{
 "cells": [
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    }
   },
   "source": [
    "# Chapter 6 - Linear Model Selection and Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
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     "slide_type": "-"
    }
   },
   "source": [
    "### [Lab 1: Subset Selection Methods](#lab1)\n",
    "- [Lab 6.5.1 Best Subset Selection](#lab-6.5.1)\n",
    "- [Lab 6.5.2 Forward and Backward Stepwise Selection](#lab-6.5.2)\n",
    "- [Lab 6.5.3 Choosing Among Models Using the Validation Set Approach and Cross-Validation](#lab-6.5.3)\n",
    "\n",
    "### [Lab 2: Ridge Regression and the Lasso](#lab2)\n",
    "- [Lab 6.6.1 Ridge Regression](#lab-6.6.1)\n",
    "- [Lab 6.6.2 The Lasso](#lab-6.6.2)\n",
    "\n",
    "### [Lab 3: PCR and PLS Regression](#lab3)\n",
    "- [Lab 6.7.1 Principal Components Regression](#lab-6.7.1)\n",
    "- [Lab 6.7.2 Partial Least Squares](#lab-6.7.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Imports and Configurations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
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   "outputs": [],
   "source": [
    "# Standard libraries\n",
    "from itertools import combinations\n",
    "\n",
    "# Use rpy2 for loading R datasets\n",
    "from rpy2.robjects.packages import importr\n",
    "from rpy2.robjects.packages import data as rdata\n",
    "from rpy2.robjects import pandas2ri\n",
    "\n",
    "# Math and data processing\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "\n",
    "# StatsModels\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# scikit-learn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Ridge, RidgeCV, Lasso, LassoCV\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from sklearn.model_selection import train_test_split, LeaveOneOut, KFold, cross_val_score\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "# Visulization\n",
    "from IPython.display import display\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "mpl.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab1'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Lab 1: Subset Selection Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.5.1'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### 6.5.1 Best Subset Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    "collapsed": false,
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     "worksheet-0"
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   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Andy Allanson</th>\n",
       "      <td>293</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>30</td>\n",
       "      <td>29</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>293</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>30</td>\n",
       "      <td>29</td>\n",
       "      <td>14</td>\n",
       "      <td>A</td>\n",
       "      <td>E</td>\n",
       "      <td>446</td>\n",
       "      <td>33</td>\n",
       "      <td>20</td>\n",
       "      <td>NaN</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>N</td>\n",
       "      <td>W</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>475.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>480.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>500.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>91.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  \\\n",
       "-Andy Allanson       293    66      1    30   29     14      1     293     66   \n",
       "-Alan Ashby          315    81      7    24   38     39     14    3449    835   \n",
       "-Alvin Davis         479   130     18    66   72     76      3    1624    457   \n",
       "-Andre Dawson        496   141     20    65   78     37     11    5628   1575   \n",
       "-Andres Galarraga    321    87     10    39   42     30      2     396    101   \n",
       "\n",
       "                   CHmRun  CRuns  CRBI  CWalks League Division  PutOuts  \\\n",
       "-Andy Allanson          1     30    29      14      A        E      446   \n",
       "-Alan Ashby            69    321   414     375      N        W      632   \n",
       "-Alvin Davis           63    224   266     263      A        W      880   \n",
       "-Andre Dawson         225    828   838     354      N        E      200   \n",
       "-Andres Galarraga      12     48    46      33      N        E      805   \n",
       "\n",
       "                   Assists  Errors  Salary NewLeague  \n",
       "-Andy Allanson          33      20     NaN         A  \n",
       "-Alan Ashby             43      10   475.0         N  \n",
       "-Alvin Davis            82      14   480.0         A  \n",
       "-Andre Dawson           11       3   500.0         N  \n",
       "-Andres Galarraga       40       4    91.5         N  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hitters dataset is in R ISLR package\n",
    "islr = importr('ISLR')\n",
    "hitters_rdf = rdata(islr).fetch('Hitters')['Hitters']\n",
    "hitters = pandas2ri.ri2py(hitters_rdf)\n",
    "display(hitters.head(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
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     "worksheet-0"
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     "slide_type": "-"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 322 entries, -Andy Allanson to -Willie Wilson\n",
      "Data columns (total 20 columns):\n",
      "AtBat        322 non-null int32\n",
      "Hits         322 non-null int32\n",
      "HmRun        322 non-null int32\n",
      "Runs         322 non-null int32\n",
      "RBI          322 non-null int32\n",
      "Walks        322 non-null int32\n",
      "Years        322 non-null int32\n",
      "CAtBat       322 non-null int32\n",
      "CHits        322 non-null int32\n",
      "CHmRun       322 non-null int32\n",
      "CRuns        322 non-null int32\n",
      "CRBI         322 non-null int32\n",
      "CWalks       322 non-null int32\n",
      "League       322 non-null object\n",
      "Division     322 non-null object\n",
      "PutOuts      322 non-null int32\n",
      "Assists      322 non-null int32\n",
      "Errors       322 non-null int32\n",
      "Salary       263 non-null float64\n",
      "NewLeague    322 non-null object\n",
      "dtypes: float64(1), int32(16), object(3)\n",
      "memory usage: 32.7+ KB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print(hitters.info())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59\n"
     ]
    }
   ],
   "source": [
    "print(hitters.Salary.isnull().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "hitters.dropna(axis=0, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(263, 20)\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "print(hitters.shape)\n",
    "print(hitters.Salary.isnull().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Score function to produce linear regression fitting and RSS for a feature set\n",
    "def score_rss(data, feature_set, endog_name):\n",
    "    \"\"\"\n",
    "    Regress score function based on RSS, residual sum of squares.\n",
    "    \"\"\"\n",
    "    # Have to use sm formula interface to avoid manually generate dummies\n",
    "    reg = smf.ols(endog_name + ' ~ ' + '+'.join(feature_set), data).fit()\n",
    "    rss = reg.mse_resid * reg.df_resid\n",
    "    return reg, (-1) * rss\n",
    "\n",
    "# For a given number of features, select the best combination by score function\n",
    "def select_k_best(data, k, endog_name, score_function):\n",
    "    \"\"\"\n",
    "    Select the best k features out of all the possible combinations.\n",
    "    Different than sklearn.feature_selection.SelectKBest.\n",
    "\n",
    "    data: data frame.\n",
    "    k: int.\n",
    "    endog_name: response name.\n",
    "    score_function: a callable with parameters X, y, feature_set\n",
    "                    returns: an iterable of (model, score).\n",
    "    \"\"\"\n",
    "    features = data.columns.drop(endog_name)\n",
    "\n",
    "    # Iterate over all feature combinations and compute scores\n",
    "    models = []\n",
    "    scores = []\n",
    "    for feature_subset in combinations(features, k):\n",
    "        model, score = score_function(data, feature_subset, endog_name)\n",
    "        models.append(model)\n",
    "        scores.append(score)\n",
    "\n",
    "    # Return the best model with the highest score\n",
    "    return models[scores.index(max(scores))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Search the best k features for k = 1 to 8, based on RSS.\n",
      "Taking long time...\n",
      "\n",
      "Best 1 features: ['CRBI']\n",
      "Best 2 features: ['Hits', 'CRBI']\n",
      "Best 3 features: ['Hits', 'CRBI', 'PutOuts']\n",
      "Best 4 features: ['Division[T.W]', 'Hits', 'CRBI', 'PutOuts']\n",
      "Best 5 features: ['Division[T.W]', 'AtBat', 'Hits', 'CRBI', 'PutOuts']\n",
      "Best 6 features: ['Division[T.W]', 'AtBat', 'Hits', 'Walks', 'CRBI', 'PutOuts']\n",
      "Best 7 features: ['Division[T.W]', 'Hits', 'Walks', 'CAtBat', 'CHits', 'CHmRun', 'PutOuts']\n",
      "Best 8 features: ['Division[T.W]', 'AtBat', 'Hits', 'Walks', 'CHmRun', 'CRuns', 'CWalks', 'PutOuts']\n"
     ]
    }
   ],
   "source": [
    "# Define features and response\n",
    "response = 'Salary'\n",
    "features = hitters.columns.drop([response])\n",
    "\n",
    "# Find the best models with 1 to p features\n",
    "print(\"\\nSearch the best k features for k = 1 to 8, based on RSS.\\nTaking long time...\\n\")\n",
    "best_models = []\n",
    "for k in range(1, 8+1):\n",
    "    best_model = select_k_best(hitters, k, response, score_rss)\n",
    "    best_models.append(best_model)\n",
    "    best_features = best_model.model.exog_names\n",
    "    best_features.remove('Intercept')\n",
    "    print(\"Best {} features: {}\".format(k, best_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.5.2'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.5.2 Forward and Backward Stepwise Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Forward stepwise selection\n",
    "def forward_select(data, endog_name, score_function):\n",
    "    \"\"\"\n",
    "    Select features by forward stepwise selection algorithm.\n",
    "\n",
    "    data: data frame.\n",
    "    endog_name: response name.\n",
    "    score_function: a callable with parameters X, y, feature_set\n",
    "                    returns: an iterable of (model, score).\n",
    "    \"\"\"\n",
    "    features = data.columns.drop(endog_name)\n",
    "    p = len(features)\n",
    "\n",
    "    # Loop number of features from 1 to p\n",
    "    selected_features = []  # start from null model\n",
    "    for j in range(1, p+1):\n",
    "        feature_candidates = [xj for xj in features if xj not in selected_features]\n",
    "        models = []\n",
    "        scores = []\n",
    "        # Loop over remaining features at the j-th step\n",
    "        for xj in feature_candidates:\n",
    "            feature_subset = selected_features + [xj]\n",
    "            model, score = score_function(data, feature_subset, endog_name)\n",
    "            models.append(model)\n",
    "            scores.append(score)\n",
    "\n",
    "        # Select the best feature at the j-th step\n",
    "        best_feature = feature_candidates[scores.index(max(scores))]\n",
    "        selected_features += [best_feature]\n",
    "        print(\" Best {} features: {}\".format(j, selected_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Forward stepwise select features based on RSS:\n",
      "\n",
      " Best 1 features: ['CRBI']\n",
      " Best 2 features: ['CRBI', 'Hits']\n",
      " Best 3 features: ['CRBI', 'Hits', 'PutOuts']\n",
      " Best 4 features: ['CRBI', 'Hits', 'PutOuts', 'Division']\n",
      " Best 5 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat']\n",
      " Best 6 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks']\n",
      " Best 7 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks']\n",
      " Best 8 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns']\n",
      " Best 9 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat']\n",
      " Best 10 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists']\n",
      " Best 11 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League']\n",
      " Best 12 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs']\n",
      " Best 13 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors']\n",
      " Best 14 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun']\n",
      " Best 15 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits']\n",
      " Best 16 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits', 'RBI']\n",
      " Best 17 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits', 'RBI', 'NewLeague']\n",
      " Best 18 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits', 'RBI', 'NewLeague', 'Years']\n",
      " Best 19 features: ['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits', 'RBI', 'NewLeague', 'Years', 'CHmRun']\n"
     ]
    }
   ],
   "source": [
    "# Define features and response\n",
    "response = 'Salary'\n",
    "features = hitters.columns.drop([response])\n",
    "\n",
    "# Run forward stepwise selection on Hitters\n",
    "print(\"\\nForward stepwise select features based on RSS:\\n\")\n",
    "forward_select(hitters, response, score_rss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Backward stepwise selection\n",
    "def backward_select(data, endog_name, score_function):\n",
    "    \"\"\"\n",
    "    Select features by backward stepwise selection algorithm.\n",
    "\n",
    "    data: data frame.\n",
    "    endog_name: response name.\n",
    "    score_function: a callable with parameters X, y, feature_set\n",
    "                    returns: an iterable of (model, score).\n",
    "    \"\"\"\n",
    "    features = list(data.columns.drop(endog_name))\n",
    "    p = len(features)\n",
    "\n",
    "    # Loop number of features from 1 to p\n",
    "    selected_features = features.copy()  # start from all the features\n",
    "    for j in range(p, 0, -1):\n",
    "        print(\"Best {} features: {}\".format(j, selected_features))\n",
    "        if j==1: break\n",
    "        feature_candidates = list(combinations(selected_features, j-1))\n",
    "        models = []\n",
    "        scores = []\n",
    "\n",
    "        # Loop over feature candidates at the j-th step\n",
    "        for feature_subset in feature_candidates:\n",
    "            model, score = score_function(data, feature_subset, endog_name)\n",
    "            models.append(model)\n",
    "            scores.append(score)\n",
    "\n",
    "        # Select the best feature at the j-th step\n",
    "        selected_features = list(feature_candidates[scores.index(max(scores))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Backward stepwise select features based on RSS:\n",
      "\n",
      "Best 19 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years', 'CAtBat', 'CHits', 'CHmRun', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors', 'NewLeague']\n",
      "Best 18 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years', 'CAtBat', 'CHits', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors', 'NewLeague']\n",
      "Best 17 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'CAtBat', 'CHits', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors', 'NewLeague']\n",
      "Best 16 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'CAtBat', 'CHits', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors']\n",
      "Best 15 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'Walks', 'CAtBat', 'CHits', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors']\n",
      "Best 14 features: ['AtBat', 'Hits', 'HmRun', 'Runs', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors']\n",
      "Best 13 features: ['AtBat', 'Hits', 'Runs', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists', 'Errors']\n",
      "Best 12 features: ['AtBat', 'Hits', 'Runs', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists']\n",
      "Best 11 features: ['AtBat', 'Hits', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'League', 'Division', 'PutOuts', 'Assists']\n",
      "Best 10 features: ['AtBat', 'Hits', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'Division', 'PutOuts', 'Assists']\n",
      "Best 9 features: ['AtBat', 'Hits', 'Walks', 'CAtBat', 'CRuns', 'CRBI', 'CWalks', 'Division', 'PutOuts']\n",
      "Best 8 features: ['AtBat', 'Hits', 'Walks', 'CRuns', 'CRBI', 'CWalks', 'Division', 'PutOuts']\n",
      "Best 7 features: ['AtBat', 'Hits', 'Walks', 'CRuns', 'CWalks', 'Division', 'PutOuts']\n",
      "Best 6 features: ['AtBat', 'Hits', 'Walks', 'CRuns', 'Division', 'PutOuts']\n",
      "Best 5 features: ['AtBat', 'Hits', 'Walks', 'CRuns', 'PutOuts']\n",
      "Best 4 features: ['AtBat', 'Hits', 'CRuns', 'PutOuts']\n",
      "Best 3 features: ['Hits', 'CRuns', 'PutOuts']\n",
      "Best 2 features: ['Hits', 'CRuns']\n",
      "Best 1 features: ['CRuns']\n"
     ]
    }
   ],
   "source": [
    "# Define features and response\n",
    "response = 'Salary'\n",
    "features = hitters.columns.drop([response])\n",
    "\n",
    "# Run backward stepwise selection on Hitters\n",
    "print(\"\\nBackward stepwise select features based on RSS:\\n\")\n",
    "backward_select(hitters, response, score_rss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='lab-6.5.3'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.5.3 Choosing Among Models Using the Validation Set Approach and Cross-Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### Forward Stepwise Selection using the Validation Set Approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Score function and forward select function\n",
    "def score_rss_valset(data_train, data_test, feature_set, endog_name):\n",
    "    \"\"\"\n",
    "    Regress score function based on RSS, residual sum of squares.\n",
    "    \"\"\"\n",
    "    # Have to use sm formula interface to avoid manually generate dummies\n",
    "    reg = smf.ols(endog_name + ' ~ ' + '+'.join(feature_set), data_train).fit()\n",
    "    y_pred = reg.predict(data_test[feature_set])\n",
    "    y_test = data_test[endog_name].values\n",
    "    rss = ((y_pred - y_test) ** 2).sum()\n",
    "    return reg, (-1) * rss\n",
    "\n",
    "def forward_select_valset(data_train, data_test, endog_name, score_function):\n",
    "    \"\"\"\n",
    "    Select features by forward stepwise selection algorithm.\n",
    "\n",
    "    data: data frame.\n",
    "    endog_name: response name.\n",
    "    score_function: a callable with parameters X, y, feature_set\n",
    "                    returns: an iterable of (model, score).\n",
    "    \"\"\"\n",
    "    features = data_train.columns.drop(endog_name)\n",
    "    p = len(features)\n",
    "    high_scores = []\n",
    "    best_features = []\n",
    "\n",
    "    # Loop number of features from 1 to p\n",
    "    selected_features = []  # start from null model\n",
    "    for j in range(1, p+1):\n",
    "        feature_candidates = [xj for xj in features if xj not in selected_features]\n",
    "        models = []\n",
    "        scores = []\n",
    "        # Loop over remaining features at the j-th step\n",
    "        for xj in feature_candidates:\n",
    "            feature_subset = selected_features + [xj]\n",
    "            model, score = score_function(data_train, data_test, feature_subset, endog_name)\n",
    "            models.append(model)\n",
    "            scores.append(score)\n",
    "\n",
    "        # Select the best feature at the j-th step\n",
    "        highest_score = max(scores)\n",
    "        high_scores.append(highest_score)\n",
    "        best_feature = feature_candidates[scores.index(highest_score)]\n",
    "        selected_features += [best_feature]\n",
    "        best_features.append(selected_features)\n",
    "\n",
    "    scores_df = pd.DataFrame(high_scores, index=range(1,p+1), columns=[''])\n",
    "    scores_df.index.name = '# of x_j'\n",
    "\n",
    "    best_score = max(high_scores)\n",
    "    best_j = high_scores.index(best_score) + 1\n",
    "    return scores_df, best_j, best_score, best_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set size =  142\n",
      "Test set size =  121\n"
     ]
    }
   ],
   "source": [
    "# Train-test split. Test set size is random with prob=0.5, as in the book.\n",
    "np.random.seed(seed=51)\n",
    "train_mask = np.random.choice([True, False], size = hitters.shape[0], replace = True)\n",
    "test_mask = np.invert(train_mask)\n",
    "print(\"Train set size = \", train_mask.sum())\n",
    "print(\"Test set size = \", test_mask.sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Now run forward stepwise selection instead of BSS as in the book to speed up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Forward stepwise select features on training set, based on RSS. \n",
      "\n",
      "Mean RSS over numbers of features:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th># of x_j</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.076650e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.714363e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.617621e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.588872e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.562742e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.508433e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.478177e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.467281e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.452479e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.449917e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.465030e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.493468e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.508188e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.557057e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.620118e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1.624116e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.698257e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.730889e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.763893e+07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      \n",
       "# of x_j              \n",
       "1         2.076650e+07\n",
       "2         1.714363e+07\n",
       "3         1.617621e+07\n",
       "4         1.588872e+07\n",
       "5         1.562742e+07\n",
       "6         1.508433e+07\n",
       "7         1.478177e+07\n",
       "8         1.467281e+07\n",
       "9         1.452479e+07\n",
       "10        1.449917e+07\n",
       "11        1.465030e+07\n",
       "12        1.493468e+07\n",
       "13        1.508188e+07\n",
       "14        1.557057e+07\n",
       "15        1.620118e+07\n",
       "16        1.624116e+07\n",
       "17        1.698257e+07\n",
       "18        1.730889e+07\n",
       "19        1.763893e+07"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The best model is the one having 10 features:\n",
      "['CRBI', 'Hits', 'Division', 'Years', 'AtBat', 'Walks', 'PutOuts', 'CWalks', 'CRuns', 'RBI', 'Errors', 'Assists', 'HmRun', 'Runs', 'NewLeague', 'League', 'CHmRun', 'CAtBat', 'CHits']\n"
     ]
    }
   ],
   "source": [
    "# Define features and response\n",
    "response = 'Salary'\n",
    "features = hitters.columns.drop([response])\n",
    "\n",
    "# Run forward stepwise selection on Hitters\n",
    "print(\"\\nForward stepwise select features on training set, based on RSS. \\n\")\n",
    "scores_valset, best_j_valset, best_score, best_features_valset = forward_select_valset(hitters[train_mask], hitters[test_mask], response, score_rss_valset)\n",
    "print(\"Mean RSS over numbers of features:\")\n",
    "mean_rss_valset = scores_valset * (-1)\n",
    "display(mean_rss_valset)\n",
    "print(\"\\nThe best model is the one having {} features:\\n{}\".format(best_j_valset, best_features_valset[best_j_valset-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Finally perform best subset selection on the full data set, and select the best 10-variable model.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Forward stepwise select features on full data set, based on RSS. \n",
      "\n",
      "The best 10 features are:\n",
      "['CRBI', 'Hits', 'PutOuts', 'Division', 'AtBat', 'Walks', 'CWalks', 'CRuns', 'CAtBat', 'Assists', 'League', 'Runs', 'Errors', 'HmRun', 'CHits', 'RBI', 'NewLeague', 'Years', 'CHmRun']\n"
     ]
    }
   ],
   "source": [
    "# Run forward stepwise selection on Hitters full date set\n",
    "print(\"\\nForward stepwise select features on full data set, based on RSS. \\n\")\n",
    "_, _, _, best_features_full = forward_select_valset(hitters, hitters, response, score_rss_valset)\n",
    "print(\"The best {} features are:\\n{}\".format(best_j_valset, best_features_full[best_j_valset-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### Model Selection using Cross-Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# 10-fold CV splits\n",
    "kf = KFold(10, random_state=55)\n",
    "# Forward stepwise selection on each split\n",
    "scores_cv_list = []\n",
    "for train_index, test_index in kf.split(hitters):\n",
    "    scores_df, _, _, _ = forward_select_valset(hitters.iloc[train_index], hitters.iloc[test_mask], response, score_rss_valset)\n",
    "    scores_cv_list.append(scores_df)\n",
    "# Combine the scores of 10 folds\n",
    "scores_cv = pd.concat(scores_cv_list, axis=1)\n",
    "scores_cv.columns = range(1, 11)\n",
    "scores_cv.columns.name = 'K-Fold'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of x_j\n",
      "1     1.988162e+07\n",
      "2     1.469190e+07\n",
      "3     1.247908e+07\n",
      "4     1.182492e+07\n",
      "5     1.148818e+07\n",
      "6     1.094343e+07\n",
      "7     1.082744e+07\n",
      "8     1.081981e+07\n",
      "9     1.079096e+07\n",
      "10    1.076345e+07\n",
      "11    1.058229e+07\n",
      "12    1.048883e+07\n",
      "13    1.043509e+07\n",
      "14    1.035223e+07\n",
      "15    1.029475e+07\n",
      "16    1.021250e+07\n",
      "17    1.019581e+07\n",
      "18    1.021123e+07\n",
      "19    1.029496e+07\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Compute mean RSS of 10 folds for each j = 1..p\n",
    "mean_rss_cv = scores_cv.mean(axis=1) * (-1)\n",
    "print(mean_rss_cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RmpiszteNGzcwb948BAcHo0OHDhVyTU47sn22b13tM+kjIjUySfKVnp6OiIgI\njBgxAs2bNzdFE0RERESKZJLka+PGjcjMzMSGDRvk3dRfeOEF5OXllbgJMREREZHamST5Gj58OIYP\nH17q94WHh5uieSIiIqJKS9F7OxIRmUJptQqPHDmCDRs2wMbGBl26dOGIPhGVC5MvIqL7lFSrsLCw\nECtWrMCcOXPg6OiIsLAw+Pv7w93d3cJRE5FScHshIqL7lFSr8MqVK6hduzY0Gg3s7Ozg7e2NM2fO\nWCpUIlIgjnwREd2npFqFOTk5cHZ2ll87OTkhOzu7TNe1VOkMS5fsYPts35rbfxgmX0RED1FcrUIn\nJyfk5ubKr3NycuDi4lKma3J7IbbP9q2nfbNvL2Rp4lQsREa6pcMgIoUqqlU4ePBgBAYGGp2rU6cO\n/v77b2RmZqKwsBBnzpyBl5dXhbUtrqVAnD9bYdcjospHdSNf4nYa9AvCIXXpCemVNywdDhEpUGm1\nCocMGYKIiAjo9Xp06dIF1apVq7C29Wu+BC7Ew2ZBFCRJqrDrElHlobrkC3cXxoq0mxYOhIiUqrRa\nhf7+/kalJyqUnT2Qkw3k5gBOzqV/PxEpjvqmHZ1dAEkCsjIsHQkRUblJGlfDF5nsw4jUSnXJl2Rj\nCzhrgMw7lg6FiKj8tHeTrzu3LRsHEZmM6pIvAICLFshi8kVECqRxM/z/HY58EamVOpMvjSH5EkJY\nOhIiovK5O/IlOO1IpFrqTL5ctIBOZ1i0SkSkIP+s+eK0I5FaqTL5kjRawxeceiQipdFy2pFI7VSZ\nfEG+c2TyRUQKo+XIF5HaqTP5cika+eKdIxEpzN2bR8GRLyLVUmfyVdR5ceSLiJTGyQWwtWOdLyIV\nU2XyxTVfRKRUkiQZbiBZ54tItVSZfMnTjhz5IiIl0mg58kWkYupMvopGvth5EZESad2AnGyIwgJL\nR0JEJqDO5Mvl7tNCnHYkIgXi/o5E6qbO5OvuyBcrRBORIsn7O7IPI1IjVSZfkr0DUMWRI19EpExF\n+zvyBpJIlVSZfAEwLLrngnsiUqKi/R35xCORKqk3+bq7uTYRkeJouMUQkZqpN/ly0QJ5uRAF+ZaO\nhIioXCQtF9wTqZlqky+J+zsSkVJpuL8jkZqpNvni/o5EpFhaTjsSqZl6ky8Nq9wTkUK5sFwOkZqp\nOPlioVUiUibJzg5wduH+jkQqpd7kS75zZPJFRAqkceOCeyKVUm3yJXF/RyJSMq0rkJkBoddbOhIi\nqmCqTb45llC2AAAgAElEQVS4vyMRKZrGFdDrgZwsS0dCRBVMvckXR76ISMEkPvFIpFrqTb645ouI\nlEzLWl9EaqXe5MvJGbC15bQjESlT0RPbHPkiUh3VJl+SJHFzbSJSrrv7O7LWF5H6qDb5AmBIvjjy\nRUQKJO/vyFpfRKqj7uRLowWyMyH0OktHQkRUPndHvvjQEJH6qDv5cnEFhACy+ag2ESmMlmu+iNTK\nzhQXLSwsxJdffonU1FQUFBSgX79+8Pf3l88fOXIEGzZsgI2NDbp06YKgoCBThAFJo4UADOu+ihav\nEhEpwd0+S/BpRyLVMUnytW/fPmi1WkyYMAGZmZl477335OSrsLAQK1aswJw5c+Do6IiwsDD4+/vD\n3d294gNxubfWV52Kvz4RkalUcQTsHTjyRaRCJpl2bN++PV5++WUAgBACtra28rkrV66gdu3a0Gg0\nsLOzg7e3N86cOWOKMP4ptMpF90SkMJIkyVsMEZG6mGTky9HREQCQk5OD+fPnY+DAgfK5nJwcODs7\ny6+dnJyQnZ1dput6eHiUK47MuvWQBsDdzhYu5Xzv47Zd0dg+27fm9q2WxhW4esXSURBRBTNJ8gUA\nN27cwLx58xAcHIwOHTrIx52cnJCbmyu/zsnJgYuLS5mumZKSUq4YRKHhKce0K5dwu5zvvZeHh0e5\n265IbJ/tW2v7Vp/0adyA/PMQeXmQqlSxdDREVEFMMu2Ynp6OiIgIDB48GIGBgUbn6tSpg7///huZ\nmZkoLCzEmTNn4OXlZYow/tlcm4VWiUiB5FpfnHokUhWTjHxt3LgRmZmZ2LBhAzZs2AAAeOGFF5CX\nl4egoCAMGTIEERER0Ov16NKlC6pVq2aKMLjmi4iUTXPP/o7Vn7BsLERUYUySfA0fPhzDhw8v9ry/\nv79R6QmT4ebaRKRk2ruFVvnEI5GqqLzI6r2lJoiIFEbLWl9EaqTq5EuytQWcXDjtSESKJGm45otI\njVSdfAEwrPvitCMRKZGG045EamQFyZcrkJUBIYSlIyEiKh95zRenHYnURP3Jl4sWKCwE8nJL/14i\nospE3t+RI19EaqL65EtiuQkiUioXF0Cy4bQjkcqoPvn654lHJl9EpCySjS3gojHU+SIi1VB/8iWP\nfPHOkYgUSOvGpx2JVEb9ydfdLYYEh+2JSIm0rkBWJoReZ+lIiKiCqD/54povIlIyjSsgBJdOEKmI\n6pOvf4oUsuMiIuWRimp9ceqRSDVUn3zJC+458kVESnR3iyE+8UikHupPvjR82pGIFEwevecTj0Rq\nYWfpAEyuaME9n3YkonKKj4/HmjVrEB4ebnR837592Lp1K2xsbNClSxcEBwebLoi7Ve7FnQxIpmuF\niMxI9cmXVKUKYO/AkS8iKpdNmzYhOjoajo6OD5xbtWoV5s+fD0dHR0ycOBHPPvssNBqNSeKQtK4Q\nAEe+iFRE/dOOgGHdFxerElE51KpVC5MmTXroufr16yM7Oxv5+fkAAEky4ZgUHxoiUh3Vj3wBMKz7\nunHN0lEQkYIEBATg+vXrDz3n6emJKVOmwNHREW3btoWLi0uZrunh4VHuOAodbPE3AKfCfFR/hPc/\narsVie2zfWtu/2GsJPlyBS5fgCgsgGRnb+loiEjBLl68iNjYWCxatAiOjo5YuHAhDhw4gPbt25f6\n3pSUlHK3JwoMo2vZ168i7xHe7+Hh8UjtVhS2z/attf2Skj6rmHaU5HITmZYNhIgUz9nZGQ4ODnBw\ncICNjQ3c3NyQlZVlsvYkewegihOXThCpiJWMfN1TbsKtqmVjISJFiomJQW5uLoKCghAUFISwsDDY\n2dmhVq1a6Ny5s2kb17qyzheRilhH8nW33AQ31yai8qhZsyYiIiIAAB06dJCPBwcHm7a8xP00rsDl\nJAghTLu4n4jMwiqmHVlolYgUTesGFBYCeTmWjoSIKoB1JF9313wJbjFERAok71HLqUciVbCK5EuS\nR77YcRGRAsn7O7LQKpEaWEXyJW+uzWlHIlIijWGLId5AEqmDdSRfWi64JyIFu9uHCU47EqmCdSRf\nRZtrc+SLiBRIXvPFkS8iVbCO5MvJGZBsAC64JyIl0t6dduSaLyJVsIrkS7KxAVw0XPNFRMpUtHQi\nk8kXkRpYRfIFwFDriyNfRKREGi6dIFIT60m+XLRA5h0Ivd7SkRARlY+TC2Brx2lHIpWwnuRL4woI\nPZCTbelIiIjKRZIkQx/G5ItIFawm+ZILrbLcBBEpkUbLdatEKmE1yZe8uTY7LyJSIq0bkJMFUVhg\n6UiI6DFZT/Ilj3wx+SIi5ZG0rHJPpBbWk3wVba7NkS8iUiLuUUukGlaTfHHNFxEpWtH+jtxiiEjx\nrCb5ktd83eHIFxEpUNH+jhz5IlI860m+OPJFREqm4RZDRGph0uQrPj4e4eHhDxyPjo7GpEmT8O9/\n/xu//vqrKUP4h4ZPOxKRcklFWwxx2pFI8exMdeFNmzYhOjoajo6ORsczMjKwbt06zJ07F87Ozpg5\ncyaaNWuGmjVrmioUAxcNAEDwaUciUiL5BpLJF5HSmWzkq1atWpg0adIDx69fv4769etDo9HAxsYG\njRo1Qnx8vKnCkEl29oCjE0e+iEiZtJx2JFILk418BQQE4Pr16w8cr127NpKTk5Geng4nJyecOnUK\nHh4eZbpmWb+vOCluVYHc7Ee6zuO2/bjYPtu35vYJ95TL4cgXkdKZLPkqjkajwdChQ/Hpp59Cq9Wi\nQYMG0Gq1ZXpvSkrKY7Wtc3QG/r5U7ut4eHg8dtuPg+2zfWttn0nfPyQ7O8DZhdOORCpg9qcddTod\nkpKS8J///AcTJ05ESkoKvL29zdO4ixbIz4fIyzNPe0REFUnjxmlHIhUw28hXTEwMcnNzERQUBACY\nMmUK7O3t0atXL7i6upolBkmjhQAM5SaqPGGWNomIKozWFbhxFUKvh2RjPZWCiNTGpMlXzZo1ERER\nAQDo0KGDfHzAgAEYMGCAKZt+OJei7TnuANWYfBGRwmhcAb0eyMmWn+AmIuWxrlunoke1WW6CiBRI\n4hOPRKpgZckXN9cmIgUrKrSayeSLSMmsK/ly4RZDRKRgLLRKpApWlXxJ3GKIiJTs7v6OglsMESma\nVSVf/2yuzeSLiJRH3t+RI19EimZdyZf8tCM7LiJrI4TA+fPnkZ2dbelQHp2GC+6J1MDsFe4tigvu\niazGrVu3EBkZidDQULRo0QLh4eFITk6Gg4MDJk+ejEaNGlk6xPIrGvnitCORolnXyFcVJ8DOjtOO\nRFZg5cqVaNWqFZo2bYqDBw/ixo0b+PLLLzFt2jR8++23lg7v0dxdt8r9HYmUzaqSL0mSABdXTjsS\nWYHk5GSEhoaiSpUqOHnyJNq2bQtHR0fUq1cPaWlplg7v0VRxBOwdOO1IpHBWlXwBMEw9cuSLSPVs\nbW3lr8+dO4emTZvKr3U6nSVCemySJBmmHnkDSaRo1pd8uWiB7CwIhXa+RFQ2Dg4OuHnzJi5fvoy/\n//5bTr4uX74MZ2dnC0f3GDRMvoiUzroW3AP/lJvIzgSKtuogItUJDQ3F5MmTodPp8OKLL0Kj0eC3\n335DVFQURowYYenwHp3GDbh0HiI/D5JDFUtHQ0SPwOqSL8lFCwEYCq0y+SJSrdatW2PevHm4c+cO\n6tWrBwDQaDR466234OPjY+HoHp2kdTX0YXcygOpPWDocInoEVpd8ySNfHLYnUr2qVauiatWqAAx1\nvqpVq4batWtbOKrHdO8WQ0y+iBTJCpOvux0X93ckUjVV1vkC/hmx5xOPRIplhQvui+rk8IlHIjVT\nZZ0vQC60ylpfRMpldcmXxP0diayCKut8AZDkaUeOfBEpldUlX//s78jki0jN1FjnC8A9+zty5ItI\nqaxwzRdHvoisQVGdr5ycHHXV+Spa88VpRyLFsr7ky4XrJYisgXrrfN3tw7jgnkixrDD5cgEkiXeN\nRCqn1jpfhj7MhtOORApmdWu+JBtbwFnDNV9EVqBq1apy4gUA/v7+8PHxwa5duywY1eORbGwBFw1v\nIIkUzPpGvgDDonuu+SJStWPHjuHLL7+ERqPBlClTULNmTSQkJOCrr75CamoqgoKCLB3io9O6AXfS\nLR0FET0i60y+NFrg5jUIISBJkqWjISITWL16NYYPH47r16/jhx9+QN26dbFmzRp07twZ06ZNs3R4\nj0frCly9DKHXGUbCiEhRrDP5ctECOh2QmwM4KfipJyIqll6vR0BAAABg7NixOH36NGbMmAEvLy8L\nR1YBNK6AEEBWJveoJVIgq0y+JE3R5toZTL6IVMre3t7odVhYGJ54Qh17IUoat7uba99m8kWkQFa3\n4B6AXG6C676IrIOrq6tqEi8A8hZDfOKRSJmscuRLLrTKJx6JVCs/Px9JSUkQQhh9XaRhw4alXiM+\nPh5r1qxBeHi40fGEhASsXLkSQgi4u7tjwoQJcHBwqOgfoXjyFkNMvoiUqMTkKysrCzY2NnBycsKN\nGzdw8OBBNGjQQNk1cgB5iyGRmQEutydSp/z8fMybN09+fe/XkiTh888/L/H9mzZtQnR0NBwdHY2O\nCyGwePFivPvuu6hduzZ2796NGzduwMPDo2J/gJLcnWoUd26zDyNSoGKTr7i4OMydOxcTJ05Ew4YN\nMW3aNHh6emLv3r3o06cPOnToYM44K5SkdTWsl+C0I5FqLVq06LHeX6tWLUyaNOmBJO3vv/+GVqvF\n1q1bkZycjNatW5s38cI9fRhHvogUqdjka926dZg8eTKaNGmCHTt2wN3dHdOnT0dmZiZmzZql6OSL\nm2sTUWkCAgJw/fr1B45nZGTg7NmzGDFiBGrXro25c+eiUaNGaNasWanXrKgkLT8nA9cAuAgdqpbh\nmuZODtk+22f7JSs2+crMzESTJk0AAGfOnIGfnx8Aw/YcBQUF5onOVOTNtXnXSETlo9VqUbt2bdSt\nWxcA0KJFCyQmJpYp+UpJSamQGEROPgAg62oKckq5poeHR4W1+yjYPtu31vZLSvrK9LTj2bNn0bRp\nU/l1Xl7e40dlSUVPO3Lki4jKqVatWsjNzcXVq1cBGJZoeHp6mjeIu087Ck47EilSsclX9erVceTI\nEcTExCAvLw+NGzcGAPzxxx+oU6eO2QI0ibsjX4JrvohU75dffnng2I8//lju68TExGDXrl2ws7PD\n2LFjsWDBAkydOhXVq1dH69atKyLUMpPsHYAqToY6X0SkOMVOOw4ZMgSffvop0tPTMWrUKNjZ2eHb\nb7/F7t278e9//9ucMVY4yd4BcKjCkS8iFfvll1+Qn5+Pbdu2IT8/Xz5eWFiI7du3o2/fvqVeo2bN\nmoiIiAAAo3WuzZo1w5w5cyo+6PLQurLOF5FCFZt8eXh44NNPPzU61rlzZ/Tp0wcuLi4mD8zkNFo+\nKUSkYnZ2dkhISEBeXh4uXbokH7exscGIESMsGFkF0boByUnco5ZIgcpV5ys2NhYNGzY0Wv+lWBpX\n4JrlFgESkWkFBgYiMDAQhw4dQtu2bS0dTsXTuAKFBUBeDuDIbdKIlKTYNV9xcXEYP3484uPjkZmZ\niWnTpuHYsWP45ptvEBMTY84YTcNFC+TlQij9yU0iKlGdOnWwe/duCCHw8ccfY/z48Th16pSlw3ps\nkoZbDBEpVbHJV1GdL19fX8TExMh1vj788ENs3brVnDGahNxxsdwEkaotWbIEDg4O+PPPP3Hnzh2M\nHTsWUVFRlg7r8Wm5xRCRUhWbfFVEna/4+PgH9kQDgH379mHKlCmYOnXqQ59EMgsWWiWyCgUFBejY\nsSNOnDiB9u3bw8fHBzqdztJhPT6NYYshPvFIpDwmq/O1adMm/O9//3toorZq1SqEhYVh5syZ2LJl\nCzIzM8sRcgWRC60y+SJSs4KCAqSnpyM2Nha+vr5IT083evpRsVjri0ixTFbnq2hftIepX78+srOz\n5Q7QIk/qcOSLyCp07doV48aNQ+PGjVG3bl1MnToVPXr0sHRYj41rvoiUy2R1vorbFw0APD09MWXK\nFDg6OqJt27ZlLl1RkfszZdWth1sA3OwkaLg3Gttn+5W6/ccRHByMoKAg2NgY7jU//vhjaLVaC0dV\nAbScdiRSKrPX+bp48SJiY2OxaNEiODo6YuHChThw4ADat29f6nsrcn8mUWhY85F+ORkZ3BuN7bP9\nStl+RSR9ubm5WLNmDa5cuYJ33nkHUVFRGDJkCBwdHSsgQgvignsixSpxzVdKSgrS0tLk1x4eHsjP\nz8eCBQseuUFnZ2c4ODjAwcEBNjY2cHNzQ1ZW1iNf75EV7e/INV9EqrZs2TI4Ozvj9u3bsLe3R3Z2\nNhYvXmzpsB6fhmu+iJSq2JGvzZs34/vvv4ckSXj//ffRpEkTbN26Fd9//z0aNWpU7oZiYmKQm5uL\noKAgBAUFISwsDHZ2dqhVqxY6d+78OD/Do9FwzReRNbhw4QLefPNNHD16FFWqVMFbb72Fd99919Jh\nPT4nF8DWjtOORApUbPK1c+dOREZG4ubNm9iyZQu2b9+Os2fPYvTo0UZ7nJWkuH3RgoODERwc/Jih\nPyYXbq5NZA2K1noV0ev1DxxTIkmSDKNfHPkiUpxieyBHR0fUqFED3t7eOHPmDAoLCxEZGVnmxKvS\nc3IGbG057Uikck2aNMHq1auRn5+PY8eOYd68efDx8bF0WBVDo+XTjkQKVGzyde+dobOzMyZOnKiO\nDbXvkiQJcNZw2pFI5QYPHgxHR0c4Oztj7dq1qF+/Pl599VVLh1UxtG5AThZEIbdJI1KSEjfWLlK0\nSF51NK7AnXRLR0FEJvTrr7+ia9eu6N+/v6VDqXCS1g0CMNxEulezdDhEVEbFJl+3b9+W93C89+si\nISEhpo3MHFy0wNXLEHodJBtbS0dDRCaQlJSEDRs2oHbt2mjXrh0CAgJQrZpKEhX5waHbTL6IFKTY\n5MvX1xeXLl164GtV0bgCQgDZWfJj20SkLm+88QaEEIiPj8eRI0cQFhaGqlWrYtasWZYO7fHJ+zty\n3ReRkhSbfL355pvmjMMiJI32nyF7Jl9EqlRQUIAzZ87gxIkTOH78OADDLhuqcM/+jhbYpI2IHlGZ\n1nyplgs31yZSu2HDhkGj0SAkJAQTJ05U9FZJD9BwiyEiJbLu5IuFVolU780338SxY8fwyy+/4OTJ\nk2jRogV8fX1VMfolaV3vjt5z2pFISaw7+ZILrXLInkitnnvuOTz33HMAgCNHjmDNmjVYuXIl1q1b\nZ+HIKkDRcgmu+SJSlFLLPH/55ZcPHJs3b55JgjE3qajj4sgXkWqdOnUKq1evxrvvvotVq1bBz88P\nM2fOtHRYFUPLaUciJSp25Gvp0qW4desW4uLikJHxz12VTqfDlStXzBKcyRWt+eKQPZFqrVq1Cm3b\ntsX//d//oV69epYOp2IVjd6zDyNSlGKTr8DAQCQnJ+PixYto166dfNzW1hZeXl5mCc7k7j4pxAX3\nRKYnMtKAhDOQWj9r1nbnzp2L+Ph4/PHHH9i/fz98fX3RtGlTs8ZgKpKdHeDswhtIIoUpNvlq1KgR\nGjVqhObNm6N69eoAgJycHGRlZaFGjRpmC9Ck5LtGJl9EpiRysqGfNx34Oxk2n66E5Oputrajo6MR\nFRWFdu3aQa/XY8GCBRgwYACCgoLMFoNJadw47UikMKUuuE9MTMSmTZswaNAgTJo0CdnZ2RgwYAB6\n9OhhjvhMi6UmiExO6HXQf/Up8HcypBd6mTXxAoCtW7di9uzZqFq1KgCgb9++iIiIUE/ypXUFblyF\nEMKwZy0RVXqlLrjfuHEjgoKC8Mcff+CZZ57BokWLsG/fPnPEZnKSrS3gxCF7IlMSP64BThwGmrSA\nNGCE+dsXQk68AKBatWqwsSm161MOjSug1xt26iAiRShTD1SvXj2cOHECrVq1grOzM/R6vanjMh+N\nliNfRCai/2MvxPb1QM0nYfPGZMMNj5lpNBocPnxYfn3o0CG4uLiYPQ5TkfjEI5HilDrtKEkS9u/f\nj+PHj2PIkCGIjY1V19C2ixa4fIFD9kQVTFyIh1jxX8DRCTbjp0MqmuY3sxEjRuDjjz/GsmXLAAB2\ndnaYNGmSRWIxiaIHhzIzANSxaChEVDalJl9DhgzB999/j0GDBsHd3R0bN27E8OHDzRGbeWi0QGEB\nkJ8HVHG0dDREqiDSb0G/aDZQWACbMVMgPWm5avKenp5YsGABUlJSIISAh4cHbC0wAmcycr1CjnwR\nKUWpyVfjxo0RFhaGrCzDegLVFCe8S9Lcsz0Hky+ixyYK8qH/YjaQfhNSv6GQfNtYOiTY2Nigbt26\n8uuxY8c+tIC0It3d31Hc4U4dREpR6pqvlJQUvPPOO3jnnXdw69YtTJw4UT1FVoF7Cq1y3RfR4xJC\nQKz6Akg6BymgM6RuoZYO6aGKbibVQF7zxQeHiBSj1ORr2bJlGDZsGNzc3FCtWjV0794dS5YsMUds\n5lG0uXYWOy6ixyV2boI48CvQwAvSkPGVdh1lZY3rkcj7O3LakUgpSk2+7ty5A19fX/l1t27dkJ2d\nbdKgzMrF0HGx0CrR4xGn/oRYvxxwqwabN6dCsnewdEjWwWjBPREpQZmedszPz5fvFNPT09VXagJg\nuQmixyCuXoZ+yTzA1hY24z6A5F7d0iHho48+eugIlxAC+fn5FojIRO6OfIk7TL6IlKLU5Cs4OBgR\nERG4ffs2vv32W/z+++/o06ePOWIzC8lFe3fBPZMvokchsjOh/zwCyMmCNHIipAaVY+/XgICARzqn\nOFUcgSpOQNoNS0dCRGVUavIVGBiI2rVrIzY2FoWFhRg9ejRatGhhjtjMgyNfRI9M6HXQL/kEuHYF\nUrdQ2AR0sXRIss6dO1s6BLOQJAmoWx9IOgdRkM/pXiIFKDX5+uyzzxAQEIABAwagSpUq5ojJvFyK\nFqtyyJ6ovMSGFcBfR4Hm/pBCX7N0OFZL8mwIkRgHpFwC6j9t6XCIqBSlJl/+/v44cOAAvv76a3h7\neyMgIAB+fn5wcnIyR3ymV7Regk87EpWLfv9uiF9+BGrXhc3r70KyUVHhUqWp1xAAIC6dh8Tki6jS\nK/Vpxw4dOmDixIn48ssvERAQgG+//Ravv/66OWIzC6lKFcDegWu+iMpBJMZBrFoEOLsYtg5yrnx7\nJa5duxYAEBcXZ+FITE/ybGD4Ivm8ZQMhojIpdeTrr7/+wsmTJ3HixAmkpaXBx8cHLVu2NEds5uPC\nzbWJykrcTDVUsNfrDZtl1/KwdEgP9fvvvyM4OBhff/01PvzwwwfOazQaC0RlInXqAzY2EMlJlo6E\niMqg1OTrP//5D9zd3dGvXz+88MIL6toTrYhGC9y8bukoiCo9kZcL/aJZQEY6pIGjITVtZemQiuXr\n64uxY8cCAEaOHPnA+XXr1pk7JJOR7B2AJz2B5AsQej0km1InNYjIgkpNvhYvXoxjx47h2LFj2Lx5\nM+rVqwdfX190797dHPGZh4sWuHwBorAQkl2pHwmRVRJ6PfTLPgOSkyB16g4psKelQyrRqFGjMGrU\nKHz44YeYMWOGpcMxOcmzAcSVi0DqVaCSjkYSkUGpmYa7uzs6d+6M1q1bIzY2Fps2bcLp06fVlXwV\nlZvIvgO4VrVsLESVlNgSBcTuB7ybQxo0WjFb9MyYMQPx8fE4duwYdDodfH190bRpU0uHVfE8GwIH\nfzMsumfyRVSplZp8rV27FsePH8etW7fg5+eHIUOGoHnz5uaIzWwkF9d/Cq0y+SJ6gP7wPoit64An\nasNmzBRFjRBHR0cjKioK7dq1g16vx4IFCzBgwAAEBQVZOrQKJXk2MPRjyeeBNh0sHQ4RlaDUHjQv\nLw9Dhw6Ft7e3Yu50y03DvdGIipN37i+IbxYAjk6GJxuLfl8UYuvWrZg9ezaqVjXcWPXt2xcRERGq\nS77kchNcdE9U6ZWafL322mvYsmUL1q1bh8LCQrRo0QIvvfSSuhbeF007stwEkRGRdhM3PnoPKCyE\nzdj3IXnUs3RI5SaEkBMvAKhWrRpsVLggXXLRAtWeYLkJIgUotQeKiorCqVOn8OKLLyIkJARnz57F\nqlWrzBGb+bgYki+RedvCgRBVHiI/D/pFEdDfugGp/zBIzf0tHdIj0Wg0OHz4sPz60KFDcHGpfHXJ\nKoRnA+B2GsTtNEtHQkQlKHXk69ixY5gzZw7s7q7xaN26Nd577z2TB2ZOUp36hrUSCXFAJxU9SED0\niIQQEMsXAhcT4NK1F3K69rF0SI9sxIgR+Pjjj7Fs2TIAgJ2dner6sCJSvYYQxw8ZRr/c/CwdDhEV\no9TkS6/Xy4kXANjb26tryhEw3C1q3SBOH4UQQr1r24jKSGz7DuLwPuDppqg6bipyU29YOqRH5unp\niQULFiAlJQVCCHh4eKivD7tL8mwIAcO6L6kZky+iyqrUacennnoKy5cvx9WrV3H16lWsWLEC9evX\nN0dsZiPZ2EDyaQXcTgMuX7B0OEQWJf7cD7FpDVC9pmGdl72DpUN6bDY2Nqhbty48PT1Vm3gBMNxI\nAgAX3RNVaqUmXyNHjkRWVhbCwsIwffp0ZGRkYMSIEeaIzbx8WgMAxKlYCwdCZDniUiL0yyKBKo6w\nGT8Nkqu7pUOi8qheE3B2gbjERfdElVmp047Ozs4YN26c0bHk5OQy7YsWHx+PNWvWIDw8XD6Wnp6O\nzz77TH594cIFvPLKKwgODi5H2BVP8mkFIUkQf8UCL/azaCxEliBup0G/KAIoyIfNmx9AqtvA0iFR\nOUmSZCi2eu4URG4OJEcnS4dERA/xSJUSp0+fjhUrVpT4PZs2bUJ0dDQcHR2Njru7u8vJ2Llz5xAV\nFVUp6u1IWjegXiMg4QxEbjYkR2dLh0RkNqIg37BZ9q0bkEKHQGrZztIhVajU1FRkZmZCCCEfa9iw\noQUjMh3JsyHE2ZOGJRRPN7F0OET0EI+UfN3bgRWnVq1amDRpEj7//PNir7Fs2TK89dZblabmjuTT\nGgjYQycAACAASURBVOJiAhB3ElDZHx+i4gghIFYuAs6fhRTQGVJ3dY38rl69Gjt27ICbm5t8TJKk\nYvumez1s9P5eixcvhkajweDBgysq3Md3d92XSE6CxOSLqFJ6pOSrLE8DBgQE4Pr168We//PPP1G3\nbl14eJR9D7LyfO+jyOscjOs/fQenpLOo1uMls7ZdGrbP9k0l9+SfSD24Bw7ezVBzSgQkhypmbd/U\nDhw4gIULF6JatWrlel9xo/dFdu7ciUuXLlW6fSKlevdsM0RElZLFNmiLjo5Gjx49yvWelJQUE0Vj\nILTVACdnZB3ah5y+r8lJpoeHh8nbLgnbZ/umbF+/5TsAQGGvV/D3jZtmb78kFZH01ahRo9yJF1Dy\n6P3Zs2cRHx+Prl274sqVK48dY4Wq7QnY2XHRPVElVmzyNWTIkIeOcAkhkJeX99gNnz9/Ht7e3o99\nnYok2dkBTVoAsQeA638DtZR7t09UFiIvD+LP/YZtaZ6pXCM4FaVZs2ZYvXo1/P394eDwT9mM0tZ8\nFTd6n5aWhvXr12PSpEk4cOBAuWIx1wji1fpPo+DSeTxZq6ZZ2y0O22f71tz+wxSbfH366acV2lBM\nTAxyc3MRFBSEjIwMODk5VcpippJPa4jYAxCnYiEx+SKVE8cOArk5kAJ7Qaokay8r2m+//QYARolS\nWdd8PcyBAweQkZGBOXPmID09HXl5eahTpw46d+5c6nvNNYKof9ITSIxDSuxh1GnTXtUjt2yf7VfW\n9ktK+opNvp544onHbrhmzZqIiIgAAHTo0EE+7urqik8++eSxr28Kkk9rQ4Xov2KBF0IsHQ6RSYmD\nvwEApPadLRqHKS1atKhCr9ejRw95ycRvv/2GK1eulCnxMit50f15oE17CwdDRPez2Jqvykqq/gTw\npCdw9iREQQEke3tLh0RkEuJ2GvDXUaCBF6TadS0djslkZGQgOjoaubm5AAxbpl29ehVvvfVWua5z\n7+h9ZVe0zRAr3RNVTky+HkLyaQ2xaxOQcNqwBoxIhcShaEDoIQV0tnQoJhUZGQkHBwdcvnwZzZs3\nx8mTJ9G4ceMyvbe40fsilW7Eq4jnUwDARfdElZQ6F3k8JsmnFQBuNUTqJg78CtjaQmrTydKhmNSN\nGzcwdepUtGrVCt27d8fMmTNx9epVS4dlUpKjM1DzSSA5qUx1GYnIvJh8PYyXD2DvYFj3RaRC4vIF\nw5RUMz9IWldLh2NS7u6G/Slr166N5ORkVKtWDXq93sJRmZ7k2RDIugNd6jVLh0JE92Hy9RCSQxXA\nuxlw5SJE2oN1j4iUThzcAwCwaR9o4UhMz9XVFZs3b8bTTz+NPXv24MiRI8jOzrZ0WKZ3d9F9wfmz\nFg6EiO7H5KsY8tQjR79IZYReB/HHXsDZBfBtY+lwTG706NGws7ND48aN0bBhQ3z33XeVazsgE5Hq\nNQIA5DP5Iqp0mHwVQ/LxM3zBdV+kNnEngPRbkPw7WsXTvG5ubggKCsKlS5fwyiuvYNasWWjbtq2l\nwzI9eeTrnIUDIaL7MfkqTu06QPWaEGeOQ+gKLR0NUYURB34DoO7aXvc6d+4cJkyYgDlz5iAtLQ1j\nxozB2bNWMBrkVhXQuiGfyRdRpcPkqxiSJBmmHrMzkX/utKXDIaoQIjcHInY/8ERtoFETS4djFqtX\nr0ZYWBi0Wi2qV6+O8ePHY/ny5ZYOy+QkSQLqNYTuWgpEVqalwyGiezD5KoHk0xoAkPtn+fZvI6qs\nxNGDQH4epIDOlXJ7L1PIy8tD3br/FJFt3bo1dDqdBSMyH8nz7v6Vl1lslagyYfJVksa+gK0tcmOZ\nfJE6iAO/AgCkgC4WjsR87OzskJmZKSebltxnzuzqGZIvFlslqlxY4b4EkrML0NAb+ef+gk1mBiSN\nuushkbqJtJuGxfaNGkOq+aSlwzGb0NBQhIeHIz09HZ999hlOnDiB0aNHWzoss5A8G9zdZojJF1Fl\nwuSrFJJPa4j40xBnjkNq09HS4RA9MvHHb4AQkKygtte9/Pz8UKdOHZw4cQJ6vR79+/c3moZUtZpP\nQqriCME9HokqFU47lkJqxpITpHxCCIgDewA7O0j+D+5RqEaZmZny/zQaDZ599ll06NAB7u7uyMy0\njgXoko0t7Bt4AX8nQxQUWDocIrqLI1+l8WwAG7eq0P91FEIIq1mkTCqTfB5IuQS0fhaSi8bS0ZjF\nyJEjSzy/bt06M0ViWfYNvZAfd8Lw379+I0uHQ0Rg8lUqycYGVVoHIHvPduDKBaBuA0uHRFRuRbW9\nbKykthcAPP/88zh79iz8/f3RpUsX65lqvI9DI29kARCXEv+/vTuPq6ra/z/+WpvD6ISIgChqzgPm\nmKGZN5VK07pdtbns2uBtnjRtIlHjW16rm6k/TUvLrnW1vKZpmTmFXjNzKIfEEBFNnBAREZBhr98f\nG47ilMPhbA7n83w8fAB7b896b5HF5+y99looKb6EqBCk+LoIAR27krviW/TWjSgpvoSH0cXF6HU/\nQNVqUHob3Qs88cQTnDx5kp9++okZM2aQn59P9+7d6datG1WqVLE7ntv4NmpmfSLjvoSoMKT4uggB\n7a8FQG/dCL0H2JxGiEv02y+QnYXqcQvKUfmXEzqdv78/3bt3p3v37hw5coTExERGjRpFnTp1eP75\n5+2O5xa+DRqDYcigeyEqEBlwfxF8gkOgQRPYuR2dn2d3HCEuiXNuLy97yvFM2dnZZGdnc/z4cXJz\nc+2O4zaGfwBE1IO9qWjTtDuOEAK58nXRVOsO6LSdsGMLtPWCRXlFpaDzctG//AThdaFhU7vjuF1G\nRgarVq1i1apVKKXo3r07CQkJhISE2B3NrVTUVej0PZBxAMIi7Y4jhNeT4usiqdbt0d/MscZ9SfEl\nPITe8D8oLEB16eF1T+rGx8ezf/9+unTpwtNPP81VV3nxeM36jeCnH2DPLim+hKgApPi6WI2aQ2AQ\nepvM9yU8h167EgB17V/sDWKD7du34+vry/Lly1mxYoVze+mUMZ988omN6dxLRTVCA3pvqtfM8yZE\nRSbF10VSDge0bAsbf0QfSkfJu0dRwekjh6zb5M2iUaHhdsdxu4kTJ9odoeKIsq76yaB7ISoGKb4u\ngWrdHr3xR/S2TVJ8iQrPedUr5gZbc9ildu3adkeoMFTV6hASat12FELYTp52vASqdQegZMoJISow\nrTV67Qrw9UN1vM7uOKIiiGoExzLR2UftTiKE15Pi6xKoWmFQJwqSNss6aaJi250MB/ah2l2LCvKe\nCUXF+amoRtYne+TWoxB2k+LrEqnW7aHgJOz8ze4oQpyX/tEaYK669LA5iagolIz7EqLCkOLrEjlv\nPcpTj6KC0kWF6J8ToVoNaNXe7jiioigpvtgr476EsJsUX5eqWWvw9ZNxX6Li2roRco6jrv0LysfH\n7jSioggNh8AqaCm+hLCdFF+XSPn5WwXYvjR01hG74wjhpM1idMZBzB8WA6Bi5JajOEUpZV39OpiO\nPplvdxwhvJpMNXEZVHQH9LZN1pQT18XaHUd4Ea01HM+CA+nog/usX6SH0uFgOhzaD0UlD4JE1rdm\nNRfiNKp+I/TvW+GP3dC4hd1xhPBaUnxdBtW6I5qPrNs7UnyJcqT3pnJsxdeYO3egD6bDoXTIO8ei\n0IFBULcBKrwuhNdBdermdcsJiYvgHHS/CyXFlxC2keLrckTUhZDa6N9+QZvFKEPG1QjX00VFmBPG\nkH00w9rg8IWwOtAisqTIirQm+42IhGrBUmyJP1W6zJBMtiqEvaT4ugxKKevWY+J36OULUbF/tTuS\nqIT0prVwNIOgXn3Jj70dQkKl0BdXpk49cDhkugkhbCYD7i+T6j0AatREz/4Ic80yu+OISkgv/xqA\n6nc9hAoNl8JLXDHl8LXGA+5LQxcX2x1HCK8lxddlUrUjMJ4bBUFV0R9PQG9YY3ckUYnotJ2wcztE\nd8S3bgO744hKREU1gsICOLDP7ihCeC0pvq6AqtcQ47l48PPHnPa2zP0lXEYvWwiA0aufzUlEpVOy\nzJDM9yWEfaT4ukLqqmYYT78GSmFO/j90siw7JK6Mzs6yZqgPrysz1AuXU6VTkEjxJYRtpPhyAdW8\nDcZjL0FxMeaE0ei0FLsjCQ+mVy2BoiJUz74oQ35EhYvVawjIGo9C2Klce/bk5GTi4+PP2r5z505e\nf/114uLieOeddygoKCjPGG6h2l6Deuh5yM/DfG8kev9euyMJD6SLitArv4GAQFTXnnbHEZWQCgyC\n2hGwd5c1aa8Qwu3KrfiaP38+U6ZMobCwsMx2rTUffPABTzzxBGPGjKFdu3ZkZGSUVwy3Mjp3R93/\nBORkY777OjrjoN2RhIfRm36ErEzUdbGogCC744jKqn4jyDkORytH3yuEpym34is8PJxhw4adtX3/\n/v1Uq1aNhQsXMnLkSHJycoiMjCyvGG5ndL8ZdcdgyDqC+W4cOivT7kjCg+hlX4NSqJ597Y4iKjEV\nVTruS249CmGHcptkNSYmhkOHDp21PTs7mx07dvDQQw8RERHB2LFjady4MdHR0X/6mnYWaZfU9t+f\n5JiPD9n/+RBj4mjC3pqKT/Vg97VfDqT98m+/IPk3DqYkEXBNN2q36+T29i/E7vaFa6n61kz3ency\nqm1nu+MI4XXcPsN9tWrViIiIoF69egC0bduWlJSUiyq+0tPTyzveOUVGRl5y27rnrajDByla9jXp\nLz+O8cIYa6yFm9p3JWnfPe2bs2cAUHDdjWXa85bzP1/bohw0ag7+gejli9A9bkFVr2l3IiG8itsf\npQoPDyc/P58DBw4AkJSURFRUlLtjlDulFOrOh1Fde8HuZMyJY9AFJ+2OJSoonX0U/fMqa93Qlm3t\njiMqOVWlGmrAIMjNQf/nQ7vjCOF13FZ8rV69mqVLl+JwOHj88ccZP348L7/8MrVq1aJDhw7uiuFW\nyjBQg56CDl3h922YU8aiiwr//C8Kr6MTvyuZXqKfTC8h3EL9pQ80boH+eRX613V2xxHCq5Trbcew\nsDASEhIA6Natm3N7dHQ0b775Znk2XWEoHx+MR4ZiTsqDLevRH/0LHhmK8pF1+oRFFxWiVy6GwCBU\nlx52xxFeQhkGxqCnMEc/hzlrCkaz6MseGiGEuDTyFtsNlK8vxuOvQNNW6PWrMaeOkytgwklvWAPH\nZHoJ4X4qsj7qloFwNAM9b6bdcYTwGlJ8uYny98d45nVoFg0b12BOfgtd6PmTy4orp1cssqaX6HGL\n3VGEF1J97oA6UeiV36J3brc7jhBeQYovN1IBQRjPjLTW69v8M+bEN9AnZRC+N9OpyZCSBG06ocLk\nyT7hfsrXF2PQUwCYMyeiC+WqvBDlTYovN1P+/hhPvQZtO8Nvv2C+H4/Oz7U7lrCJXr4QAKNXP5uT\nCG+mmrS0BuDv34v+9ku74whR6UnxZQPl64vx2AjoWPIU5L9GonNz7I4l3EwfK5leok4UtGxndxzh\n5VT/QRBcC/3NF+j0PXbHEaJSk+LLJsrhi/Hoi6iYG2DXDsx34tA52XbHEm6kE7+D4iJUz74opeyO\nI7ycCgzCuO8xKC6ybj+apt2RhKi0pPiykfLxQQ1+DnX9TbAnBfPtV9HZR+2OJdxAFxWif/gWAqug\nYmR6CVExqHbXojp1g5Qk9A+L7Y4jRKUlxZfNlGGg7n8C1bMf7EvDHPcK+ugRu2OJcmZNL3EU1S0W\nFRBodxwhnNTdj0JQFfR/P0FnHrY7jhCVkhRfFYAyDNTdj6Ju7g8H9mGOexl95OxFyUXloZd9XTK9\nRF+7o4gLSE5OJj4+/qztq1ev5pVXXiEuLo6pU6diVqJbdKpGTdQdD0F+HuasKWit7Y4kRKUjxVcF\noZRCDXgQdevdcPgA5j9fQh+ybzFlUX70rh2Q+jtcfQ2qdoTdccR5zJ8/nylTplB4xtQLBQUFzJ49\nm5EjRzJmzBhyc3PZuHGjTSnLh7ouFlpcDZt/Rq//n91xhKh0pPiqQJRSGLfdaz11lJmB+c9X0Pv3\n2h1LuJhzeomeMr1ERRYeHs6wYcPO2u5wOBgzZgz+/v4AmKaJr6+vu+OVK6UUxgNPgK8f+vMP0CeO\n2x1JiEqlXNd2FJfH6DMQ09cPPftDzHGvUPB/kyGgqt2xhAvorEzrSkKdKGjZ1u444gJiYmI4dOjs\n2/+GYRAcHAzAt99+S35+PldfffVFvWZkpD0T6V5Wu5GRZN83hGMfTyRw0WxCnnvdve27kLQv7Vc0\nUnxVUEbsbVYB9u//R8Ybw9DxE1COyvXu2hvpxMUl00v0k+klPJhpmvz73/9m//79DB069KK/l+np\n7h9KEBkZednt6mt7wrJFnPh+AXltrkFdxhuGK2nfFaR9ad+u9i9U9MltxwrM+EtvVK9bKT6Yjl6z\n3O444gpZ00sstqaX6CLTS3iyqVOnUlhYyIsvvui8/VgZKYcD48GnQRmYn06S5dCEcBEpvio41XsA\nys/fmnW6SNZc82R6/WrIzkJdfyPKP8DuOOISrV69mqVLl7Jr1y5WrFjBnj17GD16NPHx8axbt87u\neOVGNWiCuvGvcPgA+uvP7Y4jRKUgtx0rOBUcQlCf/uTM/xz94wprQlbhcXRREXrRHDAM1A232B1H\nXKSwsDASEhIA6Natm3P77Nmz7YpkC3XbveiNa9Dff4Vu1Q7VSpbDEuJKyJUvD1B94IPWU0eL5qCL\niuyOIy6DXrUEDuxDdb9ZppcQHkf5+2MMegqUwhwfj7nsa5n/S4grIMWXB/AJCUV1vxmOHEL/KGO/\nPI3OPYFe8BkEBKJuvcfuOEJcFtWyLcbQBKhaHf2faegZ49GFBXbHEsIjSfHlIVTv/uDwlatfHkgv\nngs52db4verBdscR4rKppq0wXn0XGjRB/7gc858vozMz7I4lhMeR4stDqOBacvXLA+kjh9FLF0DN\nUFTsX+2OI8QVUyGhGCPeQnXpCbuTMd94Hp38m92xhPAoUnx5ENV7gHX165sv5OqXh9Bf/RsKC1C3\n34+qxFMSCO+ifP1Qg5+1FuE+cRzznVcxV35rdywhPIYUXx5E1Sy5+pVxEL12hd1xxJ/QaSnW9ynq\nKlTMDXbHEcKllFIYvW7FeGEMBFZBz5pszQVWKFPiCPFnpPjyMNbVL4eM/argtNaYX0wHwLjjIZQh\nP2qiclLN22C89i7Ub4RO/A7znVfRWZl2xxKiQpPfCB5G1ayFur7k6tdPK+2OI85ny3rYsQXadLqs\nJVmE8CSqVhjG8LGozt0hJQkz4QX0rh12xxKiwpLiywOpPgPl6lcFpouLMb/8GJSBMeDvdscRwi2U\nvz/qkaGoOwbDsSzMcS9j/m+p3bGEqJCk+PJA1tWvm6zlPuTqV4WjV38P+/daywjVrW93HCHcRimF\ncdPfMJ4bCX4B6I/f5+jkf6LNYrujCVGhSPHloVTv065+FUvHVlHo/Fz0/FngH4C67V674whhC9Wq\nvTUOrG4DchbOQX/tXcsxCfFnpPjyUCokFNWt5OrX2pV2xxEl9OL/wvFjqJv7o2rUtDuOELZRtSMw\nXnwTn/BI9KLZ6K0b7I4kRIUhxZcHU31Kn3ycLVe/KgCdmYH+/iuoEYK66Xa74whhO1WlKqEvjwUf\nH8wP30UfOWx3JCEqBCm+PJgKqX3q6peM/bKdnj8LCgpQt9+H8g+wO44QFYJf05aou4dYk7F+MFbm\nARMCKb48nuozAHwc6IVy9ctOes8ua9mnug1QXXvaHUeICkV1vxkV0wNSf0eXzH8nhDeT4svDqZDa\nqOtvLLn69YPdcbyS1hrzyxmgdcmEqj52RxKiQlFKoe5/HOo2QK9YhLku0e5IQthKiq9KQPUZaF39\nkrFf9ti6Ebb/Cq3ao1q3tzuNEBWS8g/AeGwEBASiZ05E799rdyQhbCPFVyVgjf2KhUP75eqXm1kT\nqs4ApTDu+LvdcYSo0FREPYy/PwMn8zEnv4XOz7M7khC2kOKrklB97ii5+iXzfrmTXrMM0veguvZC\n1bvK7jhCVHiq43Wo2Ntg/170p5PQWtsdSQi3k+KrklC1aqOui4VD6WgZT+EWOj/PesLRzx/11/vs\njiOEx1ADHoTGLdDrEtErv7U7jhBuJ8VXJaJuGShPPrqRXjIPjh1F3fQ3VM1adscRwmMohy/GkOFQ\ntTp69ofo1N/tjiSEW0nxVYmoWmGnrn7JvF/lSh/aj/5uHlQPRt38N7vjCOFxVEgoxqPDwCzGnDIW\nnZNtdyQh3EaKr0pG3TIQHL7oz6ai01LsjlPp6BM5mF9+jDnyKSg4ibr9flRAoN2xhPBIqlU71G33\nQOZhzI/+hTZNuyMJ4RblWnwlJycTHx9/1vaFCxfywgsvEB8fT3x8POnp6eUZw6uoWmEYj7wABfmY\n749CHz5gd6RKQRcWYC6Zh/nKEPR3/4VqNVCDn0V1u9HuaEJ4NHXLnRDdEbZuQH8zx+44QriFo7xe\neP78+SQmJhIQcPYyK7t27eKpp56iUaNG5dW8V1Mdr0Pd9Sj6P1Mx34vHeGksqloNu2N5JG2anFi+\nCHPGRMg8DIFVUAMeRPXsh/LztzueEB5PGQbGw89jjnkeveBzdKMWqFbt7I4lRLkqtytf4eHhDBs2\n7Jz7UlNTmTdvHnFxccybN6+8Ing1o1c/a+mhQ+mYE8agT+bbHcnj6G2bMMc8T+Y7IyH7KOqm2zHe\nnIrRe4AUXkK4kKpa3ZqA1fDBnPY2OjPD7khClKtyu/IVExPDoUOHzrmva9eu3HzzzQQFBTFu3Dg2\nbNhAx44d//Q1IyMjXR3zotnZ9uW2r598icyCfHKXLcLvk/cJjXsb5XN533JPPP/LVZCSRNb09zn5\nyzpQiqCet1DjgcdxhNVxW4YzedO/v/BO6qpmqLseQX82BfO9kahuN6Jad4DIKJRSdscTwqXKrfg6\nH601ffv2JSgoCIAOHTqQmpp6UcWXXWPDIiMjbR2XdiXt64EPw4F08n9ezb6xr6EefPqSOzJPPv9L\noQ8fQH81C72uZJWAVu0xBjxIrZhuVvvy/8+WtoX3UDf0gT92oxMXo7+Ybi3CXTPUug3ZugOqVVtU\nlWp2xxTiirm9+MrLy2Po0KH861//wt/fn61bt9KjRw93x/AayuHAeOwlzLdfRf9vKdSsJROCnkEX\nFqK/+hS9fCEUFUH9RhgD/i7jToRwM6UU6oEn0Lfejf5tE2zbhP7tF6vv+t9StDKgYRNU65J1VK9q\njvKRheyF53Fb8bV69Wry8/OJjY3lnnvuYdSoUTgcDtq0aUOHDh3cFcMrqYBAjGfiMN8agV44G7NG\nCMYNfeyOVSHooiLMqePgl7VQKwz1twdQ11yPMmQWFiHsooJDUF17Qdde1vQTe1LQ2zaht22EXTvQ\nqb+jF86GwCrQ8mqrGIusDz4OMHzAx8f63MegyKHQWUdKtjtK9ll/lCGFm7BHuRZfYWFhJCQkANCt\nWzfn9u7du9O9e/fybFqcQVWvifFcvFWAffYBukZNVPsYu2PZSpvF6BnjrcKrxdUYT8fJQHohKhhl\nGNCwKaphU+h7JzovF5I2o7dtRG/bBBt/RG/8kfOtELn/Qi/u5w9BVaFKVahSDapURQWd+pySz1WV\nqqd9XRUCguQNmrgibr/tKOyjwiIxnnkd8+1XMae9jfHCaFSTVnbHsoXWGv3vydb4rsYtMJ58VQov\nITyACgyC9jGo9jHWotyH9lu3KLMyobgIiotLPppQXESgvx95OTlo577iU8fk58GJ45CZAfvSAM5Z\nxJ21TSkIDLKKsdKCLLCKVaQFVTm1PagK+U2aoYNry1U2UYYUX15GNWyK8dgIzIlvYE54A2PEW9bl\nei+itUbP+Qi9aok1vuuZ12WWeiE8kFIKwiNR4ed/MKPWRT4woouLIe8EnMiB3Bw4cRx92uecKNmW\ne8Lallty7IE/oOCk9RrneN3DAKHhqB59rSc4g6pc3smKSkWKLy+kojuiBj2FnjEec3w8xkvjvGph\naL3gM/TSBVAnCuO5UdZtBiGEV1M+PlC1uvWndNtF/l1dVFi2IMs9gc61CregjAOcWPGt9fTmgs9Q\nXXuiet6KiqhbPiciPIIUX17K6NoLMysTPe9TqwAb/qZXFCHm4rnWQN3aEdZtV5n5XwhxhZTDF6rX\ntP6Ubiv5GBIZSV6fO9CrlqBXfOP8Q3RHjF63Quv2Mo+ZF5Liy4upPgMh6wh6xTeYk/7Puv3mf/Zy\nUJWFueIb9NxPoGYoxgtjUMHec7VPCGEfVbU6qs9A9I23ozetRS9bAFs3YG7dABH1UL36obr0rNT9\nryhLii8vppSCux9FH8uCjWswXxyM6tID1b03qm7lGgdmrlmG/mwKVKthFV6h4XZHEkJ4GeVwoK7p\nBtd0Q+9ORi9biP55FXrWFPS8T60xYT36Sv/kBaT48nLK8MF45AX0N/XRq75DL19oTTbapKVVhHXs\nanfEK6Y3/A/98QQIqmrdapSxFkIIm6mGTVEPP48e+Hf0D9+iV36LXvIV+vsF1q3IZtGoxi2sSWXl\nSexKR4ovgfL1Q/31XnTfO2HzOswfvoPfNqF3bkf/ZxpHb7wV3fF6VJ16dke9ZHrzz5jT3gZ/f2tw\nfb2r7I4khBBOqkZN1G33ovvcgV6/Gr3sa9i6Ab11g/X0pI8P1LvKKsQaNbc+1gqTcWIeToov4aQc\nDujQFZ8OXa11Dld9h169lJz5n8P8z6FZa+tqWIeuKF9fu+P+Kb39V8zJb4GPjzWB6lVN7Y4khBDn\npHx9UV16QJce6MwM2JWETtmB3pVkzfCfthOWL7QKsho1oXELVKMWqMbNoUETlK+f3acgLoEUX+Kc\nVO0IVP8H0bfdS820ZI7M/xy2/4r+fRu66lRU116o62+usLfwdEoS5qQEQGM8/iqqWbTdkYQQ4qKo\nkFAI6YbqZK0MowsLIC0FXVKQsSup7Mz+Pg6IqGvNJxYaXuajWTPY1nMR5ybFl7gg5fAl6PpYGER0\nFQAAE7pJREFUshq3Qh9KRycuQa9ZVjI2YT7q2htQt9+HqhVmd1QnvScFc/woKCzA+McIVLSsHSqE\n8FzK188ah9ukJWBNFE3mYXRKkrXWZUoS7P8D9qU5J3ot/bgPrLnLSguyWmGnPo+sDzVryS1MG0jx\nJS6aCotEDfw7+q/3oX9Zi/72S/TaFej1q1E9+6FuucNaXsMmuqjQmkPn6/9Afi7qoedRHbrYlkcI\nIcqDUsoa91UrDDpb6yRrrSHnOGQcRGcchCMHIeMg/sePkb9vD/yRit6d7HwN52z81WpAg8ao+k1Q\nDRpDgyYQEioFWTmT4ktcMuXri7rmenTH69DrEtHzPkUvmYde/T2q7x3Wo9JuHH+gtYaNP2LO/RgO\nH7DWWBv8HEbMDW7LIIQQdlJKQbXqUK16mfGttUuWV9KmCceOWsXZkYNw+CD6j1RIS4GtG9FbN54q\nyKpWh/qNUQ0aoxo0gfqNrKtlUpC5jBRf4rIpw0DF3IDu2BW9YhF60Rz0FzPQyxehbr8f1bk7yjDK\nNYNO/R1zznTY+Rv4+KB63YrqdxfqtCVChBDC2ynDgJq1rNuMTVuV2aePZ8PeFHRaycD+tBTrifff\nNp0qyKpUg/qNrHG+teugakdA7TpQO1ymwrgMUnyJK6Z8/VA3/Q19XSz6my+sucI+ehf9/VcYAwej\nWrZ1eZs64yD6vzPRP6+yNrSLwRjwYIV9AEAIISoqVa06tGqPatXeuU2fyDn1lGVaCnpPivXQ1fZf\nrf2nv0BwLQiLOK0gi0DVrgNhEe49EQ8ixZdwGVWlGuqOh9A9+qK/+jf6px8w342D6A5WYeSCObZ0\n7gmrwFv2NRQVQoMmGHc8hGouTzMKIYSrqCpVoWXbMm+edV4uHN4Phw+gDx2Aw/vRhw/Aof2Q/Bv6\n922nji35uK9aDcy6DVD1G5eMLWsMYXXK/a7IlSp9qIG0nejdO9FpKXBwH8Zdj6Dax1zx60vxJVxO\nhYajHhmKvvF2axzW1o2Y2zZZa5f1vcMaO2D4XNJr6qIia96xBZ9DTrY1IPRvD6A6/6XC/xALIURl\noAKDoH5jazzYGft0YaE1yP+MwszIOIiZtBmdtNk6DiAg0LqFeXpBFlH3kn8vuIqz0Nq9E51WUmjt\n2Wk9wHC62hHgoofKpPgS5UY1aIzx/GjYtgnzyxnWFBVrloFhQLVgqBEM1WuiSj5SI+S0z2ta+/0D\nyfspEXPqO3BgHwQEWkVX7G0yzkAIISoI5esLEfWshcJP214nMpJ9KTth7y7r1mWaNbaM5O3OK2Ua\nwM8foq6yCrE6UVZf7+dvbfcv+XiOP2e++dZaW3dFCk5CQQGFugi9by+cPAmFBdafgpPokyfhwB/n\nL7RCw1HNr7YmsG1QUiRWqeayfy8pvkS5UkpZtx1btUWv/QG9eR0cy4Lso3BwP+zZVWbsgD7zBXz9\nyCgsAGWg/tIbdds9qOo13XgGQgghroQKDIJm0WUmu9Yn8+GP3daYsj0p6LRdsDvZmrOs9JiLeXFf\nP6sQU0BBSXGlT/3NAxfzGuVcaJ2LFF/CLZThg+raE7r2LLNd5+dZhVhJQaaPlXx+LBOdbX0MjGrI\nyZv6oyLr25ReCCGEKyn/AGuJpMYtnNt0YQH8kYY+lO68cmV9zC/5eBJO5qNP33eyZJ/WJVfD/MC3\n5KqYnx9BwTXJLSw6tc/Pv2S/nzVPmhsKrXOR4kvYSgUEWvf/wyKtr89xTGjJPDVCCCEqL+XrB1c1\ndek6vCGRkeRXwN8fMlJZCCGEEMKN5MqXEEKcR3JyMrNmzSI+Pr7M9vXr1zN37lwMw6BHjx7Exsba\nE1AI4ZGk+BJCiHOYP38+iYmJBAQElNleVFTEJ598wptvvklAQABxcXF06tSJ4OBgm5IKITyN3HYU\nQohzCA8PZ9iwYWdt37dvHxEREVStWhWHw0Hz5s3Zvn27DQmFEJ5KrnwJIcQ5xMTEcOjQobO25+Xl\nERQU5Pw6MDCQ3Nzci3rNyMhIl+W7FHa1K+1L+9L+uUnxJYQQlyAwMJD8/Hzn13l5eVSpUuWi/q4d\nT+1G2vy0sLQv7Xtr+xcq+uS2oxBCXIK6deuyf/9+cnJyKCoqYvv27TRr1szuWEIIDyJXvoQQ4iKs\nXr2a/Px8YmNjGTRoEAkJCZimSY8ePQgJCbE7nhDCg0jxJYQQ5xEWFkZCQgIA3bp1c27v1KkTnTp1\nsiuWEMLDyW1HIYQQQgg3kuJLCCGEEMKNpPgSQgghhHAjKb6EEEIIIdxIaa213SGEEEIIIbyFXPkS\nQgghhHAjKb6EEEIIIdxIii8hhBBCCDeS4ksIIYQQwo2k+BJCCCGEcCMpvoQQQggh3EjWdixRVFTE\n5MmTOXz4MIWFhQwYMKDM2m0LFy5k+fLlVK9eHYAhQ4YQGRnp0gwjRowgMDAQsNaUe+KJJ5z71q9f\nz9y5czEMgx49ehAbG+vStleuXMnKlSsBKCwsZPfu3UydOpUqVaoA5Xv+ycnJzJo1i/j4eA4cOMCk\nSZNQShEVFcXDDz+MYZx6j2CaJh9++CFpaWn4+vry2GOPERER4bL2d+/ezfTp0zEMA19fX5588kmC\ng4PLHH+h79OVtp+amspbb71FnTp1ALjpppvo2rWr89jyPv/33nuPrKwsAA4fPkzTpk157rnnyhzv\n6vMXriF9mPRh0od5UB+mhdZa6+XLl+sZM2ZorbU+fvy4fuyxx8rsHz9+vE5JSSm39k+ePKlffPHF\nc+4rLCzUTz31lD5+/LguLCzUL730kj569Gi5ZZk2bZr+/vvvy2wrr/P/6quv9AsvvKBfeeUVrbXW\nb731lt66davWWusPPvhA//TTT2WOX7t2rZ44caLWWusdO3bosWPHurT9119/XaempmqttV6yZIn+\n+OOPyxx/oe+TK9pfunSpXrBgwXmPL+/zL3X8+HE9bNgwnZmZWWa7q89fuI70YadIH5aqtZY+rCL3\nYXLbsUSXLl246667ANBa4+PjU2Z/amoq8+bNIy4ujnnz5rm8/bS0NE6ePMkbb7zBqFGj+P333537\n9u3bR0REBFWrVsXhcNC8eXO2b9/u8gwAKSkp/PHHH2e9Ky2v8w8PD2fYsGHOr3ft2kWrVq0AaN++\nPZs3by5zfFJSEu3atQOgWbNmpKSkuLT95557joYNGwJQXFyMr69vmeMv9H1yRfu7du1i48aNjBw5\nksmTJ5OXl1fm+PI+/1Jz5syhT58+1KxZs8x2V5+/cB3pwyzSh0kfBhW/D5Piq0RAQACBgYHk5eXx\n7rvvcvfdd5fZ37VrVx599FFGjhxJUlISGzZscGn7/v7+3Hrrrbz66qs8+uijTJgwgeLiYgDy8vII\nCgpyHhsYGEhubq5L2y81b948Bg4ceNb28jr/mJiYs35JKKWAc5/nmf8WhmE4/51c0X7pD+qOHTv4\n7rvv6NevX5njL/R9ckX7TZo04YEHHmDUqFGEh4fzxRdflDm+vM8f4NixY2zdupUbbrjhrONdff7C\ndaQPs0gfJn2YJ/RhUnydJiMjg1GjRnH99dfTrVs353atNX379qV69eo4HA46dOhAamqqS9uuU6cO\n3bt3RylFZGQkVatW5ejRo4D1A5yfn+88Ni8vzzmOwZVOnDhBeno60dHRZba74/xLlXZacO7zLP3l\ncnq2M3/wrtSaNWuYNm0aL730knN8SKkLfZ9coXPnzjRq1Mj5+e7du8vsd8f5r127lm7dupUZp1Kq\nvM9fXBnpw6QPA+nDPKEPk+KrRFZWFgkJCdx333307NmzzL68vDyGDh1Kfn4+Wmu2bt3q/M/lKitW\nrGDmzJkAZGZmkpeX53wHU7duXfbv309OTg5FRUVs376dZs2aubR9gO3bt5/VaYF7zr9Uw4YN2bZt\nGwCbNm2iZcuWZfY3b96cTZs2AfD7779Tv359l7afmJjI4sWLiY+PJzw8/Kz9F/o+uUJCQgI7d+4E\nYMuWLWf9O5f3+Ze2W3pb4Ezlff7i8kkfJn0YSB9W2m5F78PkaccS8+bNIycnh7lz5zJ37lwAevXq\nxcmTJ4mNjeWee+5h1KhROBwO2rRpQ4cOHVzafs+ePZk0aRJxcXEopXj88cf58ccfyc/PJzY2lkGD\nBpGQkIBpmvTo0YOQkBCXtg+Qnp5e5od19erVzvbL+/xLDRo0iA8++ICioiLq1q1LTEwMABMnTuTu\nu++mc+fObN68mddeew2ttUufUjFNkxkzZhAaGsrbb78NQKtWrbjzzjud7Z/r++TKd22PPPIIM2bM\nwMfHh+DgYIYMGQK45/xLnfn/4PT2y/v8xeWTPkz6MOnDLJ7QhymttXZ7q0IIIYQQXkpuOwohhBBC\nuJEUX0IIIYQQbiTFlxBCCCGEG0nxJYQQQgjhRlJ8CSGEEEK4kU98fHy83SHE5Tt06BCDBw8mJCSk\nzHwqCxYsYOnSpXTu3Nkl7Tz55JO0aNGiXB4PP1Nubi6jR49m4cKF1KhRg3r16jn3TZo0iY8++ojE\nxESWLl3K4sWL+fXXX4mOjiYgIOCy20xJSSEuLo6+ffuyZMkStmzZQosWLc57/LJly0hOTqZJkyaX\n3aYQQvow6cO8k8zzVQkopfj0009p2bIlkZGRdse5Yrt37yYrK4sJEyacc3/fvn257bbbnF/PnDmT\nDz/8kKFDh7qk/ZtuuulPj0lKSiIqKsol7Qnh7aQPkz7M20jxVQn4+fnRr18/xo8fT0JCAg5H2W/r\npEmTiIqKcv6wn/71k08+yXXXXcemTZs4fvw4d955J0lJSaSmpuLj48Pw4cOd7xS/++470tLSKCws\npF+/fs5ZtNevX89///tfioqK8Pf354EHHqBZs2bMmTOH5ORkjh49Sv369XnmmWfK5Fq3bh1ffvkl\npmkSGBjIgw8+SFBQEJMnTyYzM5MXX3yRhIQE/Pz8Lnj+0dHRzJo1C7De3TZp0oQ9e/Zwzz330KRJ\nEz766CMyMjIoLi6ma9eu9O/fH4AlS5awaNEigoKCynRCc+bM4fjx4zz88MOkp6czbdo0jh07hlKK\nAQMG4HA4WL9+PZs3b8bPz4/Y2FhmzpzJli1bMAyDpk2b8uCDDxIYGHhWnqysLL7//nscDge+vr4M\nGTKkzLtiIbyR9GHSh3kbKb4qif79+7NlyxY+++wzBg0adEl/t7CwkHHjxrFmzRrGjx/P2LFjadiw\nIePGjWPlypXOH3Q/Pz/Gjh1LZmYmw4cPp2nTpjgcDj7//HPi4+OpVq0ae/fuZcyYMbz//vsAHD58\nmHfeeeesGYT37dvHtGnTeOONNwgPD2fr1q3885//5L333uOxxx5j+vTpjBs37k+zFxQUkJiYSOvW\nrZ3boqKieP755wEYNWoUffv2pVOnThQUFPDmm28SERFBZGQkX3zxBePGjSM4OJipU6ee8/XHjx9P\nz549ufnmm53r5o0dO5ZOnToRFRVF7969mTNnDpmZmYwbNw7DMJgyZQqffvqpc2bn0jymaXL//fcz\nadIkatasSWJiIklJSdJxCYH0YdKHeRcpvioJwzB4+umnGT58+HnXtDqfa6+9FoDw8HCCg4Np2LCh\n8+ucnBzncbGxsQCEhITQtm1btmzZgo+PD1lZWYwePdp5nFKKAwcOANC0adNzLt2wdetW2rRp41wC\nIjo6mho1arBr164yC9Oey6JFi1i1ahVgLafRsmVL7r33Xuf+0rXU8vPz+e2338jJyWH27NnObbt3\n7+bIkSNcffXVBAcHO8/t119/LdNOTk4Ou3fvplevXgCEhoae8zbCpk2buOeee5zv1vv06VOm0y3N\nYxgGMTExvPbaa3To0IG2bduWWfxYCG8mfZj0Yd5Eiq9KJDQ0lEcffZRJkybRvXt35/YzO4KioqIy\nX/v6+jo/P/Ny/+lOXyFea43D4aC4uJjo6GjnuzSAjIwMQkJCWLdu3XkHkJ5rVSvTNCkuLr5gBjh7\nvMSZSts0TROAN954A39/fwCys7Px8/Nj6dKlZTKcq3M9/XxLpaenExoaesFz0VpTXFx8Vh6AZ555\nhj179rBlyxbmz5/P8uXLGT58+HnPRQhvIn2YRfqwyk+mmqhkunTpQrt27fjmm2+c26pXr05KSgpg\n/eAmJSVd1muvXLkSsDqmLVu2EB0dTXR0NJs3b2bfvn0AbNy4kRdffJGCgoILvlZ0dDS//vorBw8e\nBKx3kUeOHKFp06aXle1cgoKCaNq0KQsXLgTgxIkTxMXF8fPPP3P11VezefNmjhw5Uubczvz7jRo1\n4ocffgCs846LiyM3NxcfHx9n59S2bVuWLFlCUVERpmmyePFi2rRpc9brZWdn8/jjj1OtWjX69u3L\nXXfdRVpamsvOV4jKQPqwU6QPq7zkylclNHjw4DKdU+/evZkwYQLPPvssYWFhtGrV6rJet7CwkBEj\nRlBUVMTgwYOdTyUNGTKE9957D7DeaQ0fPvxPH5muV68ejzzyCG+//TamaeLn58eIESMICgq6rGzn\n88wzzzB9+nSGDh1KUVER1113Hddffz0A999/P6NHjyYwMPC8j1s/++yzfPjhhyxevBiAf/zjHwQH\nB9OuXTumT58OwIABA5g5cybDhw+nuLiYJk2a8NBDD531WtWrV6d///6MHj0aPz8/fHx8+Mc//uHS\n8xWiMpA+7BTpwyonpc917VQIIYQQQpQLue0ohBBCCOFGUnwJIYQQQriRFF9CCCGEEG4kxZcQQggh\nhBtJ8SWEEEII4UZSfAkhhBBCuJEUX0IIIYQQbiTFlxBCCCGEG/1/f/hqnuYwtYgAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1383cc780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plots to compare validation set and cross-validation\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 6))\n",
    "ax1 = plt.subplot(121)\n",
    "plt.plot(range(1, len(features)+1), mean_rss_valset)\n",
    "plt.title('Validation Set Approach')\n",
    "plt.xlabel('Number of Predictors')\n",
    "plt.ylabel('Lowest RSS')\n",
    "ax2 = plt.subplot(122)\n",
    "plt.plot(range(1, len(features)+1), mean_rss_cv)\n",
    "plt.title('Cross-Validation Approach')\n",
    "plt.xlabel('Number of Predictors')\n",
    "plt.ylabel('Mean of Lowest RSS')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab2'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Lab 2: Ridge Regression and the Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.6.1'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.6.1 Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 6 columns):\n",
      "League_A       263 non-null uint8\n",
      "League_N       263 non-null uint8\n",
      "Division_E     263 non-null uint8\n",
      "Division_W     263 non-null uint8\n",
      "NewLeague_A    263 non-null uint8\n",
      "NewLeague_N    263 non-null uint8\n",
      "dtypes: uint8(6)\n",
      "memory usage: 3.6+ KB\n"
     ]
    }
   ],
   "source": [
    "# Generate dummy variables for qualitative variables\n",
    "qual_vars = ['League', 'Division', 'NewLeague']\n",
    "hitters_dummies = pd.get_dummies(hitters[qual_vars])\n",
    "hitters_dummies.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 19 columns):\n",
      "AtBat          263 non-null int32\n",
      "Hits           263 non-null int32\n",
      "HmRun          263 non-null int32\n",
      "Runs           263 non-null int32\n",
      "RBI            263 non-null int32\n",
      "Walks          263 non-null int32\n",
      "Years          263 non-null int32\n",
      "CAtBat         263 non-null int32\n",
      "CHits          263 non-null int32\n",
      "CHmRun         263 non-null int32\n",
      "CRuns          263 non-null int32\n",
      "CRBI           263 non-null int32\n",
      "CWalks         263 non-null int32\n",
      "PutOuts        263 non-null int32\n",
      "Assists        263 non-null int32\n",
      "Errors         263 non-null int32\n",
      "League_N       263 non-null uint8\n",
      "Division_W     263 non-null uint8\n",
      "NewLeague_N    263 non-null uint8\n",
      "dtypes: int32(16), uint8(3)\n",
      "memory usage: 19.3+ KB\n"
     ]
    }
   ],
   "source": [
    "# Define X, y features and reponse data for scikit-learn\n",
    "dummy_vars = ['League_N', 'Division_W', 'NewLeague_N']\n",
    "response = 'Salary'\n",
    "y = hitters[response]\n",
    "# Drop response and qualitative variables, and combine with dummy data frame\n",
    "X = pd.concat([hitters.drop(qual_vars + [response], axis=1), hitters_dummies[dummy_vars]], axis=1)\n",
    "features = hitters.columns.drop([response])\n",
    "X.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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HRxMVFUVUVBShoaFoNJoARvz7SUIghBBC/ExxcTH79+8nNTXV1wWg0+lo3749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\nt9xyC/39/bz5zW/esIpsFFHnfWyiQW79RG21Pja6nTzPY3p6msnJSSY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RiGw5IiIiIk4C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1386c2b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ridge regression on full dataset, over 100 alphas from 10 to -2\n",
    "alphas = 10**np.linspace(10,-2,100)\n",
    "ridge = Ridge()\n",
    "coefs = []\n",
    "for alpha in alphas:\n",
    "    ridge.set_params(alpha=alpha*0.5)  # alpha/2 to align with R\n",
    "    ridge.fit(scale(X), y)\n",
    "    coefs.append(ridge.coef_)\n",
    "# Plot\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "plt.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "plt.xlim(1e10, 1e-2)  # reverse axis\n",
    "plt.xlabel('Regularization Parameter')\n",
    "plt.ylabel('Coefficients')\n",
    "plt.title('Ridge regression coefficients vs. regularization parameter.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Split Hitters data into train and test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Fit on training set with alpha = 4**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ridge regression coefficients:\n",
      " AtBat         0.098658\n",
      "Hits          0.446094\n",
      "HmRun         1.412107\n",
      "Runs          0.660773\n",
      "RBI           0.843403\n",
      "Walks         1.008473\n",
      "Years         2.779882\n",
      "CAtBat        0.008244\n",
      "CHits         0.034149\n",
      "CHmRun        0.268634\n",
      "CRuns         0.070407\n",
      "CRBI          0.070060\n",
      "CWalks        0.082795\n",
      "League        0.104747\n",
      "Division     -0.003739\n",
      "PutOuts       0.268363\n",
      "Assists       4.241051\n",
      "Errors      -30.768885\n",
      "NewLeague     4.123474\n",
      "dtype: float64\n",
      "\n",
      "MSE =  106216.52238\n"
     ]
    }
   ],
   "source": [
    "ridge_a4 = Ridge(alpha=4, normalize=True)\n",
    "ridge_a4.fit(X_train, y_train)\n",
    "y_pred_a4 = ridge_a4.predict(X_test)\n",
    "print('\\nRidge regression coefficients:\\n', pd.Series(ridge_a4.coef_, index=features))\n",
    "print('\\nMSE = ', mean_squared_error(y_test, y_pred_a4))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Fit on training set with alpha = 10<sup>10</sup>**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ridge regression coefficients:\n",
      " AtBat        1.317464e-10\n",
      "Hits         4.647486e-10\n",
      "HmRun        2.079865e-09\n",
      "Runs         7.726175e-10\n",
      "RBI          9.390640e-10\n",
      "Walks        9.769219e-10\n",
      "Years        3.961442e-09\n",
      "CAtBat       1.060533e-11\n",
      "CHits        3.993605e-11\n",
      "CHmRun       2.959428e-10\n",
      "CRuns        8.245247e-11\n",
      "CRBI         7.795451e-11\n",
      "CWalks       9.894387e-11\n",
      "League       7.268991e-11\n",
      "Division    -2.615885e-12\n",
      "PutOuts      2.084514e-10\n",
      "Assists     -2.501281e-09\n",
      "Errors      -1.549951e-08\n",
      "NewLeague   -2.023196e-09\n",
      "dtype: float64\n",
      "\n",
      "MSE =  172862.235804\n"
     ]
    }
   ],
   "source": [
    "ridge_a1e10 = Ridge(alpha=10**10, normalize=True)\n",
    "ridge_a1e10.fit(X_train, y_train)\n",
    "y_pred_a1e10 = ridge_a1e10.predict(X_test)\n",
    "print('\\nRidge regression coefficients:\\n', pd.Series(ridge_a1e10.coef_, index=features))\n",
    "print('\\nMSE = ', mean_squared_error(y_test, y_pred_a1e10))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Ridge regularization with cross-validation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best ridge regularization Alpha =  0.574878497699\n",
      "MSE =  99825.6489629\n"
     ]
    }
   ],
   "source": [
    "# Ridge regularization with cross-validation\n",
    "ridgecv = RidgeCV(alphas=alphas*0.5, scoring='neg_mean_squared_error', normalize=True)\n",
    "ridgecv.fit(X_train, y_train)\n",
    "print(\"The best ridge regularization Alpha = \", ridgecv.alpha_)\n",
    "ridge_cv = Ridge(alpha=ridgecv.alpha_, normalize=True)\n",
    "ridge_cv.fit(X_train, y_train)\n",
    "mse = mean_squared_error(y_test, ridge_cv.predict(X_test))\n",
    "print(\"MSE = \", mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Ridge regression on full data set with CV-optimized alpha**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AtBat         0.055838\n",
      "Hits          0.934879\n",
      "HmRun         0.369048\n",
      "Runs          1.092480\n",
      "RBI           0.878259\n",
      "Walks         1.717770\n",
      "Years         0.783515\n",
      "CAtBat        0.011318\n",
      "CHits         0.061101\n",
      "CHmRun        0.428333\n",
      "CRuns         0.121418\n",
      "CRBI          0.129351\n",
      "CWalks        0.041990\n",
      "League        0.179957\n",
      "Division      0.035737\n",
      "PutOuts      -1.597699\n",
      "Assists      24.774519\n",
      "Errors      -85.948661\n",
      "NewLeague     8.336918\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "ridge_cv.fit(X, y)\n",
    "print(pd.Series(ridge_cv.coef_, index=features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**As expected, none of the coefficients are exactly zero - ridge regression does not perform variable selection!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.6.2'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.6.2 The Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Lasso regression on training set, over 100 alphas from 10 to -2.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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Lli39bVlWVsbx48eZMWOG/1ISlF9+CQoKIj8/n9zc3IA2Cw8PD9ju8zFs2DB+/vlnFi1a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\nSSD/H6UGkBaZrhsDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14094c438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso = Lasso(max_iter=10000, normalize=True)\n",
    "coefs = []\n",
    "for alpha in alphas:\n",
    "    lasso.set_params(alpha=alpha)\n",
    "    lasso.fit(scale(X_train), y_train)\n",
    "    coefs.append(lasso.coef_)\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])\n",
    "plt.xlabel('Regularization Parameter')\n",
    "plt.ylabel('Regression Coefficients')\n",
    "plt.title('Lasso regression coefficients vs. regularization parameter.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Lasso regularization with cross-validation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best Lasso regularization Alpha =  0.574878497699\n",
      "MSE =  104960.658539\n"
     ]
    }
   ],
   "source": [
    "lassocv = LassoCV(alphas=None, cv=10, max_iter=100000, normalize=True)\n",
    "lassocv.fit(X_train, y_train)\n",
    "print(\"The best Lasso regularization Alpha = \", ridgecv.alpha_)\n",
    "lasso_cv = Lasso(max_iter=10000, normalize=True, alpha=lassocv.alpha_)\n",
    "lasso_cv.fit(X_train, y_train)\n",
    "mse = mean_squared_error(y_test, lasso_cv.predict(X_test))\n",
    "print(\"MSE = \", mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat         0.000000\n",
       "Hits          1.082446\n",
       "HmRun         0.000000\n",
       "Runs          0.000000\n",
       "RBI           0.000000\n",
       "Walks         2.906388\n",
       "Years         0.000000\n",
       "CAtBat        0.000000\n",
       "CHits         0.000000\n",
       "CHmRun        0.219367\n",
       "CRuns         0.000000\n",
       "CRBI          0.513975\n",
       "CWalks        0.000000\n",
       "League        0.368401\n",
       "Division     -0.000000\n",
       "PutOuts      -0.000000\n",
       "Assists       0.000000\n",
       "Errors      -89.064338\n",
       "NewLeague     0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(lasso_cv.coef_, index=features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "**Some coefficients are set to exact 0 by Lasso.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='lab3'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Lab 3: PCR and PLS Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.7.1'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.7.1 Principal Components Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sahpe of loading matrix: (19, 19)\n",
      "\n",
      "Head of loading matrix:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.198290</td>\n",
       "      <td>-0.383784</td>\n",
       "      <td>0.088626</td>\n",
       "      <td>0.031967</td>\n",
       "      <td>0.028117</td>\n",
       "      <td>-0.070646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.195861</td>\n",
       "      <td>-0.377271</td>\n",
       "      <td>0.074032</td>\n",
       "      <td>0.017982</td>\n",
       "      <td>-0.004652</td>\n",
       "      <td>-0.082240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.204369</td>\n",
       "      <td>-0.237136</td>\n",
       "      <td>-0.216186</td>\n",
       "      <td>-0.235831</td>\n",
       "      <td>0.077660</td>\n",
       "      <td>-0.149646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.198337</td>\n",
       "      <td>-0.377721</td>\n",
       "      <td>-0.017166</td>\n",
       "      <td>-0.049942</td>\n",
       "      <td>-0.038536</td>\n",
       "      <td>-0.136660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.235174</td>\n",
       "      <td>-0.314531</td>\n",
       "      <td>-0.073085</td>\n",
       "      <td>-0.138985</td>\n",
       "      <td>0.024299</td>\n",
       "      <td>-0.111675</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5\n",
       "0  0.198290 -0.383784  0.088626  0.031967  0.028117 -0.070646\n",
       "1  0.195861 -0.377271  0.074032  0.017982 -0.004652 -0.082240\n",
       "2  0.204369 -0.237136 -0.216186 -0.235831  0.077660 -0.149646\n",
       "3  0.198337 -0.377721 -0.017166 -0.049942 -0.038536 -0.136660\n",
       "4  0.235174 -0.314531 -0.073085 -0.138985  0.024299 -0.111675"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "X_reduced = pca.fit_transform(scale(X))\n",
    "print(\"The sahpe of loading matrix:\", pca.components_.shape)\n",
    "print(\"\\nHead of loading matrix:\")\n",
    "display(pd.DataFrame(pca.components_.T).loc[:4,:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9tg6BgXkYOrQqLl4s/eoBL688rF59BxrNs/11npmZiSpVqgAo/MBevnw5hBBw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1383b82b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PCR with number of PCs from 0 to 19, with 10-fold CV\n",
    "# For 0 PC case, regression on intercept only.\n",
    "kf = KFold(n_splits=10, shuffle=True, random_state=1)\n",
    "regr = LinearRegression()\n",
    "mse = []\n",
    "for n_pc in range(0, pca.n_components_ + 1):\n",
    "    if n_pc == 0:\n",
    "        X_regr = np.ones((len(y),1))\n",
    "    else:\n",
    "        X_regr = X_reduced[:, :n_pc]\n",
    "    scores = cross_val_score(regr, X_regr, y, cv=kf, scoring='neg_mean_squared_error')\n",
    "    mse.append(scores.mean() * (-1))\n",
    "\n",
    "# Find the n_pc with lowest MSE, or highest CV score\n",
    "min_mse = min(mse)\n",
    "min_mse_idx = mse.index(min_mse)    \n",
    "    \n",
    "# Plot MSE vs. number of PCs\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.plot(mse)\n",
    "plt.xticks(range(20), range(20))\n",
    "min_mse_marker, = plt.plot(min_mse_idx, min_mse, 'b*', markersize=15)\n",
    "plt.xlabel('Number of Principal Components')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Principal Component Regression with 10-Fold Cross-Validation')\n",
    "plt.legend([min_mse_marker], ['Best number of principal components'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "From the plot we also see that the cross-validation error is roughly the same when only one component is included in the model. This suggests that a model that uses just a small number of components might suffice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Ratio:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0     38.31 %\n",
       "1     60.15 %\n",
       "2     70.84 %\n",
       "3     79.03 %\n",
       "4     84.29 %\n",
       "5     88.63 %\n",
       "6     92.26 %\n",
       "7     94.96 %\n",
       "8     96.28 %\n",
       "9     97.25 %\n",
       "10    97.97 %\n",
       "11    98.64 %\n",
       "12    99.14 %\n",
       "13    99.46 %\n",
       "14    99.73 %\n",
       "15    99.88 %\n",
       "16    99.95 %\n",
       "17    99.98 %\n",
       "18    99.99 %\n",
       "dtype: object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evr = np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)\n",
    "print(\"Explained Variance Ratio:\")\n",
    "display(pd.Series([str(p) + ' %' for p in evr]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "PCR on training data and evaluate its test set performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VqlRB3759MXnyZPj7++d5gqAw48ePx++//47Zs2dj8eLFmDdvHubMmYNhw4Yh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x141d77978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=1)\n",
    "X_train_reduced = pca.fit_transform(scale(X_train))\n",
    "\n",
    "# PCR on training set with number of PCs from 0 to 19, with 10-fold CV\n",
    "# For 0 PC case, regression on intercept only.\n",
    "kf = KFold(n_splits=10, shuffle=True, random_state=1)\n",
    "regr = LinearRegression()\n",
    "mse = []\n",
    "for n_pc in range(0, pca.n_components_ + 1):\n",
    "    if n_pc == 0:\n",
    "        X_regr = np.ones((len(y_train),1))\n",
    "    else:\n",
    "        X_regr = X_train_reduced[:, :n_pc]\n",
    "    scores = cross_val_score(regr, X_regr, y_train, cv=kf, scoring='neg_mean_squared_error')\n",
    "    mse.append(scores.mean() * (-1))\n",
    "\n",
    "# Find the n_pc with lowest MSE, or highest CV score\n",
    "min_mse = min(mse)\n",
    "min_mse_idx = mse.index(min_mse)    \n",
    "    \n",
    "# Plot MSE vs. number of PCs\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.plot(mse)\n",
    "plt.xticks(range(20), range(20))\n",
    "min_mse_marker, = plt.plot(min_mse_idx, min_mse, 'b*', markersize=15)\n",
    "plt.xlabel('Number of Principal Components')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Principal Component Regression on Training Set with 10-Fold Cross-Validation')\n",
    "plt.legend([min_mse_marker], ['Best number of principal components'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "The lowest cross-validation error occurs when 6 components are used. Next perform PCR on the test data and compute the test MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set MSE =  111994.422736\n"
     ]
    }
   ],
   "source": [
    "X_test_reduced = pca.transform(scale(X_test))[:,:7]\n",
    "\n",
    "# Train regression model on training data \n",
    "regr = LinearRegression()\n",
    "regr.fit(X_train_reduced[:,:7], y_train)\n",
    "\n",
    "# Prediction with test data\n",
    "y_pred = regr.predict(X_test_reduced)\n",
    "print(\"Test set MSE = \", mean_squared_error(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "<a id='lab-6.7.2'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### Lab 6.7.2 Partial Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5U0id9DQq56qt0xFVQGmLDFXkAkS1a9c2/9ygQQMmTZrEvHnzeOqpp+jatSt/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\nQeHhWVcMErwwuDAsLMuJmQkhhLgZSctAEfT22ylXPe7tra/5OyGEECK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KlKFRo0Zs2bKF\nWrVqUbZs2dzHqFKlSnz//feAtTX5Bx98wMaNG6ldu/YN3SdCFAYpBoQoRP7+/nTu3JmYmBiaNm2a\ne/zyD9fs7OxLfnZ3d8/9/9/tl35xU7rWGofDQU5ODhEREbzxxhu5vztx4gRlypRh/fr119zT4Gor\nlZumSU5OznX3bL98zMCNSExMZPfu3bRs2ZIGDRrQoEEDnnnmGXr16kV8fPwV36Avz+9aYwouvn2m\nadKhQwfq1asHQEZGBpmZmVf92yNHjuDv73/VmFfbFEprnfu4XdxtcvFj26xZMxo0aEB8fDxbtmxh\n4cKFjB49+pJCRwhnkKmFQhSyO++8k7p16/Lll1/mHvPz8+PXX38FIDk5mcTExDzFvvAN9MSJEyQk\nJBAREUFERATx8fEcPnwYsHZC692793W3PI6IiGDr1q388ccfgNVScPLkSapVq5an3K7Hz8+PRYsW\nXXLbT58+TUZGBiEhIZecGxISgtaaTZs2AdaYiBvZLS4yMpLly5eTnZ2NaZq8//77zJ07Fx8fHypX\nrswPP/wAWPffgAEDSEtLw83NjZycnEviBAcH43A4WLduHWDtpLlu3brr7irXv39/9u/fz3333cdL\nL73EuXPnLmnZEcJZpGVACCfo2LHjJR96LVq0YOLEiXTv3p2AgABq1qyZp7hZWVm8+eabZGdn07Fj\nx9yZCy+99BLjxo0DrG/Qffr0ue4uhxUqVODFF19k9OjRmKaJh4cHb775pi3fYidOnEhMTEzuzw8/\n/DDt2rWjd+/ezJs3j5MnT+Lu7o6Pjw9dunS5YgaGw+Ggd+/exMbGMm/ePEJDQylVqtR1r/vkk08y\ne/Zs+vTpkzuA8ML4je7duzN9+nSWL18OQJcuXShdujR169ZlxowZV71+XFwcCxcuJCcnh9atWxMR\nEZG7PfPVtGvXjri4OObPn49SijZt2hAQEHDD95sQBUV2LRRCCCFcnHQTCCGEEC5OigEhhBDCxUkx\nIIQQQrg4KQaEEEIIFyfFgBBCCOHipBgQQgghXJwUA0IIIYSLk2JACCGEcHH/D8vrPfMv7KopAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14fe68b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kf = KFold(n_splits=10, shuffle=True, random_state=1)\n",
    "mse = []\n",
    "for i in range(1, 20):\n",
    "    pls = PLSRegression(n_components=i)\n",
    "    scores = cross_val_score(pls, scale(X_train), y_train, cv=kf, scoring='neg_mean_squared_error')\n",
    "    mse.append(scores.mean() * (-1))\n",
    "\n",
    "# Find the number of PLS directions with lowest MSE, or highest CV score\n",
    "min_mse = min(mse)\n",
    "min_mse_idx = mse.index(min_mse) + 1\n",
    "\n",
    "# Plot MSE vs. number of PLS directions\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.plot(range(1, 20), mse)\n",
    "plt.xticks(range(20), range(20))\n",
    "min_mse_marker, = plt.plot(min_mse_idx, min_mse, 'b*', markersize=15)\n",
    "plt.xlabel('Number of PLS directions')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('PLS on Training Set with 10-Fold Cross-Validation')\n",
    "plt.legend([min_mse_marker], ['Best number of PLS directions'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "The lowest MSE occurs with 2 PLS directions, which is now used for evaluating on test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "autoscroll": "json-false",
    "collapsed": false,
    "ein.tags": [
     "worksheet-0"
    ],
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104711.20627773694"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pls = PLSRegression(n_components=2)\n",
    "pls.fit(scale(X_train), y_train)\n",
    "\n",
    "mean_squared_error(y_test, pls.predict(scale(X_test)))"
   ]
  }
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