{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 9b - 2-fold cross validation\n",
    "\n",
    "We will finish Lab 9 in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>dataset</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>I</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>I</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>I</td>\n",
       "      <td>13.0</td>\n",
       "      <td>7.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>I</td>\n",
       "      <td>9.0</td>\n",
       "      <td>8.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>I</td>\n",
       "      <td>11.0</td>\n",
       "      <td>8.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  dataset     x     y\n",
       "0       I  10.0  8.04\n",
       "1       I   8.0  6.95\n",
       "2       I  13.0  7.58\n",
       "3       I   9.0  8.81\n",
       "4       I  11.0  8.33"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the Anscombe quartet data\n",
    "anscombe = sns.load_dataset(\"anscombe\")\n",
    "anscombe.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10.0</td>\n",
       "      <td>7.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.0</td>\n",
       "      <td>6.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>13.0</td>\n",
       "      <td>12.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.0</td>\n",
       "      <td>7.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>11.0</td>\n",
       "      <td>7.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>14.0</td>\n",
       "      <td>8.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>6.0</td>\n",
       "      <td>6.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>4.0</td>\n",
       "      <td>5.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>12.0</td>\n",
       "      <td>8.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>7.0</td>\n",
       "      <td>6.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>5.0</td>\n",
       "      <td>5.73</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x      y\n",
       "22  10.0   7.46\n",
       "23   8.0   6.77\n",
       "24  13.0  12.74\n",
       "25   9.0   7.11\n",
       "26  11.0   7.81\n",
       "27  14.0   8.84\n",
       "28   6.0   6.08\n",
       "29   4.0   5.39\n",
       "30  12.0   8.15\n",
       "31   7.0   6.42\n",
       "32   5.0   5.73"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Separate out the Anscombe 3 data\n",
    "anscombe_3 = anscombe[anscombe[\"dataset\"] == \"III\"]\n",
    "anscombe_3 = anscombe_3[[\"x\",\"y\"]]\n",
    "anscombe_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7faf4a113978>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Anscombe 3\n",
    "sns.regplot(x = \"x\", y = \"y\", data = anscombe_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the data in half into fold 1 and fold 2\n",
    "X_fold1, X_fold2, y_fold1, y_fold2 = train_test_split(anscombe_3[[\"x\"]], anscombe_3[\"y\"], test_size=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x\n",
       "30  12.0\n",
       "28   6.0\n",
       "25   9.0\n",
       "22  10.0\n",
       "27  14.0\n",
       "31   7.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_fold2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the fold 1 data to fit the linear model using the sci-kit learn version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_fold1 = linear_model.LinearRegression()\n",
    "lm_fold1.fit(X_fold1, y_fold1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this linear model to make predictions for the fold 2 data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "fold2_predictions = lm_fold1.predict(X_fold2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error for the fold 2 predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.756723420796892"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((y_fold2 - fold2_predictions)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's do the reverse.  Use the fold2 data to create the linear model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm_fold2 = linear_model.LinearRegression()\n",
    "lm_fold2.fit(X_fold2, y_fold2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this linear model to make predictions for the fold 1 data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "fold1_predictions = lm_fold2.predict(X_fold1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error for the fold 1 predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.604766161332178"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((y_fold1 - fold1_predictions)**2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do the two mean squared errors compare?  What might be happening here?\n",
    "\n",
    "To better understand whaat's happening, let's plot the two training data sets using `regplot()` in Seaborn.  \n",
    "\n",
    "First plot the fold 1 data, where x is `X_fold1[\"x\"]` and y is `y_fold1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7faf49f97e10>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x = X_fold1[\"x\"], y = y_fold1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next plot the fold 2 data, where x is `X_fold2[\"x\"]` and y is `y_fold2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7faf49f92630>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qZdehegCGZqfznZkTuHzSIE0jC6BSEOkWSnceYm5RMW9s3g9ASlIC119wCjdccArpKZpGlr8KrBTMLBf4XatFo4G73f2HrdaZCvwJ2Bxb9KS7zw8qk0h3c7C2if94Zh2/WrGVltg08qUTB3LXrIkM75MRbjjpkIK8R/M64HQAM0sEKoE/HGPVl919VlA5RLqjSIvzuzcr+P7TZRyojU4jn9I/k7mz85gyrn/I6aQja6/dR9OAje6+tZ3eT6TbWrX1AHOL1rK2MjqN3CM1iVumjeXqc0eSkqRpZPlg7VUKVwGPv89z55jZGmAHcJu7F7dTJpFOb3lZFQ+/tImKA7UMzEojLTmBv2zcF3/+02cO5fbLxzOgZ1qIKaUzCbwUzCwFKADuOMbTq4ER7l5jZjOAPwJjj/Eac4A5ADk5OQGmFek8lpdVcXdRMUkJ0YvXra44EL+K6aShPZlXkMdZI/qEG1I6nfbYlpwOrHb33Uc/4e6H3L0m9vUSINnM/u7yi+7+iLvnu3t+//7aHyoC8PBLm2iKRKisrmfXoQbcIcFgdL9M/vSV81QIclLaY/fRP/M+u47MbBCw293dzCYTLal9x1pXRP5q275a3qo4QH1TS3xZ38wUBmSlUtPQTKIuTyEnKdBSMLNM4BLgulbLrgdw94XAlcANZtYM1AFXub+3ASwiR6trjPDQ8nIWvrSJxuZoIWSmJDI4O5305ERqG5sZ1lunmsrJC7QU3P0I0PeoZQtbff0g8GCQGUS6Anfnz2t38d2nSqmsrgOgd0YyCWb0Sk8iLSmB2sZmmiLOdVNGh5xWOjNNNIt0cOt3H6awqJhXY2cVpSQm8KUpo/jKhWN4Y9N+Hn5pE9sP1DKsdwbXTRnN1PEDQk4snZlKQaSDOlTfxA+f2cDPX9tCJDaOPG38AO6aNZGR/TIBmDp+gEpA2pRKQaSDaWlxnli1nfueLmNvTSMAo/plcvesiVyoApCAqRREOpC3K6qZW1TMmopqADJSErnporF84byRpCbpwnUSPJWCSAew53AD9y0t439WbY8vu+L0IdwxfQKDemkaWdqPSkEkRE2RFn7x2lZ++Mx6Djc0AzBhcHQaefIoDZ9J+1MpiITk1fK9zC0qZkNVDQDZGcncemkun52co+EzCY1KQaSdbT9Qy4IlpSx5dxcAZvDZyTncdmkuvTNTQk4n3Z1KQaSd1DdFePjFTTz0Ynn88hT5I3pTWJDHpKG9Qk4nEqVSEAmYu7OsZDf3LC5h+4HoNPKArFTunDGBK04fonsjS4eiUhAJUHlVDfMWFfPyhr0AJCcaXzhvFDddNJYeqfrnJx2P/laKBOBwfRM/em4DP/3LFppj08gXjOvP3bMnckr/HiGnE3l/KgWRNvDeHdC27T9CenISe2oaOFgXvTdyTp8M7p41kWkTBmhXkXR4H1oKZnYT8Ct3P9AOeUQ6nffugNbS0sL+I03UNdUD0QvX3TxtDF88fzRpyZpGls7heLYUBgJvmtlq4CfA07rngchfPfhCOdW1jRyqb44vy0xNJHdgFjde9Hd3lxXp0D70dpzu/h2i901+DLgG2GBmC8zslICziXRozZEWfvHaFlZtOxAvhNSkBEb1y2RU30z2HG4IN6DISTiuYwqx22XuAnYBzUBv4Akze8bdvxlkQJGOaMWmfRQWFVO26zAQvTfywJ5p9M1Mwcx0BzTptI7nmMItwL8Ce4FHgW+4e5OZJQAbgGOWgpnlAr9rtWg0cLe7/7DVOgY8AMwAaoFr3H31SX4WkcDtPFjHgiVlLFqzA4hOI58/ph8b9xwhLTm64a07oElndjxbCn2AT7v71tYL3b3FzGa9329y93XA6QBmlghUAn84arXpRHdNjQU+ATwU+1WkQ2lojvDoy5t58Ply6poiAJyRk828gjxOHZYdP/tId0CTzu5DS8Hd537Ac6XH+T7TgI1HFwtwBfCL2IHrFWaWbWaD3X3ncb6uSOCeL9vNvEUlbN1XC0C/HqncPn08nz5jKAmxC9fpDmjSVbTXnMJVwOPHWD4UqGj1eHtsmUpBQrd57xHmLyrmhXV7AEhKMK45dyQ3XzyWnmnJIacTCUbgpWBmKUABcMdHeI05wByAnJycNkomcmxHGpr58fPlPPbKJpoi0bOvzx/bj7mzJzJmQFbI6USC1R5bCtOB1e6++xjPVQLDWz0eFlv2N9z9EeARgPz8fM1ISCDcnaI1O1iwpJTdh6Knkw7rnc53Zk7ksryBmkaWbqE9SuGfOfauI4Ai4EYz+y3RA8wHdTxBwlCy4xCFRcW8sWU/EJ03+PLUMVx3gaaRpXsJtBTMLBO4BLiu1bLrAdx9IbCE6Omo5URPSb02yDwiR6uubeT+Zev4zevbiF23jumTBvHtmRM0ZyDdUqCl4O5HgL5HLVvY6msHvhJkBpFjibQ4j7+xjfuXraO6NnrhujEDelA4O4/zxvYLOZ1IeHSVVOl2Vm7Zz9yiYop3HAIgKzWJWy4ey9XnjiQ58UOv/CLSpakUpNvYfaiee/9cxh/e+uu5DP/nrGF88/Lx9M9KDTGZSMehUpAur7G5hZ/+ZTM/em4DRxqj08inDetFYUEeZ+T0DjmdSMeiUpAubfm6KuYvKmHT3iMA9MlM4ZuX5fKZ/OHxaWQR+SuVgnQZ711/qOJALf17RHcHvVVRDUBigvH5s0fwtUvG0Std08gi70elIF3Ce3c/S0yAhqYIb1dU896U49mj+zCvYBK5gzSNLPJhVArSJSx8cSMNTRH21zbGL02RmGCM7pfJ4186W9PIIsdJpSCdXtmuQ7xVUU1DcwsABvTLSqV/ZgqHG5pVCCInQKUgndbB2iZ+8Ox6frliK5HYOHJWWhJDeqWTkpSgu5+JnASVgnQ6LS3O71dWcN/T69h/pBGAQT3TiLQ4PdOTSE403f1M5CSpFKRTeWvbAeYWFfPO9oMAZKYkcvO0sVz7yVG8Wr5Xdz8T+YhUCtIpVB2u53t/Xsf/rt4eX/apM4Zy+/TxDOyZBujuZyJtQaUgHVpTpIWfv7qFB57dwOGGZgDyhvRkXkEe+SP7hJxOpOtRKUiH9cqGvRQuKqa8qgaA3hnJ3HZZLld9PIdETSOLBEKlIB1Oxf5avvtUKUuLdwGQYPAvnxjBrZeOIzsjJeR0Il2bSkE6jPqmCA8t3xgdRIvNHEwe2YfCgjwmDukZcjqR7kGlIKFzd54u3sU9i0uprK4DYGDPVO6cMYGC04Zo+EykHQV9O85s4FFgEuDAF9z9tVbPTwX+BGyOLXrS3ecHmUk6lg27D1O4qJi/lO8DIDnR+OL5o7nxwjFkpupnFpH2FvS/ugeApe5+pZmlAMcaL33Z3WcFnEM6mEP1TTzw7AZ+/uoWmmPTyBfm9ufu2XmM6pcZcjqR7iuwUjCzXsAU4BoAd28EGoN6P+kcWlqc/129ne8tXcfemgYARvbN4K5ZE5k2YWDI6UQkyC2FUcAe4KdmdhqwCrjF3Y8ctd45ZrYG2AHc5u7FAWaSEK2pqGZuUTFvx+5xkJGSyI0XjeHfzhtFalJiyOlEBIIthSTgTOAmd3/dzB4AbgfuarXOamCEu9eY2Qzgj8DYo1/IzOYAcwBycnICjCxB2FvTwPeXruP3qyrw2E0OCk4bwh0zxjO4V3q44UTkb5i/96+0rV/YbBCwwt1Hxh6fD9zu7jM/4PdsAfLdfe/7rZOfn+8rV65s47QShOZIC79csZX/fGY9h+uj08jjB2UxryCPT4zuG3I6ke7FzFa5e/6HrRfYloK77zKzCjPLdfd1wDSg5KiQg4Dd7u5mNhlIAPYFlUnaz6sb91JYVMz63dFp5F7pydx66Tg+OzmHpMSEkNOJyPsJ+uyjm4Bfx8482gRca2bXA7j7QuBK4AYzawbqgKs8qE0XaRc7quv47pJSnnpnJwBm8M+Tc7jt0lz6ZGoaWaSjC2z3UVC0+6hjqm+K8N8vbeK/lpdT3xSdRj5rRG/mFeQxaWivkNOJSOi7j6R7cHeeLa3insUlbNtfC0D/rFTumD6eT50xVNPIIp2MSkFO2sY9NcxfVMKL6/cAkJRgfOG8Udx00Riy0pJDTiciJ0OlICespqGZHz+/gZ+8spmmSHT34/lj+zF3dh5jBvQIOZ2IfBQqBTlu7s4f367k35eUUXU4Oo08vE8635k5kUsnDtSuIpEuQKUgx2Vt5UEKi4pZufUAAGnJCXx56hjmTBlNWrKmkUW6CpWCfKADRxq5f9k6fvPGtvg08syPDeaOGeMZ1vtY1zcUkc5MpSDHFGlxfvP6Vu5ftp6DdU0AjBvYg8LZeZw7pl/I6UQkKCoF+TtvbN7P3KJiSnceAiArNYmvXjKOfz1nBMmaRhbp0lQKErfrYD0LlpRStGZHfNln8ofxzcvH069HaojJRKS9qBSEhuYIj72ymQefL6e2MQLAacOzmV+Qx2nDs0NOJyLtSaXQzb1QVsX8xSVs3hu9zUW/Hil88/LxXHnmMBISdIqpSHejUuimtuw9wj2LS3iurAqAxATj6nNG8tVLxtJT08gi3ZZKoZs50tDMf71QzqMvb6YxEr1w3SfH9KVwdh5jB2aFnE5EwqZS6CbcnUXv7GTBU6XsOlQPwNDsdL4zcwKXTxqkaWQRAVQK3ULpzkMUFhXz+ub9AKQkJXD9BadwwwWnkJ6iaWQR+SuVQhdWXdvIfz6znl+t2EpLbBr50okD+c7MieT01TSyiPw9lUIXFGlxfvdmBd9/uowDtdFp5NH9MymcnceUcf1DTiciHVmgpWBm2cCjwCTAgS+4+2utnjfgAWAGUAtc4+6rg8zU1a3aeoC5RWtZWxmdRu6RmsQt08Zy9bkjSUnSNLKIfLCgtxQeAJa6+5Wx+zQfvc9iOjA29t8ngIdiv8oJqjpUz71Ly3hydWV82T+eOYxvXZ7LgJ5pISYTkc4ksFIws17AFOAaAHdvBBqPWu0K4BcevVH0CjPLNrPB7r4zqFxdTWNzCz97dTM/eq6cmoZmACYN7cm8gkmcNaJ3yOlEpLMJckthFLAH+KmZnQasAm5x9yOt1hkKVLR6vD22TKVwHF5av4fCRcVs2hP9I+2dkcw3Lx/PZ/KHk6hpZBE5CUGWQhJwJnCTu79uZg8AtwN3negLmdkcYA5ATk5Om4bsjCr21zJ/cQnPlOwGIMHg82eP4OuX5NIrQ9PIInLygiyF7cB2d3899vgJoqXQWiUwvNXjYbFlf8PdHwEeAcjPz/e2j9o51DVGeGh5OQtf2kRjc3QaefKoPswryGPC4J4hpxORriCwUnD3XWZWYWa57r4OmAaUHLVaEXCjmf2W6AHmgzqe8PfcnT+v3cV3nyqlsroOgMG90rhzxgRmnTpY08gi0maCPvvoJuDXsTOPNgHXmtn1AO6+EFhC9HTUcqKnpF4bcJ5OZ/3uwxQWFfPqxn0ApCQm8KUpo/jKhWPISNGYiYi0rUC/q7j720D+UYsXtnrega8EmaGzOljXxA+fXc8vXttKJDaOPG38AO6aNZGR/TJDTiciXZV+1OxgWlqcJ1Zt576ny9hbEz2Dd2TfDObOzuPC8QNCTiciXZ1KoQN5u6KauUXFrKmoBiAjJZGbLhrLF84bSWqSLlwnIsFTKXQAe2sauG9pGb9fuT2+7IrTh3DH9AkM6qVpZBFpPyqFEDVFWvjla1v5wbPrOVwfnUaeMLgn8wrymDyqT8jpRKQ7UimE5NXyvRQuKmb97hoAeqUnc9tluXx2co6mkUUkNCqFdlZZXcd3nyphybu7gOg08mc/kcOtl+TSOzMl5HQi0t2pFAK2vKyKh1/axLb9RzAzqg41xO+NnD+iN4UFeUwa2ivklCIiUSqFAC0vq+KuP62lKdLCviONNEWi8wbZ6cnMLZjIP5w+VNPIItKhqBQC9MNnN7C3ppG6pggARvTYwbiBWXzqjGHhhhMROQaVQgAO1zfxo+c28Pb26viyHqlJDOmVRkpSAjsP1oWYTkTk/akU2lBLi/OHtyq5d2kZew43AJCUYAzNTicrLQkzo7axmWG9j74BnYhIx6BSaCPvbj/I3KK1rN4W3TpIT05k+qRBvLllP0mJ0eMGtY3NNEWc66aMDjOqiMj7Uil8RPtqGrh/2Tp++2YFHrvTw8wxe3b9AAAIgElEQVRTB/PtGRMYkp0eP/to+4FahvXO4Lopo5mqaxiJSAelUjhJzZEWfv36Nv5j2ToOxaaRcwdmUViQxzmn9I2vN3X8AJWAiHQaKoWTsGLTPgqLiinbdRiAnmlJfP2ScXzu7BEkJSaEnE5E5OSpFE7AzoN1LFhSxqI1OwAwg3/KH843Lsulb4/UkNOJiHx0KoXj0NAc4dGXN/Pg8+XxmYPTh2cz/4o8Th2WHXI6EZG2E2gpmNkW4DAQAZrdPf+o56cCfwI2xxY96e7zg8x0op4r3c38xSVs3VcLQL8eKdw+fQKfPmMoCbpwnYh0Me2xpXChu+/9gOdfdvdZ7ZDjhGzaU8M9i0t4Yd0eIDpvcM25I7n54rH0TEsOOZ2ISDC0++goRxqa+fHz5Tz2yqb4tYrOG9OPwoKJjBmQFXI6EZFgBV0KDiwzMwcedvdHjrHOOWa2BtgB3ObuxQFnOiZ3p2jNDhYsKWX3oeg08rDe6Xxn5gQuyxukC9eJSLcQdCmc5+6VZjYAeMbMytz9pVbPrwZGuHuNmc0A/giMPfpFzGwOMAcgJyenzUMW7zhIYVExb245AEBqUgI3TD2F6y84hbRk3RtZRLoP8/fGcIN+I7NCoMbd7/+AdbYA+R90DCI/P99XrlzZJpmqaxu5f9k6fvP6NlpifwzTJw3izhkTGN5H1ycSka7DzFYdfbLPsQS2pWBmmUCCux+OfX0pMP+odQYBu93dzWwykADsCyLPe5ebqDhQy7DsdMYNzKLonR1U1zYBMGZADwpn53He2H5BvL2ISKcQ5O6jgcAfYvvik4DfuPtSM7sewN0XAlcCN5hZM1AHXOUBbLosL6vi7qJikhON5ARjdUU1KzbvByArNYlbLh7L1eeOJFnTyCLSzQVWCu6+CTjtGMsXtvr6QeDBoDK85+GXNmE4+2qaqK5rii/v3yOVJbecT/8sTSOLiEA3OCW1sbmFkp0HOVzfHD9ukJ6cyOBeqTRFXIUgItJKly6F5euqmL+ohIN10auYJiYYg3qm0TsjmbqmCMN6p4ecUESkY+mSpbBtXy3zF5fwbOluABIMMlKS6NcjhR6pSdQ1RXSzGxGRY+hSpVDb2MxDyzfy8EubaGxuAeDs0X2YVzCJndV1utmNiMiH6BKl4O489e5OFjxVyo6D9QAM6ZXGt2dOZMbHotPIuYOyVAIiIh+i05fCul2HKSwq5rVN0fGGlKQErpsymhumnkJGSqf/eCIi7arTftc8WNfED55Zzy9XbCUSO63o4gkDuXvWRHL6ahpZRORkdMpS+O0b27jv6XXsP9IIwOh+mdw9eyJTc7V7SETko+h0pVBeVcPtT74LQGZKIjdPG8u1nxxFSpKmkUVEPqpOVwp1TRGygU+dMZTbp49nYM+0sCOJiHQZna4U0pITeeL6c8gf2SfsKCIiXU6n2+cydkAPFYKISEA6XSmIiEhwVAoiIhKnUhARkTiVgoiIxKkUREQkTqUgIiJxKgUREYlTKYiISJy5e9gZToiZ7QG2foSX6AfsbaM4nUF3+7ygz9xd6DOfmBHu3v/DVup0pfBRmdlKd88PO0d76W6fF/SZuwt95mBo95GIiMSpFEREJK47lsIjYQdoZ93t84I+c3ehzxyAbndMQURE3l933FIQEZH30a1KwcwSzewtM1scdpb2YGbZZvaEmZWZWamZnRN2pqCZ2dfMrNjM1prZ42bW5W7NZ2Y/MbMqM1vbalkfM3vGzDbEfu0dZsa29j6f+fuxv9vvmNkfzCw7zIxt6Vift9Vzt5qZm1m/IN67W5UCcAtQGnaIdvQAsNTdxwOn0cU/u5kNBW4G8t19EpAIXBVuqkD8DLj8qGW3A8+5+1jgudjjruRn/P1nfgaY5O6nAuuBO9o7VIB+xt9/XsxsOHApsC2oN+42pWBmw4CZwKNhZ2kPZtYLmAI8BuDuje5eHW6qdpEEpJtZEpAB7Ag5T5tz95eA/UctvgL4eezrnwP/0K6hAnasz+zuy9y9OfZwBTCs3YMF5H3+HwP8APgmENjB4G5TCsAPif5htoQdpJ2MAvYAP43tMnvUzDLDDhUkd68E7if6U9RO4KC7Lws3VbsZ6O47Y1/vAgaGGSYEXwD+HHaIIJnZFUClu68J8n26RSmY2Sygyt1XhZ2lHSUBZwIPufsZwBG63i6FvxHbj34F0UIcAmSa2efCTdX+PHpKYbc5rdDMvg00A78OO0tQzCwDuBO4O+j36halAHwSKDCzLcBvgYvM7FfhRgrcdmC7u78ee/wE0ZLoyi4GNrv7HndvAp4Ezg05U3vZbWaDAWK/VoWcp12Y2TXALOBfvGufX38K0R921sS+jw0DVpvZoLZ+o25RCu5+h7sPc/eRRA88Pu/uXfonSHffBVSYWW5s0TSgJMRI7WEbcLaZZZiZEf3MXfrgeitFwNWxr68G/hRilnZhZpcT3SVc4O61YecJkru/6+4D3H1k7PvYduDM2L/zNtUtSqEbuwn4tZm9A5wOLAg5T6BiW0VPAKuBd4n+/e5yU69m9jjwGpBrZtvN7N+Ae4FLzGwD0S2me8PM2Nbe5zM/CGQBz5jZ22a2MNSQbeh9Pm/7vHfX3uISEZEToS0FERGJUymIiEicSkFEROJUCiIiEqdSEBGROJWCiIjEqRRERCROpSDyEZnZx2PX9E8zs8zY/RwmhZ1L5GRoeE2kDZjZ/wXSgHSi15z695AjiZwUlYJIGzCzFOBNoB44190jIUcSOSnafSTSNvoCPYhei6fL3QJUug9tKYi0ATMrInpZ9lHAYHe/MeRIIiclKewAIp2dmf0r0OTuvzGzROBVM7vI3Z8PO5vIidKWgoiIxOmYgoiIxKkUREQkTqUgIiJxKgUREYlTKYiISJxKQURE4lQKIiISp1IQEZG4/w+DZ3n8oejpPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x = X_fold2[\"x\"], y = y_fold2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}