5_Goalkeeper OLS analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Goalkeeper OLS analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_formats = {'png', 'retina'}\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "import MySQLdb\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.cross_validation import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Connect DB & get Forword Player Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "213"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "db = MySQLdb.connect(\n",
    "    \"db.fastcamp.us\",\n",
    "    \"root\",\n",
    "    \"dkstncks\",\n",
    "    \"football\",\n",
    "    charset='utf8',\n",
    ")\n",
    "\n",
    "def make_query(position):\n",
    "    \"\"\"\n",
    "    \n",
    "    parameter------------\n",
    "    position : M, D, F, G\n",
    "    \n",
    "    return---------------\n",
    "    SQL_QUERY String\n",
    "    \n",
    "    \"\"\"\n",
    "    SQL_QUERY = \"\"\"\n",
    "        SELECT \n",
    "            age, tall, weight, apps_start, apps_sub, mins, goals, assists, yel, red\n",
    "            , spg, ps_x, motm, aw, tackles, inter, fouls, offsides, clear, drb, blocks\n",
    "            , owng, keyp_x, fouled, off, disp, unstch, avgp, ps_y, rating\n",
    "        FROM player\n",
    "        WHERE position like \"%{position}%\" and mins > 270\n",
    "        ;\n",
    "    \"\"\".format(position=position)\n",
    "    \n",
    "    return SQL_QUERY\n",
    "\n",
    "SQL_QUERY = make_query(\"G\")\n",
    "goalkeeper_df = pd.read_sql(SQL_QUERY, db)\n",
    "\n",
    "len(goalkeeper_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>tall</th>\n",
       "      <th>weight</th>\n",
       "      <th>apps_start</th>\n",
       "      <th>apps_sub</th>\n",
       "      <th>mins</th>\n",
       "      <th>goals</th>\n",
       "      <th>assists</th>\n",
       "      <th>yel</th>\n",
       "      <th>red</th>\n",
       "      <th>...</th>\n",
       "      <th>blocks</th>\n",
       "      <th>owng</th>\n",
       "      <th>keyp_x</th>\n",
       "      <th>fouled</th>\n",
       "      <th>off</th>\n",
       "      <th>disp</th>\n",
       "      <th>unstch</th>\n",
       "      <th>avgp</th>\n",
       "      <th>ps_y</th>\n",
       "      <th>rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.146320</td>\n",
       "      <td>41.924041</td>\n",
       "      <td>15.879078</td>\n",
       "      <td>3.099158</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>3.031142</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.764448</td>\n",
       "      <td>2.85861</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.820579</td>\n",
       "      <td>0.936049</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.940884</td>\n",
       "      <td>5.376996</td>\n",
       "      <td>6.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.353296</td>\n",
       "      <td>41.265549</td>\n",
       "      <td>15.149006</td>\n",
       "      <td>3.182919</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>3.195594</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.936049</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.736246</td>\n",
       "      <td>3.969252</td>\n",
       "      <td>4.490466</td>\n",
       "      <td>6.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.680816</td>\n",
       "      <td>40.387558</td>\n",
       "      <td>14.601451</td>\n",
       "      <td>2.680353</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>2.689157</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.667327</td>\n",
       "      <td>8.123310</td>\n",
       "      <td>6.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.586048</td>\n",
       "      <td>41.046051</td>\n",
       "      <td>15.514042</td>\n",
       "      <td>0.502566</td>\n",
       "      <td>2.12385</td>\n",
       "      <td>0.506436</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.820579</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.584804</td>\n",
       "      <td>8.036585</td>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.749808</td>\n",
       "      <td>39.290070</td>\n",
       "      <td>13.688861</td>\n",
       "      <td>2.512831</td>\n",
       "      <td>2.12385</td>\n",
       "      <td>2.546197</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.764448</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.752231</td>\n",
       "      <td>5.145727</td>\n",
       "      <td>6.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        age       tall     weight  apps_start  apps_sub      mins  goals  \\\n",
       "0  8.146320  41.924041  15.879078    3.099158   0.00000  3.031142    0.0   \n",
       "1  5.353296  41.265549  15.149006    3.182919   0.00000  3.195594    0.0   \n",
       "2  7.680816  40.387558  14.601451    2.680353   0.00000  2.689157    0.0   \n",
       "3  5.586048  41.046051  15.514042    0.502566   2.12385  0.506436    0.0   \n",
       "4  6.749808  39.290070  13.688861    2.512831   2.12385  2.546197    0.0   \n",
       "\n",
       "   assists       yel      red   ...    blocks  owng    keyp_x    fouled  off  \\\n",
       "0      0.0  0.764448  2.85861   ...       0.0   0.0  1.820579  0.936049  0.0   \n",
       "1      0.0  0.000000  0.00000   ...       0.0   0.0  0.000000  0.936049  0.0   \n",
       "2      0.0  0.000000  0.00000   ...       0.0   0.0  0.000000  0.000000  0.0   \n",
       "3      0.0  0.000000  0.00000   ...       0.0   0.0  1.820579  0.000000  0.0   \n",
       "4      0.0  0.764448  0.00000   ...       0.0   0.0  0.000000  0.000000  0.0   \n",
       "\n",
       "   disp    unstch      avgp      ps_y  rating  \n",
       "0   0.0  0.000000  6.940884  5.376996    6.62  \n",
       "1   0.0  1.736246  3.969252  4.490466    6.83  \n",
       "2   0.0  0.000000  5.667327  8.123310    6.92  \n",
       "3   0.0  0.000000  4.584804  8.036585    6.48  \n",
       "4   0.0  0.000000  5.752231  5.145727    6.48  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = goalkeeper_df.ix[:,:-1]\n",
    "scaler = StandardScaler(with_mean=False)\n",
    "X_scaled = scaler.fit_transform(X)\n",
    "\n",
    "dfX0 = pd.DataFrame(X_scaled, columns=X.columns)\n",
    "dfX = sm.add_constant(dfX0)\n",
    "dfy = pd.DataFrame(goalkeeper_df.ix[:,-1], columns=[\"rating\"])\n",
    "g_df = pd.concat([dfX, dfy], axis=1)\n",
    "g_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 rating   R-squared:                       0.999\n",
      "Model:                            OLS   Adj. R-squared:                  0.999\n",
      "Method:                 Least Squares   F-statistic:                     6102.\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          2.22e-259\n",
      "Time:                        11:50:09   Log-Likelihood:                 6.8406\n",
      "No. Observations:                 213   AIC:                             36.32\n",
      "Df Residuals:                     188   BIC:                             120.4\n",
      "Df Model:                          25                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "age            0.0255      0.018      1.430      0.154        -0.010     0.061\n",
      "tall           0.1694      0.009     18.201      0.000         0.151     0.188\n",
      "weight        -0.0773      0.022     -3.544      0.000        -0.120    -0.034\n",
      "apps_start    -0.6836      0.849     -0.805      0.422        -2.359     0.992\n",
      "apps_sub      -0.0115      0.023     -0.499      0.618        -0.057     0.034\n",
      "mins           0.6986      0.846      0.826      0.410        -0.969     2.367\n",
      "goals          0.0006      0.020      0.029      0.977        -0.038     0.039\n",
      "assists        0.0088      0.018      0.481      0.631        -0.027     0.045\n",
      "yel           -0.0420      0.021     -2.038      0.043        -0.083    -0.001\n",
      "red           -0.0078      0.023     -0.337      0.736        -0.053     0.038\n",
      "spg           -0.0064      0.020     -0.321      0.749        -0.046     0.033\n",
      "ps_x           0.0286      0.009      3.093      0.002         0.010     0.047\n",
      "motm           0.0806      0.020      3.979      0.000         0.041     0.121\n",
      "aw             0.0415      0.021      1.960      0.051        -0.000     0.083\n",
      "tackles        0.0532      0.019      2.845      0.005         0.016     0.090\n",
      "inter          0.0301      0.017      1.721      0.087        -0.004     0.065\n",
      "fouls         -0.0270      0.021     -1.292      0.198        -0.068     0.014\n",
      "offsides    6.626e-18   5.07e-18      1.307      0.193     -3.38e-18  1.66e-17\n",
      "clear          0.0129      0.020      0.640      0.523        -0.027     0.053\n",
      "drb           -0.0508      0.019     -2.693      0.008        -0.088    -0.014\n",
      "blocks     -7.269e-18   3.77e-18     -1.927      0.055     -1.47e-17  1.72e-19\n",
      "owng          -0.0087      0.017     -0.500      0.617        -0.043     0.026\n",
      "keyp_x         0.0095      0.018      0.517      0.606        -0.027     0.046\n",
      "fouled         0.0058      0.021      0.275      0.783        -0.035     0.047\n",
      "off         6.792e-18   4.97e-18      1.366      0.174     -3.02e-18  1.66e-17\n",
      "disp          -0.0175      0.019     -0.943      0.347        -0.054     0.019\n",
      "unstch        -0.0162      0.018     -0.891      0.374        -0.052     0.020\n",
      "avgp           0.0388      0.019      2.060      0.041         0.002     0.076\n",
      "ps_y           0.0286      0.009      3.093      0.002         0.010     0.047\n",
      "==============================================================================\n",
      "Omnibus:                        6.558   Durbin-Watson:                   1.995\n",
      "Prob(Omnibus):                  0.038   Jarque-Bera (JB):                6.563\n",
      "Skew:                           0.333   Prob(JB):                       0.0376\n",
      "Kurtosis:                       3.545   Cond. No.                     1.02e+16\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The smallest eigenvalue is 4.28e-27. This might indicate that there are\n",
      "strong multicollinearity problems or that the design matrix is singular.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(g_df.ix[:, -1], g_df.ix[:, :-1])\n",
    "result = model.fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find Proper Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 rating   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 1.838e+04\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          3.17e-284\n",
      "Time:                        11:50:45   Log-Likelihood:                -20.978\n",
      "No. Observations:                 213   AIC:                             55.96\n",
      "Df Residuals:                     206   BIC:                             79.49\n",
      "Df Model:                           7                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "age            0.0267      0.018      1.452      0.148        -0.010     0.063\n",
      "tall           0.1380      0.005     29.865      0.000         0.129     0.147\n",
      "ps_x           0.0336      0.010      3.525      0.001         0.015     0.052\n",
      "aw             0.0477      0.020      2.392      0.018         0.008     0.087\n",
      "offsides   -7.205e-17    2.3e-17     -3.129      0.002     -1.17e-16 -2.67e-17\n",
      "clear          0.0367      0.020      1.793      0.074        -0.004     0.077\n",
      "drb           -0.0538      0.019     -2.788      0.006        -0.092    -0.016\n",
      "avgp           0.0533      0.019      2.812      0.005         0.016     0.091\n",
      "ps_y           0.0336      0.010      3.525      0.001         0.015     0.052\n",
      "==============================================================================\n",
      "Omnibus:                        0.834   Durbin-Watson:                   2.025\n",
      "Prob(Omnibus):                  0.659   Jarque-Bera (JB):                0.649\n",
      "Skew:                           0.131   Prob(JB):                        0.723\n",
      "Kurtosis:                       3.067   Cond. No.                     2.22e+18\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The smallest eigenvalue is 8.06e-32. This might indicate that there are\n",
      "strong multicollinearity problems or that the design matrix is singular.\n"
     ]
    }
   ],
   "source": [
    "# delete features based on t-value\n",
    "remove_column_list = [\n",
    "    \"weight\", \"apps_start\", \"apps_sub\", \"mins\", \"goals\", \"assists\", \"yel\", \"red\", \"spg\", \"motm\"\n",
    "    , \"tackles\",\"inter\", \"fouls\", \"blocks\", \"owng\", \"keyp_x\", \"fouled\", \"off\", \"disp\", \"unstch\"\n",
    "]\n",
    "removed_g_df = g_df.drop(remove_column_list, axis=1) \n",
    "\n",
    "model = sm.OLS(removed_g_df.ix[:, -1], removed_g_df.ix[:, :-1])\n",
    "result = model.fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.004729</td>\n",
       "      <td>0.004729</td>\n",
       "      <td>0.086286</td>\n",
       "      <td>0.769250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tall</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005905</td>\n",
       "      <td>0.005905</td>\n",
       "      <td>0.107752</td>\n",
       "      <td>0.743053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ps_x</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.400719</td>\n",
       "      <td>0.400719</td>\n",
       "      <td>7.311599</td>\n",
       "      <td>0.007427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aw</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.278175</td>\n",
       "      <td>0.278175</td>\n",
       "      <td>5.075640</td>\n",
       "      <td>0.025323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>offsides</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.225671</td>\n",
       "      <td>0.225671</td>\n",
       "      <td>4.117637</td>\n",
       "      <td>0.043731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clear</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.042847</td>\n",
       "      <td>0.042847</td>\n",
       "      <td>0.781804</td>\n",
       "      <td>0.377626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drb</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.452490</td>\n",
       "      <td>0.452490</td>\n",
       "      <td>8.256233</td>\n",
       "      <td>0.004489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>avgp</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.060146</td>\n",
       "      <td>0.060146</td>\n",
       "      <td>1.097446</td>\n",
       "      <td>0.296061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ps_y</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.035221</td>\n",
       "      <td>0.035221</td>\n",
       "      <td>0.642656</td>\n",
       "      <td>0.423679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>205.0</td>\n",
       "      <td>11.235207</td>\n",
       "      <td>0.054806</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             df     sum_sq   mean_sq         F    PR(>F)\n",
       "age         1.0   0.004729  0.004729  0.086286  0.769250\n",
       "tall        1.0   0.005905  0.005905  0.107752  0.743053\n",
       "ps_x        1.0   0.400719  0.400719  7.311599  0.007427\n",
       "aw          1.0   0.278175  0.278175  5.075640  0.025323\n",
       "offsides    1.0   0.225671  0.225671  4.117637  0.043731\n",
       "clear       1.0   0.042847  0.042847  0.781804  0.377626\n",
       "drb         1.0   0.452490  0.452490  8.256233  0.004489\n",
       "avgp        1.0   0.060146  0.060146  1.097446  0.296061\n",
       "ps_y        1.0   0.035221  0.035221  0.642656  0.423679\n",
       "Residual  205.0  11.235207  0.054806       NaN       NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check F-value using anova table\n",
    "formula_str = \"\"\"\n",
    "rating ~ age + tall + ps_x + aw + offsides + clear + drb +  avgp + ps_y\n",
    "\"\"\"\n",
    "\n",
    "model = sm.OLS.from_formula(formula_str, data=removed_g_df)\n",
    "result = model.fit()\n",
    "table_anova = sm.stats.anova_lm(result)\n",
    "table_anova"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 rating   R-squared:                       0.998\n",
      "Model:                            OLS   Adj. R-squared:                  0.998\n",
      "Method:                 Least Squares   F-statistic:                 2.133e+04\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          5.94e-286\n",
      "Time:                        11:51:27   Log-Likelihood:                -22.063\n",
      "No. Observations:                 213   AIC:                             56.13\n",
      "Df Residuals:                     207   BIC:                             76.29\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "tall           0.1423      0.004     40.454      0.000         0.135     0.149\n",
      "ps_x           0.0685      0.019      3.591      0.000         0.031     0.106\n",
      "aw             0.0487      0.020      2.441      0.015         0.009     0.088\n",
      "clear          0.0355      0.021      1.731      0.085        -0.005     0.076\n",
      "drb           -0.0527      0.019     -2.722      0.007        -0.091    -0.015\n",
      "avgp           0.0513      0.019      2.710      0.007         0.014     0.089\n",
      "==============================================================================\n",
      "Omnibus:                        0.512   Durbin-Watson:                   1.980\n",
      "Prob(Omnibus):                  0.774   Jarque-Bera (JB):                0.371\n",
      "Skew:                           0.100   Prob(JB):                        0.831\n",
      "Kurtosis:                       3.045   Cond. No.                         54.2\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# delete features based on F-value\n",
    "remove_column_list = [\n",
    "    \"age\", \"offsides\", \"ps_y\"\n",
    "]\n",
    "removed2_g_df = removed_g_df.drop(remove_column_list, axis=1) \n",
    "\n",
    "model = sm.OLS(removed2_g_df.ix[:, -1], removed2_g_df.ix[:, :-1])\n",
    "result = model.fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 결론\n",
    "- 주요 변수 : tall, ps_x, dribble blocked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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