models_and_prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pprint import pprint\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import datetime as dt\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.dates as mdates\n",
    "import matplotlib.ticker as tkr\n",
    "import seaborn as sns\n",
    "import pickle\n",
    "\n",
    "# sklearn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import ElasticNet\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import ShuffleSplit\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 333 entries, 0 to 339\n",
      "Data columns (total 20 columns):\n",
      "FINAL_POSITION               333 non-null int64\n",
      "TEAM                         333 non-null object\n",
      "FINAL_POINTS                 333 non-null int64\n",
      "SEASON                       333 non-null object\n",
      "WAGE                         333 non-null float64\n",
      "WAGE_SCALED                  333 non-null float64\n",
      "NET_TRANSFER_SPEND           333 non-null float64\n",
      "NET_TRANSFER_SPEND_SCALED    333 non-null float64\n",
      "SQUAD_SIZE                   333 non-null int64\n",
      "AVG_AGE                      333 non-null float64\n",
      "NUM_FOREIGN_PLAYERS          333 non-null int64\n",
      "TEAM_MARKET_VALUE            333 non-null float64\n",
      "IS_ESTIMATED_MARKET_VAL      333 non-null float64\n",
      "TEAM_MARKET_VALUE_SCALED     333 non-null float64\n",
      "AVG_TIME                     333 non-null float64\n",
      "NUM_TRANSFERS_IN             333 non-null int64\n",
      "NUM_TRANSFERS_OUT            333 non-null int64\n",
      "STADIUM_CAPACITY_SCALED      333 non-null float64\n",
      "YEARS_IN_LEAGUE              333 non-null int64\n",
      "BIG_SIX                      333 non-null int64\n",
      "dtypes: float64(10), int64(8), object(2)\n",
      "memory usage: 54.6+ KB\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('data/complete_data.csv')\n",
    "df.dropna(axis=0, how='any', inplace=True)\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Drop unnecessary columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.drop(['WAGE','NET_TRANSFER_SPEND','FINAL_POSITION','IS_ESTIMATED_MARKET_VAL',\n",
    "         'TEAM_MARKET_VALUE'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM</th>\n",
       "      <th>FINAL_POINTS</th>\n",
       "      <th>SEASON</th>\n",
       "      <th>WAGE_SCALED</th>\n",
       "      <th>NET_TRANSFER_SPEND_SCALED</th>\n",
       "      <th>SQUAD_SIZE</th>\n",
       "      <th>AVG_AGE</th>\n",
       "      <th>NUM_FOREIGN_PLAYERS</th>\n",
       "      <th>TEAM_MARKET_VALUE_SCALED</th>\n",
       "      <th>AVG_TIME</th>\n",
       "      <th>NUM_TRANSFERS_IN</th>\n",
       "      <th>NUM_TRANSFERS_OUT</th>\n",
       "      <th>STADIUM_CAPACITY_SCALED</th>\n",
       "      <th>YEARS_IN_LEAGUE</th>\n",
       "      <th>BIG_SIX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Manchester United</td>\n",
       "      <td>80</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.832770</td>\n",
       "      <td>0.130414</td>\n",
       "      <td>34</td>\n",
       "      <td>24.9</td>\n",
       "      <td>18</td>\n",
       "      <td>1.381676</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>6.350441</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>70</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.077580</td>\n",
       "      <td>-0.370820</td>\n",
       "      <td>33</td>\n",
       "      <td>25.3</td>\n",
       "      <td>22</td>\n",
       "      <td>0.888269</td>\n",
       "      <td>4.1</td>\n",
       "      <td>8</td>\n",
       "      <td>12</td>\n",
       "      <td>3.175220</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Liverpool</td>\n",
       "      <td>69</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.748860</td>\n",
       "      <td>1.280492</td>\n",
       "      <td>30</td>\n",
       "      <td>24.5</td>\n",
       "      <td>21</td>\n",
       "      <td>1.135322</td>\n",
       "      <td>2.4</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>4.595714</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Leeds United</td>\n",
       "      <td>68</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.245400</td>\n",
       "      <td>2.939685</td>\n",
       "      <td>36</td>\n",
       "      <td>22.5</td>\n",
       "      <td>22</td>\n",
       "      <td>0.846926</td>\n",
       "      <td>2.9</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>3.091662</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Ipswich Town</td>\n",
       "      <td>66</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>-0.852348</td>\n",
       "      <td>0.365445</td>\n",
       "      <td>27</td>\n",
       "      <td>24.8</td>\n",
       "      <td>11</td>\n",
       "      <td>0.157233</td>\n",
       "      <td>2.3</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2.506753</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                TEAM  FINAL_POINTS   SEASON  WAGE_SCALED  \\\n",
       "0  Manchester United            80  2000-01     1.832770   \n",
       "1            Arsenal            70  2000-01     1.077580   \n",
       "2          Liverpool            69  2000-01     1.748860   \n",
       "3       Leeds United            68  2000-01     1.245400   \n",
       "4       Ipswich Town            66  2000-01    -0.852348   \n",
       "\n",
       "   NET_TRANSFER_SPEND_SCALED  SQUAD_SIZE  AVG_AGE  NUM_FOREIGN_PLAYERS  \\\n",
       "0                   0.130414          34     24.9                   18   \n",
       "1                  -0.370820          33     25.3                   22   \n",
       "2                   1.280492          30     24.5                   21   \n",
       "3                   2.939685          36     22.5                   22   \n",
       "4                   0.365445          27     24.8                   11   \n",
       "\n",
       "   TEAM_MARKET_VALUE_SCALED  AVG_TIME  NUM_TRANSFERS_IN  NUM_TRANSFERS_OUT  \\\n",
       "0                  1.381676       4.5                 1                  8   \n",
       "1                  0.888269       4.1                 8                 12   \n",
       "2                  1.135322       2.4                10                 10   \n",
       "3                  0.846926       2.9                 8                  8   \n",
       "4                  0.157233       2.3                 6                  7   \n",
       "\n",
       "   STADIUM_CAPACITY_SCALED  YEARS_IN_LEAGUE  BIG_SIX  \n",
       "0                 6.350441                9        1  \n",
       "1                 3.175220                9        1  \n",
       "2                 4.595714                9        1  \n",
       "3                 3.091662                9        0  \n",
       "4                 2.506753                1        0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create holdout set of 2016-17 season data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "holdout = df[df['SEASON'] == '2016-17']\n",
    "holdout = holdout.drop('SEASON', axis=1)\n",
    "sample = df[df['SEASON'] != '2016-17']\n",
    "sample = sample.drop('SEASON', axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Split X and y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = sample['FINAL_POINTS']\n",
    "log_y = np.log(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = sample.drop(['FINAL_POINTS','TEAM'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cross_validate = ShuffleSplit(n_splits=5, test_size=0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(250, 12)\n",
      "(250,)\n",
      "(63, 12)\n",
      "(63,)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create model pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models = {}\n",
    "models['lin_reg'] = LinearRegression()\n",
    "models['lasso_reg_1'] = Lasso(alpha = 0.001)\n",
    "models['lasso_reg_2'] = Lasso(alpha = 0.01)\n",
    "models['lasso_reg_3'] = Lasso(alpha = 0.1)\n",
    "models['lasso_reg_4'] = Lasso(alpha = 1)\n",
    "models['ridge_reg_1'] = Ridge(alpha = 0.001)\n",
    "models['ridge_reg_2'] = Ridge(alpha = 0.01)\n",
    "models['ridge_reg_3'] = Ridge(alpha = 0.1)\n",
    "models['ridge_reg_4'] = Ridge(alpha = 1)\n",
    "models['elastic_reg_1'] = ElasticNet(alpha = 0.001)\n",
    "models['elastic_reg_2'] = ElasticNet(alpha = 0.01)\n",
    "models['elastic_reg_3'] = ElasticNet(alpha = 0.1)\n",
    "models['elastic_reg_4'] = ElasticNet(alpha = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['WAGE_SCALED', 'NET_TRANSFER_SPEND_SCALED', 'SQUAD_SIZE', 'AVG_AGE',\n",
       "       'NUM_FOREIGN_PLAYERS', 'TEAM_MARKET_VALUE_SCALED', 'AVG_TIME',\n",
       "       'NUM_TRANSFERS_IN', 'NUM_TRANSFERS_OUT', 'STADIUM_CAPACITY_SCALED',\n",
       "       'YEARS_IN_LEAGUE', 'BIG_SIX'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_names = X.columns\n",
    "feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_performance = []\n",
    "\n",
    "for name, model in models.items():\n",
    "    model_features = []\n",
    "    scores = cross_val_score(model, X, y, cv=cross_validate, scoring = 'neg_mean_squared_error')\n",
    "    score_mean = np.mean(scores)\n",
    "    model.fit(X_train, y_train)\n",
    "    \n",
    "    sorted_features = sorted(zip(feature_names, model.coef_), key=lambda tup: abs(tup[1]), reverse=True)\n",
    "    \n",
    "    for feature in sorted_features:\n",
    "        model_features.append(feature)\n",
    "    \n",
    "    model_info = {\n",
    "        'model': name,\n",
    "        'avg_score': str(-score_mean),\n",
    "        'test_score': str(model.score(X_test, y_test)),\n",
    "        'features': model_features\n",
    "    }\n",
    "    \n",
    "    model_performance.append(model_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'avg_score': '97.010760335',\n",
      " 'features': [('WAGE_SCALED', 9.1325327096903077),\n",
      "              ('BIG_SIX', 5.8652552698764895),\n",
      "              ('AVG_TIME', 2.8970144000845579),\n",
      "              ('AVG_AGE', -1.4914950578450015),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1404764479010163),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84819528985323689),\n",
      "              ('SQUAD_SIZE', -0.57965489894086097),\n",
      "              ('NUM_TRANSFERS_IN', -0.41108365937482361),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17506969286613194),\n",
      "              ('YEARS_IN_LEAGUE', 0.052794858238451425),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.046458316888671303),\n",
      "              ('NUM_TRANSFERS_OUT', -0.034330316969465313)],\n",
      " 'model': 'lin_reg',\n",
      " 'test_score': '0.629055175493'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0118353119',\n",
      " 'features': [('WAGE_SCALED', 9.1265484006878239),\n",
      "              ('BIG_SIX', 5.8511556663381512),\n",
      "              ('AVG_TIME', 2.8921480284272736),\n",
      "              ('AVG_AGE', -1.490846516255693),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1353039879388531),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84565956670921227),\n",
      "              ('SQUAD_SIZE', -0.58006484524920277),\n",
      "              ('NUM_TRANSFERS_IN', -0.41084395548540958),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17482731800343271),\n",
      "              ('YEARS_IN_LEAGUE', 0.052452564191195233),\n",
      "              ('NUM_TRANSFERS_OUT', -0.034552604078569145),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.032211590097250352)],\n",
      " 'model': 'lasso_reg_1',\n",
      " 'test_score': '0.629179315204'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0237076111',\n",
      " 'features': [('WAGE_SCALED', 9.11598453133821),\n",
      "              ('BIG_SIX', 5.7620037897195084),\n",
      "              ('AVG_TIME', 2.8434531110298704),\n",
      "              ('AVG_AGE', -1.4762897420865502),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.0914677517811726),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.83504882669297809),\n",
      "              ('SQUAD_SIZE', -0.58003125845198744),\n",
      "              ('NUM_TRANSFERS_IN', -0.41104296132353474),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17390175695797946),\n",
      "              ('YEARS_IN_LEAGUE', 0.053395431006790846),\n",
      "              ('NUM_TRANSFERS_OUT', -0.035391197129578174),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0)],\n",
      " 'model': 'lasso_reg_2',\n",
      " 'test_score': '0.629712841285'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.3542266022',\n",
      " 'features': [('WAGE_SCALED', 9.1545117606547759),\n",
      "              ('BIG_SIX', 5.0004511684685857),\n",
      "              ('AVG_TIME', 2.3379340681839031),\n",
      "              ('AVG_AGE', -1.3007330454298314),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.76995034950175667),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.66234813516913149),\n",
      "              ('SQUAD_SIZE', -0.56724767913797325),\n",
      "              ('NUM_TRANSFERS_IN', -0.42103010987813849),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.16886188880166636),\n",
      "              ('YEARS_IN_LEAGUE', 0.076419148109220722),\n",
      "              ('NUM_TRANSFERS_OUT', -0.039948172711948539),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0)],\n",
      " 'model': 'lasso_reg_3',\n",
      " 'test_score': '0.632637356382'}\n",
      "\n",
      "\n",
      "{'avg_score': '103.121351715',\n",
      " 'features': [('WAGE_SCALED', 10.058135668390712),\n",
      "              ('NUM_TRANSFERS_IN', -0.51556231852634027),\n",
      "              ('SQUAD_SIZE', -0.42452513007365361),\n",
      "              ('AVG_AGE', -0.40046238765885506),\n",
      "              ('YEARS_IN_LEAGUE', 0.29358541598182669),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.25962601300013582),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.089632978357102905),\n",
      "              ('NUM_TRANSFERS_OUT', -0.00026639023074604405),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0),\n",
      "              ('AVG_TIME', 0.0),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('BIG_SIX', 0.0)],\n",
      " 'model': 'lasso_reg_4',\n",
      " 'test_score': '0.628098322517'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0108271365',\n",
      " 'features': [('WAGE_SCALED', 9.1323931113780823),\n",
      "              ('BIG_SIX', 5.8650119971263646),\n",
      "              ('AVG_TIME', 2.89698594861864),\n",
      "              ('AVG_AGE', -1.4915042386403405),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1404105481893179),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84819890511206164),\n",
      "              ('SQUAD_SIZE', -0.5796641095727304),\n",
      "              ('NUM_TRANSFERS_IN', -0.4110835825096405),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17507221922128466),\n",
      "              ('YEARS_IN_LEAGUE', 0.052792794477280303),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.046267266816435414),\n",
      "              ('NUM_TRANSFERS_OUT', -0.034331540895514233)],\n",
      " 'model': 'ridge_reg_1',\n",
      " 'test_score': '0.629055970715'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.011428838',\n",
      " 'features': [('WAGE_SCALED', 9.1311370416237594),\n",
      "              ('BIG_SIX', 5.8628239172773373),\n",
      "              ('AVG_TIME', 2.8967298290688928),\n",
      "              ('AVG_AGE', -1.4915867361135213),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1398175997792763),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84823150701318939),\n",
      "              ('SQUAD_SIZE', -0.57974696117465407),\n",
      "              ('NUM_TRANSFERS_IN', -0.41108291910587375),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17509495719795037),\n",
      "              ('YEARS_IN_LEAGUE', 0.052774249498359051),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.044548769203382091),\n",
      "              ('NUM_TRANSFERS_OUT', -0.03434255188837497)],\n",
      " 'model': 'ridge_reg_2',\n",
      " 'test_score': '0.629063121396'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.017493527',\n",
      " 'features': [('WAGE_SCALED', 9.1186074632929),\n",
      "              ('BIG_SIX', 5.8410783449953971),\n",
      "              ('AVG_TIME', 2.8941631331169284),\n",
      "              ('AVG_AGE', -1.4923989628432324),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1339028204000554),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84856387233903408),\n",
      "              ('SQUAD_SIZE', -0.58057113594250931),\n",
      "              ('NUM_TRANSFERS_IN', -0.41107907357992879),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17532241269710955),\n",
      "              ('YEARS_IN_LEAGUE', 0.052591641679328803),\n",
      "              ('NUM_TRANSFERS_OUT', -0.034452232598506813),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.02745764862729367)],\n",
      " 'model': 'ridge_reg_3',\n",
      " 'test_score': '0.62913400702'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0823661477',\n",
      " 'features': [('WAGE_SCALED', 8.9963525533798361),\n",
      "              ('BIG_SIX', 5.6363118053053771),\n",
      "              ('AVG_TIME', 2.8680194468255094),\n",
      "              ('AVG_AGE', -1.4993316402812631),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.0761814691441882),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.85247853231048265),\n",
      "              ('SQUAD_SIZE', -0.58840067507310545),\n",
      "              ('NUM_TRANSFERS_IN', -0.41129941099659528),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17760311713188595),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.13453699128204663),\n",
      "              ('YEARS_IN_LEAGUE', 0.051034305295794745),\n",
      "              ('NUM_TRANSFERS_OUT', -0.035506755939629479)],\n",
      " 'model': 'ridge_reg_4',\n",
      " 'test_score': '0.629784415364'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0197581695',\n",
      " 'features': [('WAGE_SCALED', 9.1121565492384775),\n",
      "              ('BIG_SIX', 5.8280780934971768),\n",
      "              ('AVG_TIME', 2.8910214481307568),\n",
      "              ('AVG_AGE', -1.4922940493466954),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.1296857963834481),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.84739505824248484),\n",
      "              ('SQUAD_SIZE', -0.58100235088041741),\n",
      "              ('NUM_TRANSFERS_IN', -0.41095990731812421),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17526493944220692),\n",
      "              ('YEARS_IN_LEAGUE', 0.052371668995987268),\n",
      "              ('NUM_TRANSFERS_OUT', -0.034593201551962022),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', -0.015653320271288945)],\n",
      " 'model': 'elastic_reg_1',\n",
      " 'test_score': '0.629215155579'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.110128399',\n",
      " 'features': [('WAGE_SCALED', 8.9670099574416415),\n",
      "              ('BIG_SIX', 5.545132901674469),\n",
      "              ('AVG_TIME', 2.833082988786976),\n",
      "              ('AVG_AGE', -1.4908371384693897),\n",
      "              ('STADIUM_CAPACITY_SCALED', -1.0373952434839786),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.85076135724807245),\n",
      "              ('SQUAD_SIZE', -0.58955870294740331),\n",
      "              ('NUM_TRANSFERS_IN', -0.41209169894865583),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.17802493189539936),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.17208329915434728),\n",
      "              ('YEARS_IN_LEAGUE', 0.052123612725601939),\n",
      "              ('NUM_TRANSFERS_OUT', -0.035975667515995305)],\n",
      " 'model': 'elastic_reg_2',\n",
      " 'test_score': '0.63010505866'}\n",
      "\n",
      "\n",
      "{'avg_score': '98.290075116',\n",
      " 'features': [('WAGE_SCALED', 7.803339673870231),\n",
      "              ('BIG_SIX', 3.892034643154088),\n",
      "              ('AVG_TIME', 2.3111356750054606),\n",
      "              ('AVG_AGE', -1.3990432353398117),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 1.2845542598807476),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.9193346761907214),\n",
      "              ('SQUAD_SIZE', -0.63962210855541757),\n",
      "              ('NUM_TRANSFERS_IN', -0.43843489078480286),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.30755146045029647),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.20425004377065328),\n",
      "              ('YEARS_IN_LEAGUE', 0.068210023218220214),\n",
      "              ('NUM_TRANSFERS_OUT', -0.04496811917311655)],\n",
      " 'model': 'elastic_reg_3',\n",
      " 'test_score': '0.633893375107'}\n",
      "\n",
      "\n",
      "{'avg_score': '111.538747781',\n",
      " 'features': [('WAGE_SCALED', 4.2736958297082426),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 1.8161845821850864),\n",
      "              ('BIG_SIX', 1.2863091729757397),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 1.2735893682478063),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.847177100172116),\n",
      "              ('AVG_TIME', 0.77898222068376288),\n",
      "              ('AVG_AGE', -0.72680324924073225),\n",
      "              ('NUM_TRANSFERS_IN', -0.6403843691742902),\n",
      "              ('SQUAD_SIZE', -0.63226661406513107),\n",
      "              ('YEARS_IN_LEAGUE', 0.36798568888929595),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.32157860065546101),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0045186757954844801)],\n",
      " 'model': 'elastic_reg_4',\n",
      " 'test_score': '0.602940664364'}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for model in model_performance:\n",
    "    pprint(model)\n",
    "    print('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, log_y, train_size=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "models = {}\n",
    "models['lin_reg'] = LinearRegression()\n",
    "models['lasso_reg_1'] = Lasso(alpha = 0.001)\n",
    "models['lasso_reg_2'] = Lasso(alpha = 0.01)\n",
    "models['lasso_reg_3'] = Lasso(alpha = 0.1)\n",
    "models['lasso_reg_4'] = Lasso(alpha = 1)\n",
    "models['ridge_reg_1'] = Ridge(alpha = 0.001)\n",
    "models['ridge_reg_2'] = Ridge(alpha = 0.01)\n",
    "models['ridge_reg_3'] = Ridge(alpha = 0.1)\n",
    "models['ridge_reg_4'] = Ridge(alpha = 1)\n",
    "models['elastic_reg_1'] = ElasticNet(alpha = 0.001)\n",
    "models['elastic_reg_2'] = ElasticNet(alpha = 0.01)\n",
    "models['elastic_reg_3'] = ElasticNet(alpha = 0.1)\n",
    "models['elastic_reg_4'] = ElasticNet(alpha = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_performance = []\n",
    "\n",
    "for name, model in models.items():\n",
    "    model_features = []\n",
    "    scores = cross_val_score(model, X, y, cv=cross_validate, scoring = 'neg_mean_squared_error')\n",
    "    score_mean = np.mean(scores)\n",
    "    model.fit(X_train, y_train)\n",
    "    \n",
    "    sorted_features = sorted(zip(feature_names, model.coef_), key=lambda tup: abs(tup[1]), reverse=True)\n",
    "    \n",
    "    for feature in sorted_features:\n",
    "        model_features.append(feature)\n",
    "    \n",
    "    model_info = {\n",
    "        'model': name,\n",
    "        'avg_score': str(-score_mean),\n",
    "        'test_score': str(model.score(X_test, y_test)),\n",
    "        'features': model_features\n",
    "    }\n",
    "    \n",
    "    model_performance.append(model_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'avg_score': '97.010760335',\n",
      " 'features': [('WAGE_SCALED', 0.13438502634054292),\n",
      "              ('BIG_SIX', 0.1010513458069599),\n",
      "              ('AVG_TIME', 0.067806810789744848),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.036734777583364173),\n",
      "              ('AVG_AGE', -0.025078534877570419),\n",
      "              ('SQUAD_SIZE', -0.013956390587662147),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.013095365660712538),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.012177862287912934),\n",
      "              ('NUM_TRANSFERS_IN', -0.0062735980171665755),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035838605402129971),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016671410430220621),\n",
      "              ('YEARS_IN_LEAGUE', -0.0014642215858221147)],\n",
      " 'model': 'lin_reg',\n",
      " 'test_score': '0.536211888228'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0118353119',\n",
      " 'features': [('WAGE_SCALED', 0.13566191726315449),\n",
      "              ('BIG_SIX', 0.091710225104974188),\n",
      "              ('AVG_TIME', 0.061478738037588014),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.035613799071331068),\n",
      "              ('AVG_AGE', -0.022883312483578298),\n",
      "              ('SQUAD_SIZE', -0.013763534609251666),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.012421216617962649),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.0071116988463034202),\n",
      "              ('NUM_TRANSFERS_IN', -0.0064703215634296729),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035518703274936472),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016324548617444447),\n",
      "              ('YEARS_IN_LEAGUE', -0.0010972685524373532)],\n",
      " 'model': 'lasso_reg_1',\n",
      " 'test_score': '0.536608249551'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0237076111',\n",
      " 'features': [('WAGE_SCALED', 0.15904052370215288),\n",
      "              ('AVG_TIME', 0.029799724374462308),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.028529354074566911),\n",
      "              ('BIG_SIX', 0.01978831085330646),\n",
      "              ('AVG_AGE', -0.014468534123520487),\n",
      "              ('SQUAD_SIZE', -0.012199559916433513),\n",
      "              ('NUM_TRANSFERS_IN', -0.0079505908692819264),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.0068785657611687484),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0029197292373425525),\n",
      "              ('YEARS_IN_LEAGUE', 0.0014700946943727853),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0010930979977581971),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0)],\n",
      " 'model': 'lasso_reg_2',\n",
      " 'test_score': '0.54200858185'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.3542266022',\n",
      " 'features': [('WAGE_SCALED', 0.068441844946034877),\n",
      "              ('YEARS_IN_LEAGUE', 0.013464253634044058),\n",
      "              ('NUM_TRANSFERS_IN', -0.008671221288722988),\n",
      "              ('SQUAD_SIZE', -0.0044793942127979731),\n",
      "              ('NUM_FOREIGN_PLAYERS', 2.3959742585719921e-05),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.0),\n",
      "              ('AVG_AGE', -0.0),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0),\n",
      "              ('AVG_TIME', 0.0),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('BIG_SIX', 0.0)],\n",
      " 'model': 'lasso_reg_3',\n",
      " 'test_score': '0.491228665191'}\n",
      "\n",
      "\n",
      "{'avg_score': '103.121351715',\n",
      " 'features': [('YEARS_IN_LEAGUE', 0.0013214014047206284),\n",
      "              ('WAGE_SCALED', 0.0),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.0),\n",
      "              ('SQUAD_SIZE', -0.0),\n",
      "              ('AVG_AGE', -0.0),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0),\n",
      "              ('AVG_TIME', 0.0),\n",
      "              ('NUM_TRANSFERS_IN', -0.0),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('BIG_SIX', 0.0)],\n",
      " 'model': 'lasso_reg_4',\n",
      " 'test_score': '0.0269262332132'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0108271365',\n",
      " 'features': [('WAGE_SCALED', 0.13438383418085925),\n",
      "              ('BIG_SIX', 0.10104722321862733),\n",
      "              ('AVG_TIME', 0.067805706135319541),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.036736543757086348),\n",
      "              ('AVG_AGE', -0.025078543983667156),\n",
      "              ('SQUAD_SIZE', -0.013956484678330052),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.013095475488574303),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.012176735950284002),\n",
      "              ('NUM_TRANSFERS_IN', -0.0062736666890225142),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035839154495407154),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016671195618122123),\n",
      "              ('YEARS_IN_LEAGUE', -0.0014641936415612543)],\n",
      " 'model': 'ridge_reg_1',\n",
      " 'test_score': '0.536211198441'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.011428838',\n",
      " 'features': [('WAGE_SCALED', 0.134373104975574),\n",
      "              ('BIG_SIX', 0.10101014368820989),\n",
      "              ('AVG_TIME', 0.06779576565403593),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.036752429307011614),\n",
      "              ('AVG_AGE', -0.025078624479046276),\n",
      "              ('SQUAD_SIZE', -0.013957330995293902),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.013096464811300793),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.012166601742602172),\n",
      "              ('NUM_TRANSFERS_IN', -0.0062742849950481357),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035844096122914829),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016669263382454746),\n",
      "              ('YEARS_IN_LEAGUE', -0.0014639418441292631)],\n",
      " 'model': 'ridge_reg_2',\n",
      " 'test_score': '0.536204993224'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.017493527',\n",
      " 'features': [('WAGE_SCALED', 0.13426583719951679),\n",
      "              ('BIG_SIX', 0.10064168528824886),\n",
      "              ('AVG_TIME', 0.067696500536844006),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.036910299022855246),\n",
      "              ('AVG_AGE', -0.025079286132661881),\n",
      "              ('SQUAD_SIZE', -0.013965745050461489),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.01310644363104967),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.012065538876133973),\n",
      "              ('NUM_TRANSFERS_IN', -0.0062804934575746854),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035893491386297148),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016650046398915981),\n",
      "              ('YEARS_IN_LEAGUE', -0.0014613944749588346)],\n",
      " 'model': 'ridge_reg_3',\n",
      " 'test_score': '0.536143223441'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0823661477',\n",
      " 'features': [('WAGE_SCALED', 0.13319678194438911),\n",
      "              ('BIG_SIX', 0.097176021543759844),\n",
      "              ('AVG_TIME', 0.066718028223548165),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.038395664250539009),\n",
      "              ('AVG_AGE', -0.025072683213921362),\n",
      "              ('SQUAD_SIZE', -0.014045248234667353),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.013214105319781415),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.011081826454819824),\n",
      "              ('NUM_TRANSFERS_IN', -0.0063448665240764908),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0036385318264786121),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016467600655050735),\n",
      "              ('YEARS_IN_LEAGUE', -0.001433182640412351)],\n",
      " 'model': 'ridge_reg_4',\n",
      " 'test_score': '0.535552280029'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.0197581695',\n",
      " 'features': [('WAGE_SCALED', 0.13487342905556862),\n",
      "              ('BIG_SIX', 0.095913187511990738),\n",
      "              ('AVG_TIME', 0.064511114999129912),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.036377823286018914),\n",
      "              ('AVG_AGE', -0.02398095777045417),\n",
      "              ('SQUAD_SIZE', -0.013870658769031817),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.01277438035521958),\n",
      "              ('STADIUM_CAPACITY_SCALED', -0.0095136586189523142),\n",
      "              ('NUM_TRANSFERS_IN', -0.0063809020541284412),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0035745992264167243),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0016473030232146311),\n",
      "              ('YEARS_IN_LEAGUE', -0.0012769209843952916)],\n",
      " 'model': 'elastic_reg_1',\n",
      " 'test_score': '0.536385647911'}\n",
      "\n",
      "\n",
      "{'avg_score': '97.110128399',\n",
      " 'features': [('WAGE_SCALED', 0.14263438057178363),\n",
      "              ('BIG_SIX', 0.056893710991113178),\n",
      "              ('AVG_TIME', 0.045104416961298542),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.034736288577307067),\n",
      "              ('AVG_AGE', -0.018478407039170783),\n",
      "              ('SQUAD_SIZE', -0.013182249540334237),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.01002014599411636),\n",
      "              ('NUM_TRANSFERS_IN', -0.0072117692419139843),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0033633801252768414),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0013971075427214985),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('YEARS_IN_LEAGUE', 0.0)],\n",
      " 'model': 'elastic_reg_2',\n",
      " 'test_score': '0.538268110664'}\n",
      "\n",
      "\n",
      "{'avg_score': '98.290075116',\n",
      " 'features': [('WAGE_SCALED', 0.12826373915822542),\n",
      "              ('NUM_TRANSFERS_IN', -0.010128591896460688),\n",
      "              ('YEARS_IN_LEAGUE', 0.0091043571143242553),\n",
      "              ('SQUAD_SIZE', -0.0077379435112630603),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0019599068134813131),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.0),\n",
      "              ('AVG_AGE', -0.0),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0),\n",
      "              ('AVG_TIME', 0.0),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('BIG_SIX', 0.0)],\n",
      " 'model': 'elastic_reg_3',\n",
      " 'test_score': '0.543973409141'}\n",
      "\n",
      "\n",
      "{'avg_score': '111.538747781',\n",
      " 'features': [('YEARS_IN_LEAGUE', 0.011725669900683926),\n",
      "              ('WAGE_SCALED', 0.0),\n",
      "              ('NET_TRANSFER_SPEND_SCALED', 0.0),\n",
      "              ('SQUAD_SIZE', -0.0),\n",
      "              ('AVG_AGE', -0.0),\n",
      "              ('NUM_FOREIGN_PLAYERS', 0.0),\n",
      "              ('TEAM_MARKET_VALUE_SCALED', 0.0),\n",
      "              ('AVG_TIME', 0.0),\n",
      "              ('NUM_TRANSFERS_IN', -0.0),\n",
      "              ('NUM_TRANSFERS_OUT', -0.0),\n",
      "              ('STADIUM_CAPACITY_SCALED', 0.0),\n",
      "              ('BIG_SIX', 0.0)],\n",
      " 'model': 'elastic_reg_4',\n",
      " 'test_score': '0.250873294646'}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for model in model_performance:\n",
    "    pprint(model)\n",
    "    print('\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>FINAL_POINTS</td>   <th>  R-squared:         </th> <td>   0.685</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.673</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   54.45</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 11 Jun 2017</td> <th>  Prob (F-statistic):</th> <td>5.06e-68</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:53:51</td>     <th>  Log-Likelihood:    </th> <td> -1138.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   2303.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   300</td>      <th>  BIC:               </th> <td>   2352.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    12</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "              <td></td>                 <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                 <td>   86.2303</td> <td>   17.542</td> <td>    4.916</td> <td> 0.000</td> <td>   51.710   120.751</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WAGE_SCALED</th>               <td>    8.3606</td> <td>    1.258</td> <td>    6.648</td> <td> 0.000</td> <td>    5.886    10.835</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NET_TRANSFER_SPEND_SCALED</th> <td>    0.2406</td> <td>    0.630</td> <td>    0.382</td> <td> 0.703</td> <td>   -1.000     1.481</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SQUAD_SIZE</th>                <td>   -0.4879</td> <td>    0.157</td> <td>   -3.108</td> <td> 0.002</td> <td>   -0.797    -0.179</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_AGE</th>                   <td>   -0.9650</td> <td>    0.610</td> <td>   -1.582</td> <td> 0.115</td> <td>   -2.165     0.235</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_FOREIGN_PLAYERS</th>       <td>    0.0734</td> <td>    0.147</td> <td>    0.499</td> <td> 0.618</td> <td>   -0.216     0.362</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_TIME</th>                  <td>    2.5184</td> <td>    1.231</td> <td>    2.046</td> <td> 0.042</td> <td>    0.096     4.940</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_IN</th>          <td>   -0.3747</td> <td>    0.224</td> <td>   -1.675</td> <td> 0.095</td> <td>   -0.815     0.066</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_OUT</th>         <td>   -0.0523</td> <td>    0.164</td> <td>   -0.319</td> <td> 0.750</td> <td>   -0.375     0.270</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>STADIUM_CAPACITY_SCALED</th>   <td>   -0.6482</td> <td>    0.752</td> <td>   -0.862</td> <td> 0.389</td> <td>   -2.128     0.832</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>YEARS_IN_LEAGUE</th>           <td>    0.0069</td> <td>    0.127</td> <td>    0.054</td> <td> 0.957</td> <td>   -0.243     0.257</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TEAM_MARKET_VALUE_SCALED</th>  <td>    1.2370</td> <td>    1.418</td> <td>    0.872</td> <td> 0.384</td> <td>   -1.553     4.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BIG_SIX</th>                   <td>    6.5856</td> <td>    2.071</td> <td>    3.179</td> <td> 0.002</td> <td>    2.509    10.662</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 6.038</td> <th>  Durbin-Watson:     </th> <td>   1.682</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.049</td> <th>  Jarque-Bera (JB):  </th> <td>   8.477</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.090</td> <th>  Prob(JB):          </th> <td>  0.0144</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.786</td> <th>  Cond. No.          </th> <td>1.66e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           FINAL_POINTS   R-squared:                       0.685\n",
       "Model:                            OLS   Adj. R-squared:                  0.673\n",
       "Method:                 Least Squares   F-statistic:                     54.45\n",
       "Date:                Sun, 11 Jun 2017   Prob (F-statistic):           5.06e-68\n",
       "Time:                        10:53:51   Log-Likelihood:                -1138.5\n",
       "No. Observations:                 313   AIC:                             2303.\n",
       "Df Residuals:                     300   BIC:                             2352.\n",
       "Df Model:                          12                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=============================================================================================\n",
       "                                coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "---------------------------------------------------------------------------------------------\n",
       "Intercept                    86.2303     17.542      4.916      0.000        51.710   120.751\n",
       "WAGE_SCALED                   8.3606      1.258      6.648      0.000         5.886    10.835\n",
       "NET_TRANSFER_SPEND_SCALED     0.2406      0.630      0.382      0.703        -1.000     1.481\n",
       "SQUAD_SIZE                   -0.4879      0.157     -3.108      0.002        -0.797    -0.179\n",
       "AVG_AGE                      -0.9650      0.610     -1.582      0.115        -2.165     0.235\n",
       "NUM_FOREIGN_PLAYERS           0.0734      0.147      0.499      0.618        -0.216     0.362\n",
       "AVG_TIME                      2.5184      1.231      2.046      0.042         0.096     4.940\n",
       "NUM_TRANSFERS_IN             -0.3747      0.224     -1.675      0.095        -0.815     0.066\n",
       "NUM_TRANSFERS_OUT            -0.0523      0.164     -0.319      0.750        -0.375     0.270\n",
       "STADIUM_CAPACITY_SCALED      -0.6482      0.752     -0.862      0.389        -2.128     0.832\n",
       "YEARS_IN_LEAGUE               0.0069      0.127      0.054      0.957        -0.243     0.257\n",
       "TEAM_MARKET_VALUE_SCALED      1.2370      1.418      0.872      0.384        -1.553     4.028\n",
       "BIG_SIX                       6.5856      2.071      3.179      0.002         2.509    10.662\n",
       "==============================================================================\n",
       "Omnibus:                        6.038   Durbin-Watson:                   1.682\n",
       "Prob(Omnibus):                  0.049   Jarque-Bera (JB):                8.477\n",
       "Skew:                           0.090   Prob(JB):                       0.0144\n",
       "Kurtosis:                       3.786   Cond. No.                     1.66e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.66e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = smf.ols('FINAL_POINTS ~ WAGE_SCALED + NET_TRANSFER_SPEND_SCALED + SQUAD_SIZE + \\\n",
    "              AVG_AGE + NUM_FOREIGN_PLAYERS + AVG_TIME + NUM_TRANSFERS_IN + NUM_TRANSFERS_OUT + \\\n",
    "              STADIUM_CAPACITY_SCALED + YEARS_IN_LEAGUE + TEAM_MARKET_VALUE_SCALED + BIG_SIX', data=sample)\n",
    "lm_fit = lm.fit()\n",
    "lm_fit.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Amend YEARS_IN_LEAGUE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['FIRST_SEASON'] = df['YEARS_IN_LEAGUE'].map(lambda x: 1 if x == 1 else 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "holdout = df[df['SEASON'] == '2016-17']\n",
    "holdout = holdout.drop('SEASON', axis=1)\n",
    "sample = df[df['SEASON'] != '2016-17']\n",
    "sample = sample.drop('SEASON', axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM</th>\n",
       "      <th>FINAL_POINTS</th>\n",
       "      <th>SEASON</th>\n",
       "      <th>WAGE_SCALED</th>\n",
       "      <th>NET_TRANSFER_SPEND_SCALED</th>\n",
       "      <th>SQUAD_SIZE</th>\n",
       "      <th>AVG_AGE</th>\n",
       "      <th>NUM_FOREIGN_PLAYERS</th>\n",
       "      <th>TEAM_MARKET_VALUE_SCALED</th>\n",
       "      <th>AVG_TIME</th>\n",
       "      <th>NUM_TRANSFERS_IN</th>\n",
       "      <th>NUM_TRANSFERS_OUT</th>\n",
       "      <th>STADIUM_CAPACITY_SCALED</th>\n",
       "      <th>YEARS_IN_LEAGUE</th>\n",
       "      <th>BIG_SIX</th>\n",
       "      <th>FIRST_SEASON</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Manchester United</td>\n",
       "      <td>80</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.832770</td>\n",
       "      <td>0.130414</td>\n",
       "      <td>34</td>\n",
       "      <td>24.9</td>\n",
       "      <td>18</td>\n",
       "      <td>1.381676</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>6.350441</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>70</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.077580</td>\n",
       "      <td>-0.370820</td>\n",
       "      <td>33</td>\n",
       "      <td>25.3</td>\n",
       "      <td>22</td>\n",
       "      <td>0.888269</td>\n",
       "      <td>4.1</td>\n",
       "      <td>8</td>\n",
       "      <td>12</td>\n",
       "      <td>3.175220</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Liverpool</td>\n",
       "      <td>69</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.748860</td>\n",
       "      <td>1.280492</td>\n",
       "      <td>30</td>\n",
       "      <td>24.5</td>\n",
       "      <td>21</td>\n",
       "      <td>1.135322</td>\n",
       "      <td>2.4</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>4.595714</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Leeds United</td>\n",
       "      <td>68</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>1.245400</td>\n",
       "      <td>2.939685</td>\n",
       "      <td>36</td>\n",
       "      <td>22.5</td>\n",
       "      <td>22</td>\n",
       "      <td>0.846926</td>\n",
       "      <td>2.9</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>3.091662</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Ipswich Town</td>\n",
       "      <td>66</td>\n",
       "      <td>2000-01</td>\n",
       "      <td>-0.852348</td>\n",
       "      <td>0.365445</td>\n",
       "      <td>27</td>\n",
       "      <td>24.8</td>\n",
       "      <td>11</td>\n",
       "      <td>0.157233</td>\n",
       "      <td>2.3</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2.506753</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                TEAM  FINAL_POINTS   SEASON  WAGE_SCALED  \\\n",
       "0  Manchester United            80  2000-01     1.832770   \n",
       "1            Arsenal            70  2000-01     1.077580   \n",
       "2          Liverpool            69  2000-01     1.748860   \n",
       "3       Leeds United            68  2000-01     1.245400   \n",
       "4       Ipswich Town            66  2000-01    -0.852348   \n",
       "\n",
       "   NET_TRANSFER_SPEND_SCALED  SQUAD_SIZE  AVG_AGE  NUM_FOREIGN_PLAYERS  \\\n",
       "0                   0.130414          34     24.9                   18   \n",
       "1                  -0.370820          33     25.3                   22   \n",
       "2                   1.280492          30     24.5                   21   \n",
       "3                   2.939685          36     22.5                   22   \n",
       "4                   0.365445          27     24.8                   11   \n",
       "\n",
       "   TEAM_MARKET_VALUE_SCALED  AVG_TIME  NUM_TRANSFERS_IN  NUM_TRANSFERS_OUT  \\\n",
       "0                  1.381676       4.5                 1                  8   \n",
       "1                  0.888269       4.1                 8                 12   \n",
       "2                  1.135322       2.4                10                 10   \n",
       "3                  0.846926       2.9                 8                  8   \n",
       "4                  0.157233       2.3                 6                  7   \n",
       "\n",
       "   STADIUM_CAPACITY_SCALED  YEARS_IN_LEAGUE  BIG_SIX  FIRST_SEASON  \n",
       "0                 6.350441                9        1             0  \n",
       "1                 3.175220                9        1             0  \n",
       "2                 4.595714                9        1             0  \n",
       "3                 3.091662                9        0             0  \n",
       "4                 2.506753                1        0             1  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>FINAL_POINTS</td>   <th>  R-squared:         </th> <td>   0.685</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.673</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   54.46</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 11 Jun 2017</td> <th>  Prob (F-statistic):</th> <td>5.04e-68</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:53:51</td>     <th>  Log-Likelihood:    </th> <td> -1138.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   2303.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   300</td>      <th>  BIC:               </th> <td>   2352.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    12</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "              <td></td>                 <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                 <td>   86.3968</td> <td>   16.946</td> <td>    5.098</td> <td> 0.000</td> <td>   53.049   119.745</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WAGE_SCALED</th>               <td>    8.3388</td> <td>    1.260</td> <td>    6.616</td> <td> 0.000</td> <td>    5.859    10.819</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NET_TRANSFER_SPEND_SCALED</th> <td>    0.2394</td> <td>    0.617</td> <td>    0.388</td> <td> 0.698</td> <td>   -0.976     1.455</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SQUAD_SIZE</th>                <td>   -0.4871</td> <td>    0.156</td> <td>   -3.113</td> <td> 0.002</td> <td>   -0.795    -0.179</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_AGE</th>                   <td>   -0.9715</td> <td>    0.586</td> <td>   -1.658</td> <td> 0.098</td> <td>   -2.125     0.182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_FOREIGN_PLAYERS</th>       <td>    0.0716</td> <td>    0.147</td> <td>    0.487</td> <td> 0.627</td> <td>   -0.218     0.361</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_TIME</th>                  <td>    2.5315</td> <td>    1.193</td> <td>    2.122</td> <td> 0.035</td> <td>    0.184     4.879</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_IN</th>          <td>   -0.3685</td> <td>    0.228</td> <td>   -1.614</td> <td> 0.108</td> <td>   -0.818     0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_OUT</th>         <td>   -0.0543</td> <td>    0.165</td> <td>   -0.330</td> <td> 0.741</td> <td>   -0.378     0.269</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>STADIUM_CAPACITY_SCALED</th>   <td>   -0.6475</td> <td>    0.750</td> <td>   -0.863</td> <td> 0.389</td> <td>   -2.124     0.829</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FIRST_SEASON</th>              <td>   -0.1875</td> <td>    1.727</td> <td>   -0.109</td> <td> 0.914</td> <td>   -3.587     3.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TEAM_MARKET_VALUE_SCALED</th>  <td>    1.2595</td> <td>    1.253</td> <td>    1.005</td> <td> 0.316</td> <td>   -1.207     3.726</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BIG_SIX</th>                   <td>    6.6084</td> <td>    2.085</td> <td>    3.170</td> <td> 0.002</td> <td>    2.506    10.711</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.953</td> <th>  Durbin-Watson:     </th> <td>   1.682</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.051</td> <th>  Jarque-Bera (JB):  </th> <td>   8.291</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.091</td> <th>  Prob(JB):          </th> <td>  0.0158</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.776</td> <th>  Cond. No.          </th> <td>1.57e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           FINAL_POINTS   R-squared:                       0.685\n",
       "Model:                            OLS   Adj. R-squared:                  0.673\n",
       "Method:                 Least Squares   F-statistic:                     54.46\n",
       "Date:                Sun, 11 Jun 2017   Prob (F-statistic):           5.04e-68\n",
       "Time:                        10:53:51   Log-Likelihood:                -1138.5\n",
       "No. Observations:                 313   AIC:                             2303.\n",
       "Df Residuals:                     300   BIC:                             2352.\n",
       "Df Model:                          12                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=============================================================================================\n",
       "                                coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "---------------------------------------------------------------------------------------------\n",
       "Intercept                    86.3968     16.946      5.098      0.000        53.049   119.745\n",
       "WAGE_SCALED                   8.3388      1.260      6.616      0.000         5.859    10.819\n",
       "NET_TRANSFER_SPEND_SCALED     0.2394      0.617      0.388      0.698        -0.976     1.455\n",
       "SQUAD_SIZE                   -0.4871      0.156     -3.113      0.002        -0.795    -0.179\n",
       "AVG_AGE                      -0.9715      0.586     -1.658      0.098        -2.125     0.182\n",
       "NUM_FOREIGN_PLAYERS           0.0716      0.147      0.487      0.627        -0.218     0.361\n",
       "AVG_TIME                      2.5315      1.193      2.122      0.035         0.184     4.879\n",
       "NUM_TRANSFERS_IN             -0.3685      0.228     -1.614      0.108        -0.818     0.081\n",
       "NUM_TRANSFERS_OUT            -0.0543      0.165     -0.330      0.741        -0.378     0.269\n",
       "STADIUM_CAPACITY_SCALED      -0.6475      0.750     -0.863      0.389        -2.124     0.829\n",
       "FIRST_SEASON                 -0.1875      1.727     -0.109      0.914        -3.587     3.212\n",
       "TEAM_MARKET_VALUE_SCALED      1.2595      1.253      1.005      0.316        -1.207     3.726\n",
       "BIG_SIX                       6.6084      2.085      3.170      0.002         2.506    10.711\n",
       "==============================================================================\n",
       "Omnibus:                        5.953   Durbin-Watson:                   1.682\n",
       "Prob(Omnibus):                  0.051   Jarque-Bera (JB):                8.291\n",
       "Skew:                           0.091   Prob(JB):                       0.0158\n",
       "Kurtosis:                       3.776   Cond. No.                     1.57e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.57e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = smf.ols('FINAL_POINTS ~ WAGE_SCALED + NET_TRANSFER_SPEND_SCALED + SQUAD_SIZE + \\\n",
    "              AVG_AGE + NUM_FOREIGN_PLAYERS + AVG_TIME + NUM_TRANSFERS_IN + NUM_TRANSFERS_OUT + \\\n",
    "              STADIUM_CAPACITY_SCALED + FIRST_SEASON + TEAM_MARKET_VALUE_SCALED + BIG_SIX', data=sample)\n",
    "lm2_fit = lm2.fit()\n",
    "lm2_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>FINAL_POINTS</td>   <th>  R-squared:         </th> <td>   0.684</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.675</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   72.96</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 11 Jun 2017</td> <th>  Prob (F-statistic):</th> <td>1.46e-70</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:53:51</td>     <th>  Log-Likelihood:    </th> <td> -1139.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   2298.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   303</td>      <th>  BIC:               </th> <td>   2336.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     9</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "              <td></td>                <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                <td>   80.9133</td> <td>   15.563</td> <td>    5.199</td> <td> 0.000</td> <td>   50.289   111.538</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WAGE_SCALED</th>              <td>    8.1840</td> <td>    1.204</td> <td>    6.796</td> <td> 0.000</td> <td>    5.814    10.554</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SQUAD_SIZE</th>               <td>   -0.4870</td> <td>    0.156</td> <td>   -3.129</td> <td> 0.002</td> <td>   -0.793    -0.181</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_AGE</th>                  <td>   -0.8227</td> <td>    0.547</td> <td>   -1.504</td> <td> 0.134</td> <td>   -1.899     0.254</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_FOREIGN_PLAYERS</th>      <td>    0.0719</td> <td>    0.144</td> <td>    0.498</td> <td> 0.619</td> <td>   -0.212     0.356</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_TIME</th>                 <td>    2.2182</td> <td>    1.097</td> <td>    2.023</td> <td> 0.044</td> <td>    0.060     4.376</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_IN</th>         <td>   -0.3604</td> <td>    0.207</td> <td>   -1.738</td> <td> 0.083</td> <td>   -0.768     0.048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FIRST_SEASON</th>             <td>   -0.0056</td> <td>    1.703</td> <td>   -0.003</td> <td> 0.997</td> <td>   -3.357     3.346</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TEAM_MARKET_VALUE_SCALED</th> <td>    1.3419</td> <td>    1.230</td> <td>    1.091</td> <td> 0.276</td> <td>   -1.079     3.763</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BIG_SIX</th>                  <td>    6.3349</td> <td>    2.060</td> <td>    3.075</td> <td> 0.002</td> <td>    2.281    10.389</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.680</td> <th>  Durbin-Watson:     </th> <td>   1.670</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.058</td> <th>  Jarque-Bera (JB):  </th> <td>   7.945</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.068</td> <th>  Prob(JB):          </th> <td>  0.0188</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.769</td> <th>  Cond. No.          </th> <td>1.41e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           FINAL_POINTS   R-squared:                       0.684\n",
       "Model:                            OLS   Adj. R-squared:                  0.675\n",
       "Method:                 Least Squares   F-statistic:                     72.96\n",
       "Date:                Sun, 11 Jun 2017   Prob (F-statistic):           1.46e-70\n",
       "Time:                        10:53:51   Log-Likelihood:                -1139.1\n",
       "No. Observations:                 313   AIC:                             2298.\n",
       "Df Residuals:                     303   BIC:                             2336.\n",
       "Df Model:                           9                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "============================================================================================\n",
       "                               coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "--------------------------------------------------------------------------------------------\n",
       "Intercept                   80.9133     15.563      5.199      0.000        50.289   111.538\n",
       "WAGE_SCALED                  8.1840      1.204      6.796      0.000         5.814    10.554\n",
       "SQUAD_SIZE                  -0.4870      0.156     -3.129      0.002        -0.793    -0.181\n",
       "AVG_AGE                     -0.8227      0.547     -1.504      0.134        -1.899     0.254\n",
       "NUM_FOREIGN_PLAYERS          0.0719      0.144      0.498      0.619        -0.212     0.356\n",
       "AVG_TIME                     2.2182      1.097      2.023      0.044         0.060     4.376\n",
       "NUM_TRANSFERS_IN            -0.3604      0.207     -1.738      0.083        -0.768     0.048\n",
       "FIRST_SEASON                -0.0056      1.703     -0.003      0.997        -3.357     3.346\n",
       "TEAM_MARKET_VALUE_SCALED     1.3419      1.230      1.091      0.276        -1.079     3.763\n",
       "BIG_SIX                      6.3349      2.060      3.075      0.002         2.281    10.389\n",
       "==============================================================================\n",
       "Omnibus:                        5.680   Durbin-Watson:                   1.670\n",
       "Prob(Omnibus):                  0.058   Jarque-Bera (JB):                7.945\n",
       "Skew:                           0.068   Prob(JB):                       0.0188\n",
       "Kurtosis:                       3.769   Cond. No.                     1.41e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.41e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm3 = smf.ols('FINAL_POINTS ~ WAGE_SCALED + SQUAD_SIZE + \\\n",
    "              AVG_AGE + NUM_FOREIGN_PLAYERS + AVG_TIME + NUM_TRANSFERS_IN + \\\n",
    "              FIRST_SEASON + TEAM_MARKET_VALUE_SCALED + BIG_SIX', data=sample)\n",
    "lm3_fit = lm3.fit()\n",
    "lm3_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>FINAL_POINTS</td>   <th>  R-squared:         </th> <td>   0.684</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.676</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   82.25</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 11 Jun 2017</td> <th>  Prob (F-statistic):</th> <td>1.76e-71</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:53:51</td>     <th>  Log-Likelihood:    </th> <td> -1139.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   2296.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   304</td>      <th>  BIC:               </th> <td>   2330.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     8</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "              <td></td>                <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                <td>   80.4230</td> <td>   15.512</td> <td>    5.184</td> <td> 0.000</td> <td>   49.898   110.948</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WAGE_SCALED</th>              <td>    8.2417</td> <td>    1.197</td> <td>    6.885</td> <td> 0.000</td> <td>    5.886    10.597</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SQUAD_SIZE</th>               <td>   -0.4457</td> <td>    0.132</td> <td>   -3.388</td> <td> 0.001</td> <td>   -0.705    -0.187</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_AGE</th>                  <td>   -0.7955</td> <td>    0.544</td> <td>   -1.464</td> <td> 0.144</td> <td>   -1.865     0.274</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_TIME</th>                 <td>    2.1500</td> <td>    1.087</td> <td>    1.978</td> <td> 0.049</td> <td>    0.012     4.288</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_IN</th>         <td>   -0.3554</td> <td>    0.207</td> <td>   -1.718</td> <td> 0.087</td> <td>   -0.762     0.052</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FIRST_SEASON</th>             <td>   -0.0764</td> <td>    1.695</td> <td>   -0.045</td> <td> 0.964</td> <td>   -3.412     3.259</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TEAM_MARKET_VALUE_SCALED</th> <td>    1.3997</td> <td>    1.223</td> <td>    1.144</td> <td> 0.253</td> <td>   -1.007     3.807</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BIG_SIX</th>                  <td>    6.3525</td> <td>    2.057</td> <td>    3.088</td> <td> 0.002</td> <td>    2.304    10.401</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.431</td> <th>  Durbin-Watson:     </th> <td>   1.661</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.066</td> <th>  Jarque-Bera (JB):  </th> <td>   7.457</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.066</td> <th>  Prob(JB):          </th> <td>  0.0240</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.745</td> <th>  Cond. No.          </th> <td>1.26e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           FINAL_POINTS   R-squared:                       0.684\n",
       "Model:                            OLS   Adj. R-squared:                  0.676\n",
       "Method:                 Least Squares   F-statistic:                     82.25\n",
       "Date:                Sun, 11 Jun 2017   Prob (F-statistic):           1.76e-71\n",
       "Time:                        10:53:51   Log-Likelihood:                -1139.2\n",
       "No. Observations:                 313   AIC:                             2296.\n",
       "Df Residuals:                     304   BIC:                             2330.\n",
       "Df Model:                           8                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "============================================================================================\n",
       "                               coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "--------------------------------------------------------------------------------------------\n",
       "Intercept                   80.4230     15.512      5.184      0.000        49.898   110.948\n",
       "WAGE_SCALED                  8.2417      1.197      6.885      0.000         5.886    10.597\n",
       "SQUAD_SIZE                  -0.4457      0.132     -3.388      0.001        -0.705    -0.187\n",
       "AVG_AGE                     -0.7955      0.544     -1.464      0.144        -1.865     0.274\n",
       "AVG_TIME                     2.1500      1.087      1.978      0.049         0.012     4.288\n",
       "NUM_TRANSFERS_IN            -0.3554      0.207     -1.718      0.087        -0.762     0.052\n",
       "FIRST_SEASON                -0.0764      1.695     -0.045      0.964        -3.412     3.259\n",
       "TEAM_MARKET_VALUE_SCALED     1.3997      1.223      1.144      0.253        -1.007     3.807\n",
       "BIG_SIX                      6.3525      2.057      3.088      0.002         2.304    10.401\n",
       "==============================================================================\n",
       "Omnibus:                        5.431   Durbin-Watson:                   1.661\n",
       "Prob(Omnibus):                  0.066   Jarque-Bera (JB):                7.457\n",
       "Skew:                           0.066   Prob(JB):                       0.0240\n",
       "Kurtosis:                       3.745   Cond. No.                     1.26e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.26e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm4 = smf.ols('FINAL_POINTS ~ WAGE_SCALED + SQUAD_SIZE + \\\n",
    "              AVG_AGE + AVG_TIME + NUM_TRANSFERS_IN + \\\n",
    "              FIRST_SEASON + TEAM_MARKET_VALUE_SCALED + BIG_SIX', data=sample)\n",
    "lm4_fit = lm4.fit()\n",
    "lm4_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>FINAL_POINTS</td>   <th>  R-squared:         </th> <td>   0.683</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.675</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   93.72</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 11 Jun 2017</td> <th>  Prob (F-statistic):</th> <td>3.35e-72</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:53:51</td>     <th>  Log-Likelihood:    </th> <td> -1139.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   313</td>      <th>  AIC:               </th> <td>   2296.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   305</td>      <th>  BIC:               </th> <td>   2326.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     7</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>   77.7542</td> <td>   15.344</td> <td>    5.067</td> <td> 0.000</td> <td>   47.561   107.947</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>WAGE_SCALED</th>      <td>    9.0734</td> <td>    0.952</td> <td>    9.534</td> <td> 0.000</td> <td>    7.201    10.946</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SQUAD_SIZE</th>       <td>   -0.3797</td> <td>    0.118</td> <td>   -3.209</td> <td> 0.001</td> <td>   -0.613    -0.147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_AGE</th>          <td>   -0.7290</td> <td>    0.541</td> <td>   -1.348</td> <td> 0.179</td> <td>   -1.793     0.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AVG_TIME</th>         <td>    2.2657</td> <td>    1.083</td> <td>    2.093</td> <td> 0.037</td> <td>    0.135     4.396</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NUM_TRANSFERS_IN</th> <td>   -0.3605</td> <td>    0.207</td> <td>   -1.743</td> <td> 0.082</td> <td>   -0.768     0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>FIRST_SEASON</th>     <td>   -0.2769</td> <td>    1.687</td> <td>   -0.164</td> <td> 0.870</td> <td>   -3.597     3.043</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>BIG_SIX</th>          <td>    7.0131</td> <td>    1.976</td> <td>    3.550</td> <td> 0.000</td> <td>    3.126    10.901</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.317</td> <th>  Durbin-Watson:     </th> <td>   1.661</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.070</td> <th>  Jarque-Bera (JB):  </th> <td>   6.926</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.100</td> <th>  Prob(JB):          </th> <td>  0.0313</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.701</td> <th>  Cond. No.          </th> <td>1.25e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:           FINAL_POINTS   R-squared:                       0.683\n",
       "Model:                            OLS   Adj. R-squared:                  0.675\n",
       "Method:                 Least Squares   F-statistic:                     93.72\n",
       "Date:                Sun, 11 Jun 2017   Prob (F-statistic):           3.35e-72\n",
       "Time:                        10:53:51   Log-Likelihood:                -1139.9\n",
       "No. Observations:                 313   AIC:                             2296.\n",
       "Df Residuals:                     305   BIC:                             2326.\n",
       "Df Model:                           7                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "====================================================================================\n",
       "                       coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------------\n",
       "Intercept           77.7542     15.344      5.067      0.000        47.561   107.947\n",
       "WAGE_SCALED          9.0734      0.952      9.534      0.000         7.201    10.946\n",
       "SQUAD_SIZE          -0.3797      0.118     -3.209      0.001        -0.613    -0.147\n",
       "AVG_AGE             -0.7290      0.541     -1.348      0.179        -1.793     0.335\n",
       "AVG_TIME             2.2657      1.083      2.093      0.037         0.135     4.396\n",
       "NUM_TRANSFERS_IN    -0.3605      0.207     -1.743      0.082        -0.768     0.047\n",
       "FIRST_SEASON        -0.2769      1.687     -0.164      0.870        -3.597     3.043\n",
       "BIG_SIX              7.0131      1.976      3.550      0.000         3.126    10.901\n",
       "==============================================================================\n",
       "Omnibus:                        5.317   Durbin-Watson:                   1.661\n",
       "Prob(Omnibus):                  0.070   Jarque-Bera (JB):                6.926\n",
       "Skew:                           0.100   Prob(JB):                       0.0313\n",
       "Kurtosis:                       3.701   Cond. No.                     1.25e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.25e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm5 = smf.ols('FINAL_POINTS ~ WAGE_SCALED + SQUAD_SIZE + \\\n",
    "              AVG_AGE + AVG_TIME + NUM_TRANSFERS_IN + \\\n",
    "              FIRST_SEASON + BIG_SIX', data=sample)\n",
    "lm5_fit = lm5.fit()\n",
    "lm5_fit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"final_model.pkl\", \"wb\") as output_file:\n",
    "    pickle.dump(lm5_fit, output_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with open(\"holdout.pkl\", \"wb\") as output_file:\n",
    "    pickle.dump(holdout, output_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM</th>\n",
       "      <th>FINAL_POINTS</th>\n",
       "      <th>WAGE_SCALED</th>\n",
       "      <th>NET_TRANSFER_SPEND_SCALED</th>\n",
       "      <th>SQUAD_SIZE</th>\n",
       "      <th>AVG_AGE</th>\n",
       "      <th>NUM_FOREIGN_PLAYERS</th>\n",
       "      <th>TEAM_MARKET_VALUE_SCALED</th>\n",
       "      <th>AVG_TIME</th>\n",
       "      <th>NUM_TRANSFERS_IN</th>\n",
       "      <th>NUM_TRANSFERS_OUT</th>\n",
       "      <th>STADIUM_CAPACITY_SCALED</th>\n",
       "      <th>YEARS_IN_LEAGUE</th>\n",
       "      <th>BIG_SIX</th>\n",
       "      <th>FIRST_SEASON</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>93</td>\n",
       "      <td>1.800705</td>\n",
       "      <td>0.723608</td>\n",
       "      <td>25</td>\n",
       "      <td>26.6</td>\n",
       "      <td>20</td>\n",
       "      <td>4.183895</td>\n",
       "      <td>3.6</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>3.425896</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>321</th>\n",
       "      <td>Tottenham Hotspur</td>\n",
       "      <td>86</td>\n",
       "      <td>0.363881</td>\n",
       "      <td>0.670245</td>\n",
       "      <td>24</td>\n",
       "      <td>25.2</td>\n",
       "      <td>16</td>\n",
       "      <td>3.485225</td>\n",
       "      <td>2.9</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3.008104</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>Manchester City</td>\n",
       "      <td>78</td>\n",
       "      <td>1.904607</td>\n",
       "      <td>3.842168</td>\n",
       "      <td>25</td>\n",
       "      <td>28.2</td>\n",
       "      <td>21</td>\n",
       "      <td>4.267166</td>\n",
       "      <td>3.2</td>\n",
       "      <td>12</td>\n",
       "      <td>6</td>\n",
       "      <td>4.595714</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>Liverpool</td>\n",
       "      <td>76</td>\n",
       "      <td>1.022920</td>\n",
       "      <td>-0.057633</td>\n",
       "      <td>28</td>\n",
       "      <td>25.6</td>\n",
       "      <td>17</td>\n",
       "      <td>3.023778</td>\n",
       "      <td>2.4</td>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>4.595714</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>75</td>\n",
       "      <td>1.540949</td>\n",
       "      <td>2.241265</td>\n",
       "      <td>28</td>\n",
       "      <td>27.1</td>\n",
       "      <td>21</td>\n",
       "      <td>4.001103</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5.013506</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  TEAM  FINAL_POINTS  WAGE_SCALED  NET_TRANSFER_SPEND_SCALED  \\\n",
       "320            Chelsea            93     1.800705                   0.723608   \n",
       "321  Tottenham Hotspur            86     0.363881                   0.670245   \n",
       "322    Manchester City            78     1.904607                   3.842168   \n",
       "323          Liverpool            76     1.022920                  -0.057633   \n",
       "324            Arsenal            75     1.540949                   2.241265   \n",
       "\n",
       "     SQUAD_SIZE  AVG_AGE  NUM_FOREIGN_PLAYERS  TEAM_MARKET_VALUE_SCALED  \\\n",
       "320          25     26.6                   20                  4.183895   \n",
       "321          24     25.2                   16                  3.485225   \n",
       "322          25     28.2                   21                  4.267166   \n",
       "323          28     25.6                   17                  3.023778   \n",
       "324          28     27.1                   21                  4.001103   \n",
       "\n",
       "     AVG_TIME  NUM_TRANSFERS_IN  NUM_TRANSFERS_OUT  STADIUM_CAPACITY_SCALED  \\\n",
       "320       3.6                 5                  9                 3.425896   \n",
       "321       2.9                 4                  5                 3.008104   \n",
       "322       3.2                12                  6                 4.595714   \n",
       "323       2.4                 6                 11                 4.595714   \n",
       "324       4.0                 5                  5                 5.013506   \n",
       "\n",
       "     YEARS_IN_LEAGUE  BIG_SIX  FIRST_SEASON  \n",
       "320               25        1             0  \n",
       "321               25        1             0  \n",
       "322               15        1             0  \n",
       "323               25        1             0  \n",
       "324               25        1             0  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "holdout.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "holdout.drop(['NET_TRANSFER_SPEND_SCALED','NUM_FOREIGN_PLAYERS','TEAM_MARKET_VALUE_SCALED',\n",
    "              'NUM_TRANSFERS_OUT','STADIUM_CAPACITY_SCALED','YEARS_IN_LEAGUE'], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['TEAM', 'FINAL_POINTS', 'WAGE_SCALED', 'SQUAD_SIZE', 'AVG_AGE',\n",
       "       'AVG_TIME', 'NUM_TRANSFERS_IN', 'BIG_SIX', 'FIRST_SEASON'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "holdout.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "holdout_X = holdout.drop('FINAL_POINTS', axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "holdout['PREDICTED_POINTS'] = lm5_fit.predict(holdout_X).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "actual_table = holdout[['TEAM','FINAL_POINTS']].sort_values(by='FINAL_POINTS', ascending=False)\n",
    "predicted_table = holdout[['TEAM','PREDICTED_POINTS']].sort_values(by='PREDICTED_POINTS', ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM</th>\n",
       "      <th>PREDICTED_POINTS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>Manchester United</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>Manchester City</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>Liverpool</td>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>321</th>\n",
       "      <td>Tottenham Hotspur</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>326</th>\n",
       "      <td>Everton</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>329</th>\n",
       "      <td>West Bromwich Albion</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>Stoke City</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331</th>\n",
       "      <td>Leicester City</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>West Ham United</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>328</th>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>327</th>\n",
       "      <td>Southampton</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>Swansea City</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>339</th>\n",
       "      <td>Sunderland</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>335</th>\n",
       "      <td>Burnley</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>336</th>\n",
       "      <td>Watford</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>337</th>\n",
       "      <td>Hull City</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>338</th>\n",
       "      <td>Middlesbrough</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     TEAM  PREDICTED_POINTS\n",
       "325     Manchester United                79\n",
       "320               Chelsea                78\n",
       "324               Arsenal                75\n",
       "322       Manchester City                74\n",
       "323             Liverpool                68\n",
       "321     Tottenham Hotspur                65\n",
       "326               Everton                50\n",
       "329  West Bromwich Albion                50\n",
       "332            Stoke City                49\n",
       "331        Leicester City                47\n",
       "330       West Ham United                46\n",
       "328           Bournemouth                44\n",
       "327           Southampton                44\n",
       "334          Swansea City                44\n",
       "339            Sunderland                44\n",
       "333        Crystal Palace                43\n",
       "335               Burnley                42\n",
       "336               Watford                38\n",
       "337             Hull City                38\n",
       "338         Middlesbrough                38"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predicted_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM</th>\n",
       "      <th>FINAL_POINTS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>321</th>\n",
       "      <td>Tottenham Hotspur</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>Manchester City</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>Liverpool</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>Manchester United</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>326</th>\n",
       "      <td>Everton</td>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>327</th>\n",
       "      <td>Southampton</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>328</th>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>West Ham United</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>329</th>\n",
       "      <td>West Bromwich Albion</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331</th>\n",
       "      <td>Leicester City</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>Stoke City</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>Swansea City</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>335</th>\n",
       "      <td>Burnley</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>336</th>\n",
       "      <td>Watford</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>337</th>\n",
       "      <td>Hull City</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>338</th>\n",
       "      <td>Middlesbrough</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>339</th>\n",
       "      <td>Sunderland</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     TEAM  FINAL_POINTS\n",
       "320               Chelsea            93\n",
       "321     Tottenham Hotspur            86\n",
       "322       Manchester City            78\n",
       "323             Liverpool            76\n",
       "324               Arsenal            75\n",
       "325     Manchester United            69\n",
       "326               Everton            61\n",
       "327           Southampton            46\n",
       "328           Bournemouth            46\n",
       "330       West Ham United            45\n",
       "329  West Bromwich Albion            45\n",
       "331        Leicester City            44\n",
       "332            Stoke City            44\n",
       "333        Crystal Palace            41\n",
       "334          Swansea City            41\n",
       "335               Burnley            40\n",
       "336               Watford            40\n",
       "337             Hull City            34\n",
       "338         Middlesbrough            28\n",
       "339            Sunderland            24"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "actual_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Chart of predicted vs actual points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11ce96320>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ocKzTkUQqHBUxEREpVwsWzKNjx1SSkpKYO/c96tc/lsjISKdjiVRI2iMmIiLl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\n/w8oEL1GUGhubgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ce817b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 17))\n",
    "\n",
    "val = np.linspace(20,100,10)\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.scatter(holdout['PREDICTED_POINTS'],holdout['FINAL_POINTS'], alpha = 1)\n",
    "plt.plot(val,val,'k--')\n",
    "plt.title('Actual vs. predicted points')\n",
    "plt.xlabel('Predicted Points')\n",
    "plt.ylabel('Actual Points')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}