2_Forward OLS analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forward 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 Forward Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "611"
      ]
     },
     "execution_count": 4,
     "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 position not like \"%D%\" and mins > 270\n",
    "        ;\n",
    "    \"\"\".format(position=position)\n",
    "    \n",
    "    return SQL_QUERY\n",
    "\n",
    "# forword\n",
    "SQL_QUERY = make_query(\"F\")\n",
    "forward_df = pd.read_sql(SQL_QUERY, db)\n",
    "\n",
    "len(forward_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>const</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>...</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>1</td>\n",
       "      <td>8.382932</td>\n",
       "      <td>9.541107</td>\n",
       "      <td>6.649772</td>\n",
       "      <td>2.985339</td>\n",
       "      <td>0.820926</td>\n",
       "      <td>3.276870</td>\n",
       "      <td>3.344336</td>\n",
       "      <td>2.398933</td>\n",
       "      <td>3.995343</td>\n",
       "      <td>...</td>\n",
       "      <td>1.313059</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.015096</td>\n",
       "      <td>3.009618</td>\n",
       "      <td>3.162057</td>\n",
       "      <td>3.701969</td>\n",
       "      <td>3.353454</td>\n",
       "      <td>2.286773</td>\n",
       "      <td>8.088244</td>\n",
       "      <td>7.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6.945858</td>\n",
       "      <td>9.699247</td>\n",
       "      <td>7.181753</td>\n",
       "      <td>2.686805</td>\n",
       "      <td>0.615694</td>\n",
       "      <td>2.803518</td>\n",
       "      <td>1.170518</td>\n",
       "      <td>2.398933</td>\n",
       "      <td>4.439270</td>\n",
       "      <td>...</td>\n",
       "      <td>1.313059</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.612077</td>\n",
       "      <td>3.762023</td>\n",
       "      <td>1.149839</td>\n",
       "      <td>2.005233</td>\n",
       "      <td>2.624442</td>\n",
       "      <td>3.353934</td>\n",
       "      <td>8.501999</td>\n",
       "      <td>7.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>6.945858</td>\n",
       "      <td>9.699247</td>\n",
       "      <td>7.093090</td>\n",
       "      <td>0.298534</td>\n",
       "      <td>1.231389</td>\n",
       "      <td>0.341144</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>2.626118</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.403019</td>\n",
       "      <td>0.451443</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.388238</td>\n",
       "      <td>0.874814</td>\n",
       "      <td>1.088940</td>\n",
       "      <td>9.783304</td>\n",
       "      <td>6.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>5.987809</td>\n",
       "      <td>9.224827</td>\n",
       "      <td>6.383781</td>\n",
       "      <td>3.582407</td>\n",
       "      <td>0.410463</td>\n",
       "      <td>3.609751</td>\n",
       "      <td>3.678769</td>\n",
       "      <td>1.999111</td>\n",
       "      <td>2.219635</td>\n",
       "      <td>...</td>\n",
       "      <td>1.313059</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.821134</td>\n",
       "      <td>1.504809</td>\n",
       "      <td>1.149839</td>\n",
       "      <td>2.005233</td>\n",
       "      <td>2.624442</td>\n",
       "      <td>3.887515</td>\n",
       "      <td>10.450651</td>\n",
       "      <td>7.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>7.664395</td>\n",
       "      <td>9.751960</td>\n",
       "      <td>7.004426</td>\n",
       "      <td>1.691692</td>\n",
       "      <td>2.668009</td>\n",
       "      <td>1.997285</td>\n",
       "      <td>1.839385</td>\n",
       "      <td>1.599289</td>\n",
       "      <td>1.331781</td>\n",
       "      <td>...</td>\n",
       "      <td>1.313059</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.410567</td>\n",
       "      <td>1.805771</td>\n",
       "      <td>1.437298</td>\n",
       "      <td>2.159482</td>\n",
       "      <td>2.332838</td>\n",
       "      <td>1.295838</td>\n",
       "      <td>8.795631</td>\n",
       "      <td>6.98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   const       age      tall    weight  apps_start  apps_sub      mins  \\\n",
       "0      1  8.382932  9.541107  6.649772    2.985339  0.820926  3.276870   \n",
       "1      1  6.945858  9.699247  7.181753    2.686805  0.615694  2.803518   \n",
       "2      1  6.945858  9.699247  7.093090    0.298534  1.231389  0.341144   \n",
       "3      1  5.987809  9.224827  6.383781    3.582407  0.410463  3.609751   \n",
       "4      1  7.664395  9.751960  7.004426    1.691692  2.668009  1.997285   \n",
       "\n",
       "      goals   assists       yel   ...      blocks  owng    keyp_x    fouled  \\\n",
       "0  3.344336  2.398933  3.995343   ...    1.313059   0.0  2.015096  3.009618   \n",
       "1  1.170518  2.398933  4.439270   ...    1.313059   0.0  1.612077  3.762023   \n",
       "2  0.000000  0.000000  0.000000   ...    2.626118   0.0  0.403019  0.451443   \n",
       "3  3.678769  1.999111  2.219635   ...    1.313059   0.0  2.821134  1.504809   \n",
       "4  1.839385  1.599289  1.331781   ...    1.313059   0.0  1.410567  1.805771   \n",
       "\n",
       "        off      disp    unstch      avgp       ps_y  rating  \n",
       "0  3.162057  3.701969  3.353454  2.286773   8.088244    7.37  \n",
       "1  1.149839  2.005233  2.624442  3.353934   8.501999    7.25  \n",
       "2  0.000000  1.388238  0.874814  1.088940   9.783304    6.22  \n",
       "3  1.149839  2.005233  2.624442  3.887515  10.450651    7.50  \n",
       "4  1.437298  2.159482  2.332838  1.295838   8.795631    6.98  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = forword_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(forword_df.ix[:,-1], columns=[\"rating\"])\n",
    "f_df = pd.concat([dfX, dfy], axis=1)\n",
    "f_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 rating   R-squared:                       0.919\n",
      "Model:                            OLS   Adj. R-squared:                  0.915\n",
      "Method:                 Least Squares   F-statistic:                     234.8\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          5.79e-296\n",
      "Time:                        11:29:21   Log-Likelihood:                 461.08\n",
      "No. Observations:                 611   AIC:                            -864.2\n",
      "Df Residuals:                     582   BIC:                            -736.1\n",
      "Df Model:                          28                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.6388      0.091     62.193      0.000         5.461     5.817\n",
      "age           -0.0091      0.005     -1.700      0.090        -0.020     0.001\n",
      "tall           0.0084      0.008      1.100      0.272        -0.007     0.023\n",
      "weight         0.0038      0.008      0.474      0.635        -0.012     0.020\n",
      "apps_start     0.0661      0.049      1.357      0.175        -0.030     0.162\n",
      "apps_sub   -8.385e-05      0.009     -0.010      0.992        -0.017     0.017\n",
      "mins          -0.1498      0.049     -3.037      0.002        -0.247    -0.053\n",
      "goals          0.1742      0.011     15.252      0.000         0.152     0.197\n",
      "assists        0.0666      0.008      8.427      0.000         0.051     0.082\n",
      "yel           -0.0201      0.006     -3.101      0.002        -0.033    -0.007\n",
      "red           -0.0062      0.005     -1.249      0.212        -0.016     0.004\n",
      "spg            0.0837      0.009      9.308      0.000         0.066     0.101\n",
      "ps_x           0.0165      0.003      4.818      0.000         0.010     0.023\n",
      "motm           0.0212      0.009      2.400      0.017         0.004     0.039\n",
      "aw             0.0829      0.008     10.207      0.000         0.067     0.099\n",
      "tackles        0.0656      0.007      8.841      0.000         0.051     0.080\n",
      "inter          0.0489      0.007      6.859      0.000         0.035     0.063\n",
      "fouls         -0.0192      0.007     -2.778      0.006        -0.033    -0.006\n",
      "offsides      -0.0112      0.005     -2.212      0.027        -0.021    -0.001\n",
      "clear          0.0051      0.007      0.758      0.449        -0.008     0.018\n",
      "drb           -0.0179      0.006     -2.772      0.006        -0.031    -0.005\n",
      "blocks         0.0056      0.005      1.038      0.300        -0.005     0.016\n",
      "owng          -0.0046      0.005     -0.917      0.360        -0.014     0.005\n",
      "keyp_x         0.0994      0.008     12.079      0.000         0.083     0.116\n",
      "fouled         0.0396      0.007      5.871      0.000         0.026     0.053\n",
      "off           -0.0101      0.006     -1.615      0.107        -0.022     0.002\n",
      "disp           0.0097      0.007      1.341      0.180        -0.005     0.024\n",
      "unstch        -0.0047      0.008     -0.627      0.531        -0.020     0.010\n",
      "avgp           0.0326      0.010      3.383      0.001         0.014     0.052\n",
      "ps_y           0.0165      0.003      4.818      0.000         0.010     0.023\n",
      "==============================================================================\n",
      "Omnibus:                       44.878   Durbin-Watson:                   1.984\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              105.265\n",
      "Skew:                           0.398   Prob(JB):                     1.39e-23\n",
      "Kurtosis:                       4.871   Cond. No.                     8.85e+15\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 3.21e-27. This might indicate that there are\n",
      "strong multicollinearity problems or that the design matrix is singular.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(f_df.ix[:, -1], f_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:                       0.915\n",
      "Model:                            OLS   Adj. R-squared:                  0.913\n",
      "Method:                 Least Squares   F-statistic:                     429.4\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          2.74e-307\n",
      "Time:                        11:30:44   Log-Likelihood:                 449.12\n",
      "No. Observations:                 611   AIC:                            -866.2\n",
      "Df Residuals:                     595   BIC:                            -795.6\n",
      "Df Model:                          15                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.6896      0.067     84.360      0.000         5.557     5.822\n",
      "mins          -0.0836      0.009     -8.811      0.000        -0.102    -0.065\n",
      "goals          0.1689      0.011     15.172      0.000         0.147     0.191\n",
      "assists        0.0665      0.008      8.568      0.000         0.051     0.082\n",
      "yel           -0.0228      0.006     -3.603      0.000        -0.035    -0.010\n",
      "spg            0.0836      0.009      9.704      0.000         0.067     0.100\n",
      "ps_x           0.0156      0.003      4.572      0.000         0.009     0.022\n",
      "motm           0.0235      0.009      2.711      0.007         0.006     0.041\n",
      "aw             0.0802      0.007     11.491      0.000         0.066     0.094\n",
      "tackles        0.0691      0.007      9.406      0.000         0.055     0.084\n",
      "inter          0.0469      0.007      7.214      0.000         0.034     0.060\n",
      "fouls         -0.0153      0.007     -2.338      0.020        -0.028    -0.002\n",
      "drb           -0.0165      0.006     -2.563      0.011        -0.029    -0.004\n",
      "keyp_x         0.1012      0.008     12.456      0.000         0.085     0.117\n",
      "fouled         0.0385      0.006      6.022      0.000         0.026     0.051\n",
      "avgp           0.0347      0.009      3.755      0.000         0.017     0.053\n",
      "ps_y           0.0156      0.003      4.572      0.000         0.009     0.022\n",
      "==============================================================================\n",
      "Omnibus:                       45.982   Durbin-Watson:                   1.973\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              104.109\n",
      "Skew:                           0.421   Prob(JB):                     2.47e-23\n",
      "Kurtosis:                       4.839   Cond. No.                     1.82e+17\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 4.06e-30. This might indicate that there are\n",
      "strong multicollinearity problems or that the design matrix is singular.\n"
     ]
    }
   ],
   "source": [
    "# delete feature based on t-value\n",
    "remove_column_list = [\n",
    "    \"age\", \"tall\", \"weight\", \"apps_start\", \"apps_sub\", \"red\", \"clear\", \"blocks\", \"owng\", \"unstch\", \"offsides\", \"disp\", \"off\"\n",
    "]\n",
    "removed_f_df = f_df.drop(remove_column_list, axis=1) \n",
    "\n",
    "model = sm.OLS(removed_f_df.ix[:, -1], removed_f_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>mins</th>\n",
       "      <td>1.0</td>\n",
       "      <td>44.227823</td>\n",
       "      <td>44.227823</td>\n",
       "      <td>3199.652899</td>\n",
       "      <td>1.467266e-241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>goals</th>\n",
       "      <td>1.0</td>\n",
       "      <td>14.209164</td>\n",
       "      <td>14.209164</td>\n",
       "      <td>1027.959101</td>\n",
       "      <td>9.237160e-132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>assists</th>\n",
       "      <td>1.0</td>\n",
       "      <td>7.687434</td>\n",
       "      <td>7.687434</td>\n",
       "      <td>556.145853</td>\n",
       "      <td>2.536368e-87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yel</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.116096</td>\n",
       "      <td>0.116096</td>\n",
       "      <td>8.398942</td>\n",
       "      <td>3.892666e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>spg</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.702216</td>\n",
       "      <td>5.702216</td>\n",
       "      <td>412.525675</td>\n",
       "      <td>4.544223e-70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ps_x</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.716860</td>\n",
       "      <td>0.716860</td>\n",
       "      <td>51.861086</td>\n",
       "      <td>1.807262e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>motm</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.835558</td>\n",
       "      <td>2.835558</td>\n",
       "      <td>205.137890</td>\n",
       "      <td>3.429509e-40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>aw</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.351298</td>\n",
       "      <td>2.351298</td>\n",
       "      <td>170.104197</td>\n",
       "      <td>2.240872e-34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tackles</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.572391</td>\n",
       "      <td>5.572391</td>\n",
       "      <td>403.133490</td>\n",
       "      <td>7.421342e-69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>inter</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.060663</td>\n",
       "      <td>1.060663</td>\n",
       "      <td>76.733450</td>\n",
       "      <td>2.031578e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fouls</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.004059</td>\n",
       "      <td>0.004059</td>\n",
       "      <td>0.293674</td>\n",
       "      <td>5.880784e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drb</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.007110</td>\n",
       "      <td>0.007110</td>\n",
       "      <td>0.514381</td>\n",
       "      <td>4.735300e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>keyp_x</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3.789535</td>\n",
       "      <td>3.789535</td>\n",
       "      <td>274.153114</td>\n",
       "      <td>6.326110e-51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fouled</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.551940</td>\n",
       "      <td>0.551940</td>\n",
       "      <td>39.930013</td>\n",
       "      <td>5.162150e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>avgp</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.194879</td>\n",
       "      <td>0.194879</td>\n",
       "      <td>14.098477</td>\n",
       "      <td>1.905189e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ps_y</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.050659</td>\n",
       "      <td>0.050659</td>\n",
       "      <td>3.664879</td>\n",
       "      <td>5.604998e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>595.0</td>\n",
       "      <td>8.224503</td>\n",
       "      <td>0.013823</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",
       "mins        1.0  44.227823  44.227823  3199.652899  1.467266e-241\n",
       "goals       1.0  14.209164  14.209164  1027.959101  9.237160e-132\n",
       "assists     1.0   7.687434   7.687434   556.145853   2.536368e-87\n",
       "yel         1.0   0.116096   0.116096     8.398942   3.892666e-03\n",
       "spg         1.0   5.702216   5.702216   412.525675   4.544223e-70\n",
       "ps_x        1.0   0.716860   0.716860    51.861086   1.807262e-12\n",
       "motm        1.0   2.835558   2.835558   205.137890   3.429509e-40\n",
       "aw          1.0   2.351298   2.351298   170.104197   2.240872e-34\n",
       "tackles     1.0   5.572391   5.572391   403.133490   7.421342e-69\n",
       "inter       1.0   1.060663   1.060663    76.733450   2.031578e-17\n",
       "fouls       1.0   0.004059   0.004059     0.293674   5.880784e-01\n",
       "drb         1.0   0.007110   0.007110     0.514381   4.735300e-01\n",
       "keyp_x      1.0   3.789535   3.789535   274.153114   6.326110e-51\n",
       "fouled      1.0   0.551940   0.551940    39.930013   5.162150e-10\n",
       "avgp        1.0   0.194879   0.194879    14.098477   1.905189e-04\n",
       "ps_y        1.0   0.050659   0.050659     3.664879   5.604998e-02\n",
       "Residual  595.0   8.224503   0.013823          NaN            NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check F-value using anova table\n",
    "formula_str = \"\"\"\n",
    "rating ~ mins + goals + assists + yel + spg + ps_x\n",
    "+ motm + aw + tackles + inter + fouls + drb + keyp_x\n",
    "+ fouled + avgp + ps_y\n",
    "\"\"\"\n",
    "\n",
    "model = sm.OLS.from_formula(formula_str, data=removed_f_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:                       0.914\n",
      "Model:                            OLS   Adj. R-squared:                  0.912\n",
      "Method:                 Least Squares   F-statistic:                     486.5\n",
      "Date:                Mon, 27 Jun 2016   Prob (F-statistic):          1.93e-307\n",
      "Time:                        11:32:34   Log-Likelihood:                 443.11\n",
      "No. Observations:                 611   AIC:                            -858.2\n",
      "Df Residuals:                     597   BIC:                            -796.4\n",
      "Df Model:                          13                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.6694      0.068     83.946      0.000         5.537     5.802\n",
      "mins          -0.0838      0.010     -8.803      0.000        -0.102    -0.065\n",
      "goals          0.1726      0.011     15.448      0.000         0.151     0.195\n",
      "assists        0.0662      0.008      8.461      0.000         0.051     0.082\n",
      "yel           -0.0280      0.006     -4.658      0.000        -0.040    -0.016\n",
      "spg            0.0801      0.008      9.458      0.000         0.063     0.097\n",
      "ps_x           0.0319      0.007      4.640      0.000         0.018     0.045\n",
      "motm           0.0248      0.009      2.841      0.005         0.008     0.042\n",
      "aw             0.0769      0.007     11.273      0.000         0.063     0.090\n",
      "tackles        0.0593      0.007      8.766      0.000         0.046     0.073\n",
      "inter          0.0452      0.007      6.918      0.000         0.032     0.058\n",
      "keyp_x         0.1016      0.008     12.432      0.000         0.086     0.118\n",
      "fouled         0.0331      0.006      5.391      0.000         0.021     0.045\n",
      "avgp           0.0329      0.009      3.613      0.000         0.015     0.051\n",
      "==============================================================================\n",
      "Omnibus:                       47.274   Durbin-Watson:                   1.982\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              120.209\n",
      "Skew:                           0.394   Prob(JB):                     7.89e-27\n",
      "Kurtosis:                       5.025   Cond. No.                         155.\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",
    "    \"fouls\", \"drb\", \"ps_y\"\n",
    "]\n",
    "removed2_f_df = removed_f_df.drop(remove_column_list, axis=1) \n",
    "\n",
    "model = sm.OLS(removed2_f_df.ix[:, -1], removed2_f_df.ix[:, :-1])\n",
    "result = model.fit()\n",
    "print(result.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 결론\n",
    "- 주요변수 : goals, keypass, shots per game, aerial won, assists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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