T4-1-Linear Regression- Datos ficticios.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelos de Regresión Lineal\n",
    "## Modelos con datos simulados\n",
    "\n",
    "$Y=\\alpha+\\beta X$\n",
    "\n",
    "X:100 valores distribuidos según una normal con media 1.5 y desviación 2.5\n",
    "\n",
    "$Y=5+1.9*X + \\epsilon$\n",
    "\n",
    "$\\epsilon$ está distribuído según una N(0,0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=1.5+2.5*np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "res=0+0.8*np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred=5+2.8*x\n",
    "y_act=5+2.8*x+res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=pd.DataFrame(\n",
    "    {\"x\":x.tolist(),\n",
    "     \"y_act\":y_act.tolist(),\n",
    "     \"y_pred\":y_pred.tolist(),\n",
    "    }\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y_act</th>\n",
       "      <th>y_pred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.710247</td>\n",
       "      <td>-5.791908</td>\n",
       "      <td>-5.388691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.640003</td>\n",
       "      <td>17.906376</td>\n",
       "      <td>17.992008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.780662</td>\n",
       "      <td>15.591119</td>\n",
       "      <td>15.585853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.279585</td>\n",
       "      <td>17.591745</td>\n",
       "      <td>19.782838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.061602</td>\n",
       "      <td>5.303374</td>\n",
       "      <td>4.827513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6.201527</td>\n",
       "      <td>22.702186</td>\n",
       "      <td>22.364275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.676909</td>\n",
       "      <td>7.370178</td>\n",
       "      <td>6.895346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.134579</td>\n",
       "      <td>5.825537</td>\n",
       "      <td>5.376822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-1.386763</td>\n",
       "      <td>0.775243</td>\n",
       "      <td>1.117064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1.795293</td>\n",
       "      <td>9.891360</td>\n",
       "      <td>10.026820</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           x      y_act     y_pred\n",
       "0  -3.710247  -5.791908  -5.388691\n",
       "1   4.640003  17.906376  17.992008\n",
       "2   3.780662  15.591119  15.585853\n",
       "3   5.279585  17.591745  19.782838\n",
       "4  -0.061602   5.303374   4.827513\n",
       "..       ...        ...        ...\n",
       "95  6.201527  22.702186  22.364275\n",
       "96  0.676909   7.370178   6.895346\n",
       "97  0.134579   5.825537   5.376822\n",
       "98 -1.386763   0.775243   1.117064\n",
       "99  1.795293   9.891360  10.026820\n",
       "\n",
       "[100 rows x 3 columns]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_mean=[np.mean(y_act) for i in range(1,len(x)+1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efd70319860>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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vw91vmdmB7r7OzA4E3s7GvUQkfrMfe4Mf3PtSm32v/PB0BvQtjykiidLjcfIWNNlvB152958lHVoITAxfTwTu6em9RCQmSZOLrd73fTw749bEoRFD+rNixngl+DyVjZb8x4EJwAtm9ly472pgBrDAzC4FGoHzsnAvEelt7SYXG920nhmLbwHg5ns1JDLfaRZKEUlrT1U15atSzD1TXR3MzS6xSzcLpaY1EJFINVMXYatWpT5YIgthFzoleRHZK6y9e1h7P2v5EtbuEzEUUkOeC4KSvEipa+1UNYMJE6CxEXNP1N4fOvhjHZfnS55cLGLFJ8kPSvIipay1U7WxMdhu10dXsXsHEzctj14IO/n97sHXujol+jyijleRUlZTszfBRzELFsDuyvvVKdur1PEqIim1NGbQeVpWFt0yj+p8Vads3lCSFyklrR2rFnSsNvft3/l79uyJLsFEdb6qUzZvKMmLlIqk+rkRdKwO2rU9s/c2NweLcbc3fXr6TlmJnZK8SIlYPflbiadWW3Vp6exUJZja2uhOWckLSvIixSTFcMa3t2ynZuoiRjZt6Nm1o0owtbVBJ2tLS/BVCT6vKMmL5INsjDVPMZyx+eJL+dGXvgMQ/VBTe5WVKsEUESV5kbhla6z5tGkdyjEVu3cwZelcAAb99PqgpJJORQXMnKkSTBHROHmRuHV3rHlDQ5DYV66EYcNg48aUp7VglHk4zj1dkq+uDlrrSuYFJ904+awu/yci3dCVseatib2xMUjYrY20iAQPUFadVEuvrtbDSyVG5RqRuGU61nzy5MTcMkCHKQhSMmtbS9eQx5KjJC8St0wSb0MD3HZbZok9mXvb8ouGPJYclWtE4taaYFvr61VVe2vjkycHSXjPnu5du7o69f2U1EuGkrxIPkiVeCdPhlmzun/Nfv1UhhGVa0TyVn195udWVsKgQW2377hDLXZRS14kb2VSopk0CX7xi9zHIgVLLXmRfJDqidfy8s7fpwQvnVCSF4lbiidet3/5UpaOOpy0Y2lSdaqKtKMkLxK3K67oMB3BgJ07OHz968w9+gz2pJorUmPbJUNK8iJxamiIfFp1v21bmLjqScqNoCO1slJj26XL1PEq0psaGoKWe2tiL4tuZxnsPW/jxqD1/utfK7lLl6glL9JbGhrgkkvattyjFshOJWp1JpE0lORFesu0abBrV8+uoQWypYuU5EV6SzYStBbIli5SkhfJtohVnlYPSbMyU2ttvnVsfGUl9O3b9hyNqJFuUJIX6YqoZfomT4Y+fYLRLxde2GbMu0+YwJxjxnPDyRexwyIecCovh3nzYPfu4H0bNsDs2ZotUnpMK0OJZKr1oaXkMe0VFXDCCfDQQ2nf2gJ888wr+ejql5n43H2pT9LCHdJN6VaGUpIXyVTUMn0Z2jl0P/rt3NHhwac25s1Ta126TMv/iWRDDztO+23e1PlJX/5y8FWJXrJENXmRdJJr8GkeXMqanTs1Fl6ySi15kSjta/ARU/86dJhdJtW+jGksvGSRWvIiUaZNS18/D6VK5tavX/fvq7HwkkVK8iJRetKi3rUreirgzuaJ11h4ySIleZEoPWlRty7GXVHRdn9FBcyZE/0DoLJSna6SVVlJ8mZ2h5m9bWYvJu0bZmYPmNn/hl/3y8a9RHrNGWd02JXRgOPWJ1Nra4MHmFI90BT1A2DmzKyELtIqWy35O4HT2+2bCjzk7h8EHgq3RfJD1JOrye7r+NBSZGdqeXnqJ1Nra4MHnFpagq/J+6N+AIhkUdYehjKzGuCP7n54uP0q8Cl3X2dmBwKPuPuH011DD0NJr4h6crW+Png9bVpQj+/K/w2zrk0bLJJFcT0Mtb+7rwtfvwnsn+okM6sD6gCqNKpAekOqUTPNzcFiHtu2ZTSipgP925U81Ssdrx78upCyWeTu9e4+1t3HjhgxojfCkVIXNWpm48buJXjNDil5LJdJ/q2wTEP49e0c3kskcxGt7oyLM5WVqqVLwchlkl8ITAxfTwTuyeG9RDKXYmRLc5/+bBo4pPP3to6ASdWZKpKHstLxamb/DXwKGA68BXwP+AOwAKgCGoHz3P2ddNfpbsfrp3/9aR58/cEuv09EJF+cdvBpPDDhgW69N+cdr+5+QcShU7NxfRER6Z6imKCsuz/9pDTVTF0EwFnLlzBl6VxGNa2PHv+uhTykwBVFkhdJaGgIhkg2NgYPKO3ZEyTq6dOpeWFo4rSzli/hxj/NpN+e3emvpxkhpcApyUtxaGgIxrlv3Lh3X+vUwI2N+IUX8kKf/uzq24+h27biBuWZ9Edp/LsUOCV5KXypnmBtx4Ahu3fA7h3BjkzGG/Trp/HvUvA0C6UUroYGGD4cLrywew8xpVNZCXfcoeGRUvDUkpfC1NAAl1wSzNueTZWVsGFDdq8pEiMleSk8DQ0wcWLkcnzd1revpvqVoqNyjRSW1vp7thN8dTXMnq3yjBQdteSlsGS47mqXaCy8FDG15KWwNDZm93qaQVKKnJK8FJbOFsHujGaQlBKjJC/5J2Jpvpqpi/Ce1OI1g6SUICV5yS+TJ8OECUFZxj14WrWujss/+20A1uyT4cIy5eUwaZJa7VLylOQlXsmt9uHDYdasDmurWnMzU5bOBeCGky/qMBd8Si0t8ItfqNUuJU9JXuLTvtWePO9MOyObNnDRCdXcfO+NQYt88OD019acMyKAkrzEpaEBbrutQ6s9Sll1FdeeffjeHS0t6d+gETMigJK8xGXatIwTPGZtk3ZnY+UrK1WaEQkpyUs8ujJP+9e+1jZpp3tv6wgaEQGU5CUumdbMKyuDDtRM3lterhE0Iu0oyUssnvrqlTT36Z/+pKhW+fTpHUfYVFTAnDlK8CLtKMlLr6uZuogvbDmYqad/nXcGDkm9fkdlZXSrvLY2OKYx8CKdMs+086sXjB071pctWxZ3GJIjrQtoJ3vjvydjqWrsmjRMJGNm9rS7j011TLNQSq9ITvBnLV/ClKVzGb1lQ/QIGy2gLZIVKtdI10XMLZNKzdRFHRL8zQ/PYnTT+vRDKPUwk0hWKMlL17Qu2pE0twx1dR0S/eIX13Uoz0w4vpqbX7ir8/ngNf2vSNaoJi9dU1OTek73pBp6qtr7ihnjgxdlZelb8NXVQYJXJ6pIxlSTl+yJqpWvXJkyuf/jR/9Kvz5JvzBWVUUv/GGmzlaRLFO5Rromola+sf9gHp11Ca9f/1kenXUJZy1fwooZ44MEn1zD37q1y9cWke5TS166Zvr0oAafVFffYeUM2bWNyu1bABjdtJ6bH54FDccEJySfv3FjkOzbTzCmOrxITijJS9eEtfLtU6bSb+0a1u4znKHbtjB41/a25zU3BxOJtb5O1tISPOw0eHBQ/qmqUh1eJEdUrpEuDYkEqHlhKIdMuI2D//Nebjj5Iga1T/CtVq6MruG/844W9BDpBWrJl7rWIZGtre3WIZHQIfGmeqBpVNN6LOrarTX2VB2tqr+L9Aq15EtdqrnZk0stofYJfsbiWxidLsFDUIKJmkxM9XeRXqGWfKlLMyQSUo95v/mFu2D3jvTXbb9wx7Rpqr+LxEAt+VIXUTbZMXJUhwR/wbFVwUNNnc0r036K4Npa1d9FYqIkX+pSlFNagH5rVifGu0PwxOp1nz8iOCFdPV3T/orkFSX5Upc0N3sLQYIvA4xgvPvMh2ex4ojNbd8TVWefN08tdZE8oyQvUFtLzfm3snafER3+QViKTlgt2iFSOHKe5M3sdDN71cxeM7Opub5fyctkzHvSOav3fR+Xf/bbAIxs2pD6mqlq8KqzixSEnI6uMbNy4Fbg08Bq4CkzW+juL+XyviUrkzHv7c4Z3bSeGYtvAaBpxAEMXb+u43U1pl2kYOW6JX8s8Jq7v+7uO4H5wNk5vmfpymTMe4pzKnbv4OYX7mLoTT/RmHaRIpPrJD8KWJW0vTrcl2BmdWa2zMyWrV+/PsfhFLlOxrxfMf9ZWhojzmlsVK1dpAjF3vHq7vXuPtbdx44YMSLucApbVFmlqoqaqYu457m1rN1neOpzzIJSjmrtIkUl10l+DTAmaXt0uE9yIcXQxuY+/bn8iHMT2w8d/LHU73XvOIpGRAperpP8U8AHzewgM+sHnA8szPE9S0vyaJpp02DiRKiuxs1Yvc8Ipp7+dRYeNg6AO/r9g4n/eCT6Wp09ySoiBSeno2vcfbeZfR24HygH7nD35bm8Z0lJNZpmzhwuP2USC88f1+bUFTPGQ81l6RfR1igakaKT8wnK3P0+4L5c36ckRYymmbJ0bqL1vvwHn2FQ//DbnK6lrlE0IkUp9o5X6YGIpD2qaT2PzrqEFTd8lkEf/sDeB6KiWurl5RpFI1KklOQL2bBhKXe3zjuD+94HohoaouecmTNHCV6kSGk++QLVtH0XZU1bGZzJya0PRK1YEWxrbneRkqEkX4Bqpi7irOVLmLmrk4U7krWWdmprldRFSojKNfkoYpKx3z+zOrGQx5Slc9MvvdeeRs6IlCS15PNJQwNccQVs3Lh3X1hTv3z+s4kRM5BmxkiAvn1h16692xo5I1Ky1JLPF61j3pMTfKtwWGSrFTPGU1Yd0TKvrITZszX/jIgAYO4edwwJY8eO9WXLlsUdRjxqaoJWe4QWjMV/X8MZRxwY7Gj/IBQELXYldJGSY2ZPu/vYVMfUks8XnUwpUFZdtTfBg2aMFJGMqCafL6qqolvyUTV1jZQRkU6oJZ8nLj/iXJr79O94oLJSLXQR6Ta15GP2vXteZM7jjRCOnJmydC6jt2zQg0oikhVqyWdTJotoh3bs3kPN1EVBgg9NvOVqRr/7thbsEJGsUUs+WzJZRDvU+kBTshUzxuc6QhEpQRpCmS1RQyCrqxNzxjy/ajNn3/pYm8Ov/PB0BvQtz318IlK00g2hVEs+WzpZRLt96/2LY8dw/blH5joqESlxSvLZEjEEcvPwAzi6XYJXaUZEeos6XrMlYhHt7x73pcT2b+uOV4IXkV6llny2tHauTptGS+NK1u4znBtOvigxqZiSu4jEQUk+izZt28l7m5oZmbTv5WtPZ2A/dayKSDxUrsmS+6b+lP6TJjG6aT1lOKOb1nPzw7MY+D/z4w5NREqYknwP/XP9VmqmLuLIWddTsbvdSk2ty+6JiMRE5Zpuamlxan/1JI+/Hsz/HrmIRyezS4qI5JJa8t3w4EtvcfDV9yUS/M0XHBO9iIeW3RORGKkl3wVbtu/i6GsfYE9L8JTwYSP34Z7LPk6f8rJgCGWqRTy07J6IxEhJPkMzH/xfbnrwH4ntRZefxGEj92170sCBe5N8ZSXMnKlJxkQkVkrynXhjw3uMu/GRxPbFJ9bw/bMOa3tSqqX4tm3rnQBFRNLQBGURWlqcibP/xv/7370dqs9c82mGDerX8eQMJicTEckVTVDWRUteeZtL7nwqsf3zLx7NOceMin5DJ5OTiYjERUk+ydYdu/nItQ+wc08LAIccMIQ/fuOkoGM1naj1WTWyRkRipiGUoVuXvMbh37s/keD/+I2TWPzNkztP8JBycjKNrBGRfFDyLfkVG97jU0kdqxedUM21Zx/etYskTU7GypVan1VE8kbJJnl355I7n+KRV9cn9i37zmkMH9y/exesrVVSF5G8U5JJ/pFX3+bi2Xs7Vn923lF8/iOjY4xIRCQ3SirJN+/czUd/+CDbdu0B4EP7D2bR5Z+gbyZ1dxGRAlQySf4Xj7zGDYtfTWzf+/WTOGL0vmneISJS+Io+yTdufI9P/uSRxHbtcVVM/9wR8QUkItKLijbJuzuXzlnGw6+8ndjXo45VEZEC1KNitJl9wcyWm1mLmY1td+wqM3vNzF41s8/0LMyuWfqP9Rx01X2JBP+Tc49kxYzxSvAiUnJ62pJ/Efg88MvknWZ2KHA+cBgwEnjQzD7k7nt6eL+0mnfu5tjpD7F1x24ADh4xiPu/ebI6VkWkZPUoybv7ywBm1v7Q2cB8d98BvGFmrwHHAo/35H7p/PIv/+S6P72S2P7DZR/n6DFDc3U7EZGCkKua/CjgiaTt1eG+nLj3+bWJBH/BsWO47vNH5upWIiIFpdMkb2YPAgekODTN3e/paQBmVgfUAVR1c0KvcYe8j3EfHsH15x7J+4YM6AeZgZUAAAVTSURBVGlIIiJFo9Mk7+6ndeO6a4AxSdujw32prl8P1EMwn3w37sXg/n2Yfcmx3XmriEhRy1WP5ELgfDPrb2YHAR8E/paje4mISISeDqH8nJmtBk4AFpnZ/QDuvhxYALwELAYuy/XIGhER6ahHSd7d73b30e7e3933d/fPJB2b7u7vd/cPu/ufeh5qhIaGYPm9srLga0NDzm4lIlJoCvuJ1/YLaDc2BtugaX9FRCj0laGmTdub4Fs1Nwf7RUSkwJO8FtAWEUmrsJN81Lh6LaAtIgIUepLXAtoiImkVdpKvrYX6eqiuBrPga329Ol1FREKFPboGtIC2iEgahd2SFxGRtJTkRUSKmJK8iEgRU5IXESliSvIiIkXM3Ls1hXtOmNl6oBEYDmyIOZxMFEqcUDixKs7sUpzZl4+xVrv7iFQH8irJtzKzZe4+Nu44OlMocULhxKo4s0txZl8hxQoq14iIFDUleRGRIpavSb4+7gAyVChxQuHEqjizS3FmXyHFmp81eRERyY58bcmLiEgWKMmLiBSxvE7yZvYNM3vFzJab2Q1xx5OOmV1pZm5mw+OOJRUz+0n4Wf7dzO42s6Fxx5TMzE43s1fN7DUzmxp3PFHMbIyZLTGzl8J/l1fEHVM6ZlZuZs+a2R/jjiWKmQ01s7vCf58vm9kJcceUipl9K/yev2hm/21mA+KOKRN5m+TNbBxwNnCUux8G3BhzSJHMbAzwL0A+rzv4AHC4ux8J/AO4KuZ4EsysHLgV+FfgUOACMzs03qgi7QaudPdDgeOBy/I4VoArgJfjDqITM4HF7n4IcBR5GK+ZjQIuB8a6++FAOXB+vFFlJm+TPDAJmOHuOwDc/e2Y40nnJmAKkLe92O7+Z3ffHW4+AYyOM552jgVec/fX3X0nMJ/gB3zecfd17v5M+HoLQUIaFW9UqZnZaGA88Ku4Y4liZvsCJwO3A7j7TnffHG9UkfoAA82sD1ABrI05nozkc5L/EPAJM3vSzP5iZh+LO6BUzOxsYI27Px93LF3wZeBPcQeRZBSwKml7NXmaOJOZWQ1wDPBkvJFE+jlB46Ml7kDSOAhYD8wOy0q/MrNBcQfVnruvIagmrATWAe+6+5/jjSozsa4MZWYPAgekODSNILZhBL8SfwxYYGYHewxjPjuJ82qCUk3s0sXp7veE50wjKDk09GZsxcbMBgO/A77p7k1xx9OemZ0JvO3uT5vZp+KOJ40+wEeAb7j7k2Y2E5gKXBNvWG2Z2X4Ev10eBGwG/sfMLnT3efFG1rlYk7y7nxZ1zMwmAb8Pk/rfzKyFYGKg9b0VX6uoOM3sCIJv+vNmBkEJ5BkzO9bd3+zFEIH0nyeAmV0MnAmcGscPyzTWAGOStkeH+/KSmfUlSPAN7v77uOOJ8HHgLDM7AxgA7GNm89z9wpjjam81sNrdW38buosgyeeb04A33H09gJn9HjgRyPskn8/lmj8A4wDM7ENAP/Js5jd3f8Hd3+fuNe5eQ/AP9iNxJPjOmNnpBL+6n+XuzXHH085TwAfN7CAz60fQobUw5phSsuCn+e3Ay+7+s7jjieLuV7n76PDf5fnAw3mY4An/r6wysw+Hu04FXooxpCgrgePNrCL8N3AqedhBnEo+L+R9B3CHmb0I7AQm5lnrs9DcAvQHHgh/63jC3b8Wb0gBd99tZl8H7icYtXCHuy+POawoHwcmAC+Y2XPhvqvd/b4YYyp03wAawh/wrwOXxBxPB2Ep6S7gGYJy57MUyPQGmtZARKSI5XO5RkREekhJXkSkiCnJi4gUMSV5EZEipiQvIlLElORFRIqYkryISBH7/z+abkjA3dvXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y_pred)\n",
    "plt.plot(x,y_act,'ro')\n",
    "plt.title(\"Valor actual vs predicción\")\n",
    "plt.plot(x,y_mean,'g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[\"SSR\"]=(data.y_pred-np.mean(y_act))**2\n",
    "data[\"SST\"]=(data.y_act-np.mean(y_act))**2\n",
    "data[\"SSD\"]=(data.y_pred-y_act)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y_act</th>\n",
       "      <th>y_pred</th>\n",
       "      <th>SSR</th>\n",
       "      <th>SST</th>\n",
       "      <th>SSD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.710247</td>\n",
       "      <td>-5.791908</td>\n",
       "      <td>-5.388691</td>\n",
       "      <td>205.119345</td>\n",
       "      <td>216.831649</td>\n",
       "      <td>0.162583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.640003</td>\n",
       "      <td>17.906376</td>\n",
       "      <td>17.992008</td>\n",
       "      <td>82.060249</td>\n",
       "      <td>80.516149</td>\n",
       "      <td>0.007333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.780662</td>\n",
       "      <td>15.591119</td>\n",
       "      <td>15.585853</td>\n",
       "      <td>44.256507</td>\n",
       "      <td>44.326594</td>\n",
       "      <td>0.000028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.279585</td>\n",
       "      <td>17.591745</td>\n",
       "      <td>19.782838</td>\n",
       "      <td>117.712555</td>\n",
       "      <td>74.968728</td>\n",
       "      <td>4.800890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.061602</td>\n",
       "      <td>5.303374</td>\n",
       "      <td>4.827513</td>\n",
       "      <td>16.857457</td>\n",
       "      <td>13.176342</td>\n",
       "      <td>0.226443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6.201527</td>\n",
       "      <td>22.702186</td>\n",
       "      <td>22.364275</td>\n",
       "      <td>180.391165</td>\n",
       "      <td>189.582324</td>\n",
       "      <td>0.114184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.676909</td>\n",
       "      <td>7.370178</td>\n",
       "      <td>6.895346</td>\n",
       "      <td>4.153245</td>\n",
       "      <td>2.443340</td>\n",
       "      <td>0.225466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.134579</td>\n",
       "      <td>5.825537</td>\n",
       "      <td>5.376822</td>\n",
       "      <td>12.648512</td>\n",
       "      <td>9.658173</td>\n",
       "      <td>0.201345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-1.386763</td>\n",
       "      <td>0.775243</td>\n",
       "      <td>1.117064</td>\n",
       "      <td>61.093500</td>\n",
       "      <td>66.553839</td>\n",
       "      <td>0.116841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1.795293</td>\n",
       "      <td>9.891360</td>\n",
       "      <td>10.026820</td>\n",
       "      <td>1.195793</td>\n",
       "      <td>0.917885</td>\n",
       "      <td>0.018349</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           x      y_act     y_pred         SSR         SST       SSD\n",
       "0  -3.710247  -5.791908  -5.388691  205.119345  216.831649  0.162583\n",
       "1   4.640003  17.906376  17.992008   82.060249   80.516149  0.007333\n",
       "2   3.780662  15.591119  15.585853   44.256507   44.326594  0.000028\n",
       "3   5.279585  17.591745  19.782838  117.712555   74.968728  4.800890\n",
       "4  -0.061602   5.303374   4.827513   16.857457   13.176342  0.226443\n",
       "..       ...        ...        ...         ...         ...       ...\n",
       "95  6.201527  22.702186  22.364275  180.391165  189.582324  0.114184\n",
       "96  0.676909   7.370178   6.895346    4.153245    2.443340  0.225466\n",
       "97  0.134579   5.825537   5.376822   12.648512    9.658173  0.201345\n",
       "98 -1.386763   0.775243   1.117064   61.093500   66.553839  0.116841\n",
       "99  1.795293   9.891360  10.026820    1.195793    0.917885  0.018349\n",
       "\n",
       "[100 rows x 6 columns]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5240.787641807268, 72.62292194887115, 5330.609179012229)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(data.SSR),sum(data.SSD),sum(data.SST)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5313.41056375614"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(data.SSR)+sum(data.SSD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.983149855074987"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2=sum(data.SSR)/sum(data.SST)\n",
    "R2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  1.,  5.,  5., 26., 21., 17., 12.,  8.,  4.]),\n",
       " array([-2.42163771, -1.96036461, -1.49909151, -1.0378184 , -0.5765453 ,\n",
       "        -0.1152722 ,  0.34600091,  0.80727401,  1.26854711,  1.72982021,\n",
       "         2.19109332]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data.y_pred-y_act)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "SST=SSR+SSD\n",
    "\\end{equation}\n",
    "\n",
    "La ecuación anterior sólo se cumple con los parámetros óptimos de la regresión."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El valor de $R^2$ es el valor que es capaz de ser interpretado por la regresión $1-R^2$ indica ese porcentaje de datos que tienen un error no explicable por el modelo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Obteniendo la recta de regresión"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "Y=\\alpha+\\beta*X\\\\\n",
    "\\beta=\\frac{\\sum_{i=1}^{n}(x_{i}-\\overline{x})(y_{i}-\\overline{y})}{\\sum_{i=1}^{n}(x_{i}-\\overline{x})^{2}}\\\\\n",
    "\\alpha=\\overline{y}-\\beta \\overline{X}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_mean=np.mean(data.x)\n",
    "y_mean=np.mean(data.y_act)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[\"beta_n\"]=(data.x-x_mean)*(data.y_act-y_mean)\n",
    "data[\"beta_d\"]=(data.x-x_mean)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.7986220247814035, 2.80656255063415)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta=sum(data.beta_n)/sum(data.beta_d)\n",
    "alpha=y_mean-beta*x_mean\n",
    "alpha,beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El modelo lineal obtenido por la regresión $4.946441214652191 + 1.928281316863629*X$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "data[\"y_model\"]=alpha+beta*data.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y_act</th>\n",
       "      <th>y_pred</th>\n",
       "      <th>SSR</th>\n",
       "      <th>SST</th>\n",
       "      <th>SSD</th>\n",
       "      <th>beta_n</th>\n",
       "      <th>beta_d</th>\n",
       "      <th>y_model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.710247</td>\n",
       "      <td>-5.791908</td>\n",
       "      <td>-5.388691</td>\n",
       "      <td>205.119345</td>\n",
       "      <td>216.831649</td>\n",
       "      <td>0.162583</td>\n",
       "      <td>76.327562</td>\n",
       "      <td>26.868295</td>\n",
       "      <td>-5.614418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.640003</td>\n",
       "      <td>17.906376</td>\n",
       "      <td>17.992008</td>\n",
       "      <td>82.060249</td>\n",
       "      <td>80.516149</td>\n",
       "      <td>0.007333</td>\n",
       "      <td>28.415823</td>\n",
       "      <td>10.028535</td>\n",
       "      <td>17.821080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.780662</td>\n",
       "      <td>15.591119</td>\n",
       "      <td>15.585853</td>\n",
       "      <td>44.256507</td>\n",
       "      <td>44.326594</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>15.362559</td>\n",
       "      <td>5.324303</td>\n",
       "      <td>15.409286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.279585</td>\n",
       "      <td>17.591745</td>\n",
       "      <td>19.782838</td>\n",
       "      <td>117.712555</td>\n",
       "      <td>74.968728</td>\n",
       "      <td>4.800890</td>\n",
       "      <td>32.957245</td>\n",
       "      <td>14.488441</td>\n",
       "      <td>19.616108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.061602</td>\n",
       "      <td>5.303374</td>\n",
       "      <td>4.827513</td>\n",
       "      <td>16.857457</td>\n",
       "      <td>13.176342</td>\n",
       "      <td>0.226443</td>\n",
       "      <td>5.571275</td>\n",
       "      <td>2.355669</td>\n",
       "      <td>4.625731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>6.201527</td>\n",
       "      <td>22.702186</td>\n",
       "      <td>22.364275</td>\n",
       "      <td>180.391165</td>\n",
       "      <td>189.582324</td>\n",
       "      <td>0.114184</td>\n",
       "      <td>65.103578</td>\n",
       "      <td>22.356915</td>\n",
       "      <td>22.203594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.676909</td>\n",
       "      <td>7.370178</td>\n",
       "      <td>6.895346</td>\n",
       "      <td>4.153245</td>\n",
       "      <td>2.443340</td>\n",
       "      <td>0.225466</td>\n",
       "      <td>1.244723</td>\n",
       "      <td>0.634106</td>\n",
       "      <td>6.698410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.134579</td>\n",
       "      <td>5.825537</td>\n",
       "      <td>5.376822</td>\n",
       "      <td>12.648512</td>\n",
       "      <td>9.658173</td>\n",
       "      <td>0.201345</td>\n",
       "      <td>4.160164</td>\n",
       "      <td>1.791950</td>\n",
       "      <td>5.176327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-1.386763</td>\n",
       "      <td>0.775243</td>\n",
       "      <td>1.117064</td>\n",
       "      <td>61.093500</td>\n",
       "      <td>66.553839</td>\n",
       "      <td>0.116841</td>\n",
       "      <td>23.331867</td>\n",
       "      <td>8.179484</td>\n",
       "      <td>0.906585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1.795293</td>\n",
       "      <td>9.891360</td>\n",
       "      <td>10.026820</td>\n",
       "      <td>1.195793</td>\n",
       "      <td>0.917885</td>\n",
       "      <td>0.018349</td>\n",
       "      <td>0.308569</td>\n",
       "      <td>0.103733</td>\n",
       "      <td>9.837224</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           x      y_act     y_pred         SSR         SST       SSD  \\\n",
       "0  -3.710247  -5.791908  -5.388691  205.119345  216.831649  0.162583   \n",
       "1   4.640003  17.906376  17.992008   82.060249   80.516149  0.007333   \n",
       "2   3.780662  15.591119  15.585853   44.256507   44.326594  0.000028   \n",
       "3   5.279585  17.591745  19.782838  117.712555   74.968728  4.800890   \n",
       "4  -0.061602   5.303374   4.827513   16.857457   13.176342  0.226443   \n",
       "..       ...        ...        ...         ...         ...       ...   \n",
       "95  6.201527  22.702186  22.364275  180.391165  189.582324  0.114184   \n",
       "96  0.676909   7.370178   6.895346    4.153245    2.443340  0.225466   \n",
       "97  0.134579   5.825537   5.376822   12.648512    9.658173  0.201345   \n",
       "98 -1.386763   0.775243   1.117064   61.093500   66.553839  0.116841   \n",
       "99  1.795293   9.891360  10.026820    1.195793    0.917885  0.018349   \n",
       "\n",
       "       beta_n     beta_d    y_model  \n",
       "0   76.327562  26.868295  -5.614418  \n",
       "1   28.415823  10.028535  17.821080  \n",
       "2   15.362559   5.324303  15.409286  \n",
       "3   32.957245  14.488441  19.616108  \n",
       "4    5.571275   2.355669   4.625731  \n",
       "..        ...        ...        ...  \n",
       "95  65.103578  22.356915  22.203594  \n",
       "96   1.244723   0.634106   6.698410  \n",
       "97   4.160164   1.791950   5.176327  \n",
       "98  23.331867   8.179484   0.906585  \n",
       "99   0.308569   0.103733   9.837224  \n",
       "\n",
       "[100 rows x 9 columns]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "SSR=sum((data.y_model-y_mean)**2)\n",
    "SST=sum((data.y_act-np.mean(y_act))**2)\n",
    "SSD=sum((data.y_model-y_act)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5261.690295025998, 68.91888398623135, 5330.609179012229)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SSR,SSD,SST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9870711054455878"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2=SSR/SST\n",
    "R2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efd6fbad160>]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_mean=[np.mean(y_act) for i in range(1,len(x)+1)]\n",
    "plt.plot(x,y_pred)\n",
    "plt.plot(x,data.y_act,'ro')\n",
    "plt.plot(x,data.y_model,'b')\n",
    "plt.title(\"Valor actual vs modelo\")\n",
    "plt.plot(x,y_mean,'g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Seleccionar alguna variable y descartar otras.\n",
    "* Conocer la relación entre la variable predictora y la variable de salida\n",
    "* Error en los valores que han sido predecidos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**P_Valor**\n",
    "\n",
    "Es necesario calcularse un estadístico t y un p_valor que garantice que la hipotesis nula es rechazada ($\\beta=0$) y que si existe covarianza entre las variables predictoras y a predecir.\n",
    "\n",
    "El test es a dos colas. p_valor < nivel de significancia. Pueden existir casos dónde el p_valor por ser tan grande no tiene gran significancia para el modelo.\n",
    "\n",
    "**Estadístico F**\n",
    "\n",
    "Se usa para comprobar que el conjunto de parémtros beta asociado a cada variable predictora sea significativo o no.\n",
    "\n",
    "Mirar el cambio al añadir una nueva variable predictora. Qué tanto se influencian entre sí. Ayuda a analizar la significancia en conjunto, puesto que se puede caer en el error de que individualmente se acepten y en conjunto no (p_valor muy grande)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error estándar de los residuos (RSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8386023600174581"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSE=np.sqrt(SSD/(len(data)-2))\n",
    "RSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuanto menor sea RSE es mejor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.933296723360357"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_mean[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09387378321650652"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSE/y_mean[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
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  "toc": {
   "base_numbering": 1,
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   "number_sections": true,
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
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