -0.26871206 |\n",
       "| 11 | 553         |  9.701754   | 133         | 365         | 6.403509    | 121         | 556         | 9.754386    | 136         | 355         | ...         |  4.113095   |  4.408965   |  -3         | -0.05263158 | -0.06138948 | -0.06580544 |  10         |  0.17543860 |  0.20463161 |  0.21935148 |\n",
       "\n"
      ],
      "text/plain": [
       "   W1MaxWAbs W1MaxWRel W1maxRPM W1MedWAbs W1MedWRel W1medRPM W2MaxWAbs\n",
       "0  398        8.747253 122      206       4.527473  100      397      \n",
       "4  511        8.964912 128      294       5.157895  109      523      \n",
       "7  524       10.174757 130      262       5.087379  107      476      \n",
       "8  541        8.868852 128      351       5.754098  118      472      \n",
       "9  547        9.596491 143      291       5.105263  116      169      \n",
       "11 553        9.701754 133      365       6.403509  121      556      \n",
       "   W2MaxWRel W2maxRPM W2MedWAbs ... W2DifWRelFFM1 W2DifWRelFFM2 W1.2MaxDifWAbs\n",
       "0  8.725275  122      224       ...  4.479981      4.544592       1           \n",
       "4  9.175439  122      295       ...  4.552187      4.889881     -12           \n",
       "7  9.242718  125      245       ...  4.958966      5.566747      48           \n",
       "8  7.737705  130      333       ...  2.792441      3.020719      69           \n",
       "9  2.964912  130      302       ... -3.215855     -3.248973     378           \n",
       "11 9.754386  136      355       ...  4.113095      4.408965      -3           \n",
       "   W1.2MaxDifWRel W1.2MaxDifWRelFFM1 W1.2MaxDifWRelFFM2 W1.2MedDifWAbs\n",
       "0   0.02197802     0.02589585         0.02626932        -18           \n",
       "4  -0.21052632    -0.23958880        -0.25736216         -1           \n",
       "7   0.93203883     1.03043453         1.15672661         17           \n",
       "8   1.13114754     1.38617564         1.49949379         18           \n",
       "9   6.63157895     9.13979775         9.23392354        -11           \n",
       "11 -0.05263158    -0.06138948        -0.06580544         10           \n",
       "   W1.2MedDifWRel W1.2MedDifWRelFFM1 W1.2MedDifWRelFFM2\n",
       "0  -0.39560440    -0.46612522        -0.47284774       \n",
       "4  -0.01754386    -0.01996573        -0.02144685       \n",
       "7   0.33009709     0.36494556         0.40967401       \n",
       "8   0.29508197     0.36161104         0.39117229       \n",
       "9  -0.19298246    -0.26597295        -0.26871206       \n",
       "11  0.17543860     0.20463161         0.21935148       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "handle_target <- read.csv('handle_target_fusion_31_03_20.csv', row.name = 1)\n",
    "\n",
    "head(handle_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>W1.2MedDifWRelFFM1</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>0</th><td>-0.46612522</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-0.01996573</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 0.36494556</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 0.36161104</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>-0.26597295</td></tr>\n",
       "\t<tr><th scope=row>11</th><td> 0.20463161</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       "  & W1.2MedDifWRelFFM1\\\\\n",
       "\\hline\n",
       "\t0 & -0.46612522\\\\\n",
       "\t4 & -0.01996573\\\\\n",
       "\t7 &  0.36494556\\\\\n",
       "\t8 &  0.36161104\\\\\n",
       "\t9 & -0.26597295\\\\\n",
       "\t11 &  0.20463161\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | W1.2MedDifWRelFFM1 |\n",
       "|---|---|\n",
       "| 0 | -0.46612522 |\n",
       "| 4 | -0.01996573 |\n",
       "| 7 |  0.36494556 |\n",
       "| 8 |  0.36161104 |\n",
       "| 9 | -0.26597295 |\n",
       "| 11 |  0.20463161 |\n",
       "\n"
      ],
      "text/plain": [
       "   W1.2MedDifWRelFFM1\n",
       "0  -0.46612522       \n",
       "4  -0.01996573       \n",
       "7   0.36494556       \n",
       "8   0.36161104       \n",
       "9  -0.26597295       \n",
       "11  0.20463161       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "target <- handle_target['W1.2MedDifWRelFFM1']\n",
    "head(target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the dataframe for the analysis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>W1.2MedDifWRelFFM1</th><th scope=col>rs10034661</th><th scope=col>rs10063949</th><th scope=col>rs1024610</th><th scope=col>rs1024611</th><th scope=col>rs1042713</th><th scope=col>rs1045485</th><th scope=col>rs10491003</th><th scope=col>rs1049305</th><th scope=col>rs1049434</th><th scope=col>...</th><th scope=col>W2t10Ox</th><th scope=col>W2t10Lac</th><th scope=col>Sumat</th><th scope=col>Peso</th><th scope=col>Edad</th><th scope=col>Altura</th><th scope=col>tpcgrasa1</th><th scope=col>tpcgrasa2</th><th scope=col>PerCue</th><th scope=col>PerCin</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>0</th><td>-0.46612522 </td><td>3           </td><td>2           </td><td>2           </td><td>3           </td><td>1           </td><td>2           </td><td>3           </td><td>2           </td><td>2           </td><td>...         </td><td>-2.0232114  </td><td>-3.097318301</td><td>-0.3922638  </td><td>-2.126728   </td><td> 1.5320336  </td><td>-2.5170879  </td><td> 0.37659536 </td><td>0.02830971  </td><td>-2.2056212  </td><td>-1.727334   </td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-0.01996573 </td><td>3           </td><td>2           </td><td>2           </td><td>2           </td><td>2           </td><td>3           </td><td>3           </td><td>3           </td><td>1           </td><td>...         </td><td>-6.3662307  </td><td>-2.757204339</td><td>-1.1831671  </td><td>-1.302237   </td><td> 1.5320336  </td><td>-0.4031637  </td><td>-0.43175736 </td><td>0.03866565  </td><td>-0.8281578  </td><td>-1.462643   </td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 0.36494556 </td><td>3           </td><td>3           </td><td>2           </td><td>3           </td><td>2           </td><td>3           </td><td>3           </td><td>2           </td><td>1           </td><td>...         </td><td> 0.3654492  </td><td>-1.311720003</td><td>-1.5384033  </td><td>-1.734113   </td><td> 0.3759592  </td><td>-1.3426856  </td><td>-0.86426995 </td><td>0.23888577  </td><td>-2.2056212  </td><td>-1.674395   </td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 0.36161104 </td><td>3           </td><td>3           </td><td>3           </td><td>2           </td><td>2           </td><td>3           </td><td>3           </td><td>1           </td><td>2           </td><td>...         </td><td> 0.7997511  </td><td>-1.991947926</td><td>-0.1366087  </td><td>-0.988145   </td><td> 1.3393546  </td><td>-1.1078051  </td><td> 0.61849286 </td><td>1.07832946  </td><td>-0.9659042  </td><td>-1.356766   </td></tr>\n",
       "\t<tr><th scope=row>9</th><td>-0.26597295 </td><td>3           </td><td>2           </td><td>3           </td><td>2           </td><td>3           </td><td>1           </td><td>3           </td><td>2           </td><td>3           </td><td>...         </td><td>-1.1546076  </td><td> 0.006221597</td><td> 1.6788303  </td><td>-1.302237   </td><td>-0.9727944  </td><td>-1.8124465  </td><td> 2.13407275 </td><td>1.66913269  </td><td>-1.5168895  </td><td>-1.219127   </td></tr>\n",
       "\t<tr><th scope=row>11</th><td> 0.20463161 </td><td>3           </td><td>2           </td><td>3           </td><td>2           </td><td>2           </td><td>3           </td><td>3           </td><td>2           </td><td>2           </td><td>...         </td><td> 0.5826001  </td><td>-1.311720003</td><td>-0.7283498  </td><td>-1.302237   </td><td>-0.7801153  </td><td>-0.9903649  </td><td>-0.07384767 </td><td>0.33604799  </td><td>-1.1036505  </td><td>-1.303828   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       "  & W1.2MedDifWRelFFM1 & rs10034661 & rs10063949 & rs1024610 & rs1024611 & rs1042713 & rs1045485 & rs10491003 & rs1049305 & rs1049434 & ... & W2t10Ox & W2t10Lac & Sumat & Peso & Edad & Altura & tpcgrasa1 & tpcgrasa2 & PerCue & PerCin\\\\\n",
       "\\hline\n",
       "\t0 & -0.46612522  & 3            & 2            & 2            & 3            & 1            & 2            & 3            & 2            & 2            & ...          & -2.0232114   & -3.097318301 & -0.3922638   & -2.126728    &  1.5320336   & -2.5170879   &  0.37659536  & 0.02830971   & -2.2056212   & -1.727334   \\\\\n",
       "\t4 & -0.01996573  & 3            & 2            & 2            & 2            & 2            & 3            & 3            & 3            & 1            & ...          & -6.3662307   & -2.757204339 & -1.1831671   & -1.302237    &  1.5320336   & -0.4031637   & -0.43175736  & 0.03866565   & -0.8281578   & -1.462643   \\\\\n",
       "\t7 &  0.36494556  & 3            & 3            & 2            & 3            & 2            & 3            & 3            & 2            & 1            & ...          &  0.3654492   & -1.311720003 & -1.5384033   & -1.734113    &  0.3759592   & -1.3426856   & -0.86426995  & 0.23888577   & -2.2056212   & -1.674395   \\\\\n",
       "\t8 &  0.36161104  & 3            & 3            & 3            & 2            & 2            & 3            & 3            & 1            & 2            & ...          &  0.7997511   & -1.991947926 & -0.1366087   & -0.988145    &  1.3393546   & -1.1078051   &  0.61849286  & 1.07832946   & -0.9659042   & -1.356766   \\\\\n",
       "\t9 & -0.26597295  & 3            & 2            & 3            & 2            & 3            & 1            & 3            & 2            & 3            & ...          & -1.1546076   &  0.006221597 &  1.6788303   & -1.302237    & -0.9727944   & -1.8124465   &  2.13407275  & 1.66913269   & -1.5168895   & -1.219127   \\\\\n",
       "\t11 &  0.20463161  & 3            & 2            & 3            & 2            & 2            & 3            & 3            & 2            & 2            & ...          &  0.5826001   & -1.311720003 & -0.7283498   & -1.302237    & -0.7801153   & -0.9903649   & -0.07384767  & 0.33604799   & -1.1036505   & -1.303828   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | W1.2MedDifWRelFFM1 | rs10034661 | rs10063949 | rs1024610 | rs1024611 | rs1042713 | rs1045485 | rs10491003 | rs1049305 | rs1049434 | ... | W2t10Ox | W2t10Lac | Sumat | Peso | Edad | Altura | tpcgrasa1 | tpcgrasa2 | PerCue | PerCin |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0 | -0.46612522  | 3            | 2            | 2            | 3            | 1            | 2            | 3            | 2            | 2            | ...          | -2.0232114   | -3.097318301 | -0.3922638   | -2.126728    |  1.5320336   | -2.5170879   |  0.37659536  | 0.02830971   | -2.2056212   | -1.727334    |\n",
       "| 4 | -0.01996573  | 3            | 2            | 2            | 2            | 2            | 3            | 3            | 3            | 1            | ...          | -6.3662307   | -2.757204339 | -1.1831671   | -1.302237    |  1.5320336   | -0.4031637   | -0.43175736  | 0.03866565   | -0.8281578   | -1.462643    |\n",
       "| 7 |  0.36494556  | 3            | 3            | 2            | 3            | 2            | 3            | 3            | 2            | 1            | ...          |  0.3654492   | -1.311720003 | -1.5384033   | -1.734113    |  0.3759592   | -1.3426856   | -0.86426995  | 0.23888577   | -2.2056212   | -1.674395    |\n",
       "| 8 |  0.36161104  | 3            | 3            | 3            | 2            | 2            | 3            | 3            | 1            | 2            | ...          |  0.7997511   | -1.991947926 | -0.1366087   | -0.988145    |  1.3393546   | -1.1078051   |  0.61849286  | 1.07832946   | -0.9659042   | -1.356766    |\n",
       "| 9 | -0.26597295  | 3            | 2            | 3            | 2            | 3            | 1            | 3            | 2            | 3            | ...          | -1.1546076   |  0.006221597 |  1.6788303   | -1.302237    | -0.9727944   | -1.8124465   |  2.13407275  | 1.66913269   | -1.5168895   | -1.219127    |\n",
       "| 11 |  0.20463161  | 3            | 2            | 3            | 2            | 2            | 3            | 3            | 2            | 2            | ...          |  0.5826001   | -1.311720003 | -0.7283498   | -1.302237    | -0.7801153   | -0.9903649   | -0.07384767  | 0.33604799   | -1.1036505   | -1.303828    |\n",
       "\n"
      ],
      "text/plain": [
       "   W1.2MedDifWRelFFM1 rs10034661 rs10063949 rs1024610 rs1024611 rs1042713\n",
       "0  -0.46612522        3          2          2         3         1        \n",
       "4  -0.01996573        3          2          2         2         2        \n",
       "7   0.36494556        3          3          2         3         2        \n",
       "8   0.36161104        3          3          3         2         2        \n",
       "9  -0.26597295        3          2          3         2         3        \n",
       "11  0.20463161        3          2          3         2         2        \n",
       "   rs1045485 rs10491003 rs1049305 rs1049434 ... W2t10Ox    W2t10Lac    \n",
       "0  2         3          2         2         ... -2.0232114 -3.097318301\n",
       "4  3         3          3         1         ... -6.3662307 -2.757204339\n",
       "7  3         3          2         1         ...  0.3654492 -1.311720003\n",
       "8  3         3          1         2         ...  0.7997511 -1.991947926\n",
       "9  1         3          2         3         ... -1.1546076  0.006221597\n",
       "11 3         3          2         2         ...  0.5826001 -1.311720003\n",
       "   Sumat      Peso      Edad       Altura     tpcgrasa1   tpcgrasa2  PerCue    \n",
       "0  -0.3922638 -2.126728  1.5320336 -2.5170879  0.37659536 0.02830971 -2.2056212\n",
       "4  -1.1831671 -1.302237  1.5320336 -0.4031637 -0.43175736 0.03866565 -0.8281578\n",
       "7  -1.5384033 -1.734113  0.3759592 -1.3426856 -0.86426995 0.23888577 -2.2056212\n",
       "8  -0.1366087 -0.988145  1.3393546 -1.1078051  0.61849286 1.07832946 -0.9659042\n",
       "9   1.6788303 -1.302237 -0.9727944 -1.8124465  2.13407275 1.66913269 -1.5168895\n",
       "11 -0.7283498 -1.302237 -0.7801153 -0.9903649 -0.07384767 0.33604799 -1.1036505\n",
       "   PerCin   \n",
       "0  -1.727334\n",
       "4  -1.462643\n",
       "7  -1.674395\n",
       "8  -1.356766\n",
       "9  -1.219127\n",
       "11 -1.303828"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data <- cbind(target, handle_genetic, handle_physical)\n",
    "\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>82</li>\n",
       "\t<li>207</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 82\n",
       "\\item 207\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 82\n",
       "2. 207\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  82 207"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train/test partition<a class=\"anchor\" id=\"4\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'caret' was built under R version 3.6.2\"Loading required package: lattice\n",
      "Loading required package: ggplot2\n",
      "Warning message:\n",
      "\"package 'ggplot2' was built under R version 3.6.3\""
     ]
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>70</li>\n",
       "\t<li>207</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 70\n",
       "\\item 207\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 70\n",
       "2. 207\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  70 207"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>12</li>\n",
       "\t<li>207</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 12\n",
       "\\item 207\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 12\n",
       "2. 207\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  12 207"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(caret)\n",
    "\n",
    "set.seed(10)\n",
    "id_df <- createDataPartition(data$W1.2MedDifWRelFFM1,p = 0.85,list = FALSE)\n",
    "data_train <- data[id_df,]\n",
    "data_test <- data[-id_df,]\n",
    "\n",
    "dim(data_train)\n",
    "\n",
    "dim(data_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression coupled with PCA<a class=\"anchor\" id=\"5\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the model <a class=\"anchor\" id=\"6\" ></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* #### We calculate the main components with the training set "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_train <- prcomp(data_train[, -1], scale. = TRUE)#no se tiene en cuenta la variable objetivo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of 5\n",
      " $ sdev    : num [1:70] 3.1 2.7 2.65 2.64 2.6 ...\n",
      " $ rotation: num [1:206, 1:70] -0.08605 0.00783 -0.06329 0.08574 0.07935 ...\n",
      "  ..- attr(*, \"dimnames\")=List of 2\n",
      "  .. ..$ : chr [1:206] \"rs10034661\" \"rs10063949\" \"rs1024610\" \"rs1024611\" ...\n",
      "  .. ..$ : chr [1:70] \"PC1\" \"PC2\" \"PC3\" \"PC4\" ...\n",
      " $ center  : Named num [1:206] 2.51 2.34 2.49 2.5 2.26 ...\n",
      "  ..- attr(*, \"names\")= chr [1:206] \"rs10034661\" \"rs10063949\" \"rs1024610\" \"rs1024611\" ...\n",
      " $ scale   : Named num [1:206] 0.631 0.679 0.558 0.608 0.674 ...\n",
      "  ..- attr(*, \"names\")= chr [1:206] \"rs10034661\" \"rs10063949\" \"rs1024610\" \"rs1024611\" ...\n",
      " $ x       : num [1:70, 1:70] -7.85 -3.86 -2.74 -3.65 -7.65 ...\n",
      "  ..- attr(*, \"dimnames\")=List of 2\n",
      "  .. ..$ : chr [1:70] \"4\" \"7\" \"9\" \"11\" ...\n",
      "  .. ..$ : chr [1:70] \"PC1\" \"PC2\" \"PC3\" \"PC4\" ...\n",
      " - attr(*, \"class\")= chr \"prcomp\"\n"
     ]
    }
   ],
   "source": [
    "str(pca_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* #### Importance variables analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "perc_variance <- cumsum(pca_train$sdev^2)/sum(pca_train$sdev^2)*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sV/3XeE0I6LuLvQ7o5nyP4Wh5GkiDu8sa9l9Y5XmyQE4MhIwCOsB2RfRaK+30T9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\ncmYAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Percentage of explained accumulated variance vs PCs\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(perc_variance,main=\"Percentage of explained accumulated variance vs PCs\",xlim=c(1,70),xlab = 'Number of principal components', ylab = 'Percentage of explained accumulated variance')\n",
    "abline(v = which(pca_train$rotation[1,] == max(pca_train$rotation[1,])))\n",
    "grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it can be apreciated in the plot shown, the principal component to which target variable contribution is the biggest is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>PC24:</strong> 0.120466032304783"
      ],
      "text/latex": [
       "\\textbf{PC24:} 0.120466032304783"
      ],
      "text/markdown": [
       "**PC24:** 0.120466032304783"
      ],
      "text/plain": [
       "    PC24 \n",
       "0.120466 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca_train$rotation[1,][which(pca_train$rotation[1,] == max(pca_train$rotation[1,]))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With an acumulated proportion of explained variance of:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "61.1764373773722"
      ],
      "text/latex": [
       "61.1764373773722"
      ],
      "text/markdown": [
       "61.1764373773722"
      ],
      "text/plain": [
       "[1] 61.17644"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "perc_variance[24]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, in order to have consistent results, the smallest number of principal components for the analysis will be 24."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align: justify;\">Now, it is shown a plot ot the target variable influence in the set of principal components obtained in train with the objetive of checking if for a certain number of principal component makes or does not make sense to use in the model the target variable.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"Target variable contribution to principal components\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(pca_train$rotation[1,], main = 'Target variable contribution to principal components', \n",
    "     xlab = 'Principal components obtained in train', xlim = c(1,70),ylab = 'Target variable contribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows an uniform distribution of the target variable contribution, so it makes sense to keep the target variable for the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, in order to put in context the target variable contribution, we show down below an histogram of the original variables (included the target variable) contribution to the first principal component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ek9iGQBRFIPIlkAkdSDSBZAJPUgkgUQ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\ngg==",
      "text/plain": [
       "Plot with title \"Original predictors contribution to the first principal component\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(pca_train$rotation[,1], breaks = 'FD',main = 'Original predictors contribution to the first principal component', \n",
    "     xlab = 'Original predictors contribution', ylab = 'Frequency contribution', col = 'blue', xlim=c(-0.25,0.25))\n",
    "abline(v = max(pca_train$rotation[1,]), col = 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is similar to the normal, with the target variable being one of the most contributing variables, located to the right of the distribution (contribution of 0.12). It seems that with greater frequency the variables of the original space contribute between a -0.1 and 0.1 to the main component.\n",
    "\n",
    "The number of main components will be chosen taking into account that up to 95% of the explained variance is to be preserved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>57:</strong> 95.3629916281491"
      ],
      "text/latex": [
       "\\textbf{57:} 95.3629916281491"
      ],
      "text/markdown": [
       "**57:** 95.3629916281491"
      ],
      "text/plain": [
       "      57 \n",
       "95.36299 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(perc_variance) <- 1 : length(perc_variance)\n",
    "\n",
    "perc_variance[which(perc_variance >= 95)][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have then that by choosing a total of 57 main components we can reach 95% of the explained variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* #### We train the regression model with the training set and the number of main components indicated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'pls' was built under R version 3.6.2\"\n",
      "Attaching package: 'pls'\n",
      "\n",
      "The following object is masked from 'package:caret':\n",
      "\n",
      "    R2\n",
      "\n",
      "The following object is masked from 'package:stats':\n",
      "\n",
      "    loadings\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(pls)\n",
    "\n",
    "pcr_model <- pcr(formula = W1.2MedDifWRelFFM1 ~ ., data = data_train, scale. = TRUE, ncomp = 57)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We project the pcr model in test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_test <- predict(pcr_model, newdata = data_test, ncomp = 57)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-validation<a class=\"anchor\" id=\"7\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the MSE error as a validation criterion during cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "60"
      ],
      "text/latex": [
       "60"
      ],
      "text/markdown": [
       "60"
      ],
      "text/plain": [
       "[1] 60"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1)\n",
    "pcr_model <- pcr(formula = W1.2MedDifWRelFFM1 ~ ., data = data_train, scale. = TRUE,\n",
    "                  validation = \"CV\")\n",
    "pcr_model_CV <- MSEP(pcr_model, estimate = \"CV\")\n",
    "which.min(pcr_model_CV$val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3YuvBqEkDIjpOeNbkxf+9LLQSgpL0J6\n3skZQY8OwL6eg5DyIqTnNT5H9a0PRSgpK0J6waPPjY9OPnD05iBkQkgvePjB8pDPFCkpJ0J6\nwaMrncSNcpgUVd8J6RVpPhF+WIMcPbpmHt0T0ivSvK9ProUnpL4TUo+dLPeU1HNCyoOQek5I\neRBSzwkpD0LqOSHlQUg9J6Q8CKnnhJQJJfWbkDIhpH4TUiaE1G9CyoSQ+k1ImRBSvwkpF0rq\nNSHlQki9JqRcCKnXhJQLIfWakHIhpF4TUi6E1GtCyoaS+kxI2RBSnwkpG0LqMyFlQ0h9JqRs\nCKnPhJQPJfWYkPIhpB4TUj6E1GNCyoeQekxI+RBSjwkpH0LqMSFlREn9JaSMCKm/hJQRIfWX\nkDIipP4SUkaE1F9CyomSektIORFSbwkpJ0LqLSHlREi9JaScCKm3hJQVJfWVkLIipL4SUlaE\n1FdCyoqQ+kpIWRFSXwkpK0LqKyHlRUk9JaS8CKmnhJQXIfWUkPIipJ4SUl6E1FNCyoyS+klI\nmRFSPwkpM0LqJyFlRkj9JKTMCKmfhJQZIfWTkHKjpF4SUm6E1EtCyo2Qeil9SItxUUyXrQ4x\naELqpYQhFfWMk6I2b2WIj6CkPkod0ryYb7bb9bxYtDHERxBSH6UOqSw21fSmGLcxxGdQUg+l\nDqkoTm6ED/EZhNRDqUOaHUIq2xjiQ/wpSVqdSxrS9GuxLL53k5v5/b0NQrrrspuRkDqXNKS9\nerLctDHEh/gTkkVS51IeR1qtFovptN7lML/bkZAeGF3eElLXnNmQoz8hKalrQsrS6HJaSB3r\nIKRFWYzvHo4V0kOjP5NK6lbSbaRpUS62X/Ueh0k7Q3yM0eWUkLqVMKTV/iS7YrbZrqdOEXrP\n6PYEXUgY0qw6djTfH4l1itC7Rhf/Cqlbyc/+LqYnN6KH+CB/1uiE1KnkIX3v1+mcIvSmv5tG\nSupS0lW72eEw7GbmFKF3/dnr/fd8B9JJGNKmPK7PFVcWSMWpF4f4JH8Pw17cElJKSY8jzQ/5\nlPc/IGuJ1MSfM4NGd++lVc5syNbfU1UvVvSElJCQ8vVn5e1iz4OQEhJSvu58vm90/QG0pquQ\nHEdqw8VRWiGlI6QhuTzdQUnJWLUblItVOiElI6RBuThKK6RkhDQsoz87wUkiaUg/X9P6vIXp\n/KetIT6dkDqS8hSh8ck5QD7Y15Lzg0tCSiVhSPOi/F7VU+tl6aTVlozu3qQtCUMqi9VxeuVj\nFGkIKZHkn0e6diNsCP5QUhqWSAMnpDTSbiMt1/WUbaR0hJRGyt3fk5O9dmPX/k5ESUmkPY40\nr48jldMvx5GSeRyS1AI4s2HoHmbib1lEENLgPcpESBGENHgPMvFZ2hBCGr77mQgphJCG724m\nPpQeQ0jD1yAkJb1LSB/gTiU+lB5ESB+gQUhKepOQPsHNyxe7Bn8UIX2G6yn5MG0YIX2Ka6H4\nNG0YIX2Mvwule3/MgucI6YNcpuRj6XGE9FFGd7eKlPQ6IX2Y0ej2Hm8hvU5In2d087SgUS3x\nyxkGIX2iupabwcjpBUL6UA9LUdJThMR1QnqKkLhBSc8QEjcI6RlC4hYlPUFI3CKkJwiJm5TU\nnJC4SUjNCYnblNSYkLhDSU0JiTuE1JSQuEdJDQmJe4TUkJC4S0nNCIm7ngjpo5sTEvc1zuOz\n/zyMkLhPSI0IiQca5vHhfx5GSDzSLA8hJZilh0PQ3LXLpFz/wueWJCQeu+xj9Hd7SEgpZunh\nEDzjysWNr1/v+GNLEhJNnFx06Opl8YSUZJYeDsGTDn8j8+qFWkdXpj6LkGjozwrd1XqE1OYs\nPRyCp40uryr5YOH0UYREY9f31Pl7ZRUh8brR2T/ba7c+hZB4w5Ud4UJqcZYeDkGIaycGfWRJ\nQuId1/48jJBam6WHQxDj2ocnPrEkIfGeJme0fgAhEe8DSxIS8YTU0iw9HII2fV5JQqINH1eS\nkGjFp5UkJNrxYSUJiZZ8VklCoi2X5+CNhpyWkGjL+acr6rPyah29nHYJidb8uc7D4cYAWxIS\n7bl1SRQhvThLD4cghf3nlT7htFYh0aY/13k4fHlohESrbiQzuJKERBeEJCQCCElIRBhaSUKi\nE0ISEhEGVpKQ6IaQhESEYZUkJDoipPhX0cEQdE1I8a+igyHo3KBKEhJdEdKrfr6mRWU6/2lr\nCDIypJIShrQZF/9NWhmCrAjpJfOi/F7VU+tlWczbGIKsCOklZbE6Tq+Kso0hyMuASkoYUlHc\nuhE2BHkR0isskbg0nJLSbiMt1/WUbST2hPSKycleu/GmlSHIzGBKSnscaV4fRyqnX44jURvM\nJe6c2UC3BnK5SCHRuSFcx7iDkBZlMV60OwTZyT2llCGtpkW52H45RYhr8i4pYUiruqB5Mdts\n19Pi7jJJSB9ISA3NqmNH8/2R2E0xbmMIcpZ1SclPESqmJzeihyBnQmo4Xz3j936dzilC/JFz\nSUlX7WaH0xk2M6cI8YeQGtmUx/W54soCqTj14hDkLeOSkh5Hmh/yKe8ujyyRPla+JTmzgR4R\nUiwhfapsSxISfSKkZ5/EcSSuybUkIdEvmZZk1Y5+EVIgIX2wJ0oa/dfe62lGSPRM8yZGN6a7\n4Nrf9E3DJi6WQh2X5Nrf9E2zJP48qtuSXPub3mmSxJXHdFqSK63SP4/3HVx9QJclufY3fXQ/\npVv3dliSJRL9dCelV+5pm2t/01dXUnp4zKizklz7m/4aXWowS/uv6irX/mZYOirJmQ0MzPU1\nwrZHFRKDc9bN7xph2+fjCYkh+p/P3y+2QkgM1dVs2kpJSHyYdkoSEh9GSBChlZKExKcREkRo\noyQh8XlaKElIfB4hQYT4koTEBxISRAgvSUh8IiFBhOiShMRneuKCrk0eKiQ+U9OQqowapCQk\nPlSjkg4JPUxJSHyoJldSOf2k7f2HColP9aiky6v03328kPhYDy7n+tTjhcQHe/Zak7cfLyQ+\nWdjVj4XER7u5uiYkeMb1Yp4980FIfLqrCyUhwbMC/vyfkCDgD9IKCYQEIUZ3bzYgJBASxBjd\nudWEkGB7kc4LH58VElRGN6YbEhLURlemmhMS1IQEEUZ/Jp4gJNgbXfz7FCHBr9HZP88REhyM\njv95mpDgQEgQYbQVErxt9PJFwYUE/42EBO9rdMH8a4QEJ4QEHRISBBASBBASBBASBBASBBAS\nBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBBASBOhpSJCZF97l\n8eH0Y8RU39iwvp1hDZPy3S2kPMYxTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH\n9rsyTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/H\nSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/HSTtU2hEH9rsyTJ/HSTsUDJeQIICQIICQIICQIICQ\nIICQIICQIICQIICQIICQIICQIICQIICQIICQIICQIEDikOZlUc437Y6xOHxPrQ62GB+fvMVx\nNrOimK22bQ9T+SlaH+b0CvWtfjer6se2bn+cE2lDmtQ/yHGrY6wOf0ug1cHm9ZOXm5bHKevn\nrktq+We3Kfc/thaHWZ2E1Op3s0zzyzmTNKSfolxtV2Xx0+IYu6cv2h9sVcw21bJv1u4482qA\neTHdtv+zm+5/bG0Os6q/kW3bw+z+97N78s20mKd5x+0lDWleLHf//S6+2htiUUwO6w5tDjbd\nj1EN1eY4ZbH5HaXtn93375KizWEW/5+11e/mu0pouynKJO+4X0lDmhbVeuvJ/5ji7X6GvyEl\nGKweqv1xqndEy8OsD///aXOYRbE4TLb63cyKVZJxziQNqShO/2nF6nKUNgfbFJME48zr91+7\nw0yK9f6Z2xxmWixnuy3/tofZjovtV1mve6d4E/waWkh/RmlzsEW14tDyOLt1rvbfel/F9zZF\nSLVJy8PsnrUeqWx7nPNBWx/hdLBhhbQup+2Ps5iW9Rp+m8PUqz7th1Tsct1u6gVsyyFVOxtm\n1Y9NSGGjtDfYppwkGWe3zt/yW29c7SluP6S9TbUzuuWQqm2kdevjnA/a+ggnypQhtT7YZJxm\nnP3+pxaHmdW7tvbPnOBXVD13q8Oc1JPmHVcP0foIJ/b7UNYt70M522vX2mDr8WSdYpzK/52D\nrQxTHA3huzk7NpHmHVeP1voIJ77q//Ut91vPrfkNqd3BlvU2c9vj7I8j1SspLQ5zGlKK72ba\n8i9n/+Tr6jeU5h1XGdyZDceQWh1sfeyo/TMbNtNqG6n1n137ZzbMq/fzpj5G2vIvZ7ypdjZ8\nD/bMhu34uP+zRYcV4jYHm/3/f3ir45T/n7vtn93vj63FYTb772be8jDVcijZT+0obUib+lzc\nlgc5hNTmYCcrQ+1+U7vnHu/PB2j7Z/f7Y2tzmE2q72Y5OTx5kndcJW1IMFBCggBCggBCggBC\nggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBC\nggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCggBCysb+TwSWs/0fU9+uZmUxW3b7kjgS\nUjYOf22zrEua72+M112/LGpCysb+j7xuJvVfM/4qyt3SaPP1mxVdE1I2Dn8tuSi32/UhoFkx\n6/I1cSCkbBz+Wnv177z42t/YTKu/Er6cFMXE9lKXhJSN0yXSpFid3LPYby8tunldVISUjX1I\n63obqTj7vZVVVt/FuJvXRUVI2TjutdtchlQUVuu6JqRsnB5HOg9pXhTT1erGbCQhpGycxjM9\nbiMtd8un7Vd5PL5EN4SUjdOQvg577X5+t4yW87FtpC4JKRunIR2PI03+76sr/C475IefjbNQ\nZvWZDetptS98Oy6+7bXrmJCycb7EmZyca/e9n/7p6IWxFVJGLlbdvqdFMfneT9dnNuioS0KC\nAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKC\nAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAEKCAP8AbZ+dtdDdCWkAAAAASUVO\nRK5CYII=",
      "text/plain": [
       "Plot with title \"MSE vs PCs\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(pcr_model_CV$val, main = \"MSE vs PCs\", type = \"l\",\n",
    "     ylab = \"MSE\",\n",
    "     col = \"blue\", xlab = \"PCs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the number of components increases the value of the MSE decreases, we keep 60 components."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RMSE error in the test prediction after cross-validation<a class=\"anchor\" id=\"8\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Returning to the index of contents](#index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we convert the MSE error in RMSE error with the aim of having an error in the same units as target variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.500809839780857"
      ],
      "text/latex": [
       "0.500809839780857"
      ],
      "text/markdown": [
       "0.500809839780857"
      ],
      "text/plain": [
       "[1] 0.5008098"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions <- predict(pcr_model, newdata = data_test, ncomp = 60)\n",
    "test_rmse <- sqrt(mean((predictions - data_test$W1.2MedDifWRelFFM1)^2))\n",
    "test_rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Percentage of accumulated explained variance with the number of principal components optimized: 96.851\"\n"
     ]
    }
   ],
   "source": [
    "print(paste('Percentage of accumulated explained variance with the number of principal components optimized:',summary(pca_train)$importance[3,60]*100))"
   ]
  }
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