nfl_Regression_multi.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>3d%</th>\n",
       "      <th>3d%_allowed</th>\n",
       "      <th>TOP</th>\n",
       "      <th>date</th>\n",
       "      <th>first_downs</th>\n",
       "      <th>first_downs_allowed</th>\n",
       "      <th>ha</th>\n",
       "      <th>margin</th>\n",
       "      <th>opp</th>\n",
       "      <th>pass_yards</th>\n",
       "      <th>...</th>\n",
       "      <th>rush_yards</th>\n",
       "      <th>rush_yards_allowed</th>\n",
       "      <th>sacked</th>\n",
       "      <th>sacks</th>\n",
       "      <th>takeaways</th>\n",
       "      <th>team</th>\n",
       "      <th>total_points</th>\n",
       "      <th>total_yards</th>\n",
       "      <th>total_yards_allowed</th>\n",
       "      <th>turnovers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.307692</td>\n",
       "      <td>0.285714</td>\n",
       "      <td>28.350000</td>\n",
       "      <td>9/10/2009</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>away</td>\n",
       "      <td>-3</td>\n",
       "      <td>PIT</td>\n",
       "      <td>234</td>\n",
       "      <td>...</td>\n",
       "      <td>86</td>\n",
       "      <td>36</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>TEN</td>\n",
       "      <td>3</td>\n",
       "      <td>320</td>\n",
       "      <td>357</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.285714</td>\n",
       "      <td>0.307692</td>\n",
       "      <td>36.183333</td>\n",
       "      <td>9/10/2009</td>\n",
       "      <td>19</td>\n",
       "      <td>18</td>\n",
       "      <td>home</td>\n",
       "      <td>3</td>\n",
       "      <td>TEN</td>\n",
       "      <td>321</td>\n",
       "      <td>...</td>\n",
       "      <td>36</td>\n",
       "      <td>86</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>PIT</td>\n",
       "      <td>3</td>\n",
       "      <td>357</td>\n",
       "      <td>320</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.363636</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>29.116667</td>\n",
       "      <td>9/13/2009</td>\n",
       "      <td>16</td>\n",
       "      <td>19</td>\n",
       "      <td>away</td>\n",
       "      <td>-12</td>\n",
       "      <td>ATL</td>\n",
       "      <td>163</td>\n",
       "      <td>...</td>\n",
       "      <td>96</td>\n",
       "      <td>68</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>MIA</td>\n",
       "      <td>26</td>\n",
       "      <td>259</td>\n",
       "      <td>281</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.400000</td>\n",
       "      <td>0.363636</td>\n",
       "      <td>30.883333</td>\n",
       "      <td>9/13/2009</td>\n",
       "      <td>19</td>\n",
       "      <td>16</td>\n",
       "      <td>home</td>\n",
       "      <td>12</td>\n",
       "      <td>MIA</td>\n",
       "      <td>213</td>\n",
       "      <td>...</td>\n",
       "      <td>68</td>\n",
       "      <td>96</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>ATL</td>\n",
       "      <td>26</td>\n",
       "      <td>281</td>\n",
       "      <td>259</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>26.550000</td>\n",
       "      <td>9/13/2009</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>away</td>\n",
       "      <td>5</td>\n",
       "      <td>CIN</td>\n",
       "      <td>227</td>\n",
       "      <td>...</td>\n",
       "      <td>75</td>\n",
       "      <td>86</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>DEN</td>\n",
       "      <td>19</td>\n",
       "      <td>302</td>\n",
       "      <td>307</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        3d%  3d%_allowed        TOP       date  first_downs  \\\n",
       "0  0.307692     0.285714  28.350000  9/10/2009           18   \n",
       "1  0.285714     0.307692  36.183333  9/10/2009           19   \n",
       "2  0.363636     0.400000  29.116667  9/13/2009           16   \n",
       "3  0.400000     0.363636  30.883333  9/13/2009           19   \n",
       "4  0.250000     0.333333  26.550000  9/13/2009           10   \n",
       "\n",
       "   first_downs_allowed    ha  margin  opp  pass_yards    ...      rush_yards  \\\n",
       "0                   19  away      -3  PIT         234    ...              86   \n",
       "1                   18  home       3  TEN         321    ...              36   \n",
       "2                   19  away     -12  ATL         163    ...              96   \n",
       "3                   16  home      12  MIA         213    ...              68   \n",
       "4                   16  away       5  CIN         227    ...              75   \n",
       "\n",
       "   rush_yards_allowed  sacked  sacks  takeaways team  total_points  \\\n",
       "0                  36       1      4          3  TEN             3   \n",
       "1                  86       4      1          2  PIT             3   \n",
       "2                  68       4      2          0  MIA            26   \n",
       "3                  96       2      4          4  ATL            26   \n",
       "4                  86       3      3          2  DEN            19   \n",
       "\n",
       "   total_yards  total_yards_allowed  turnovers  \n",
       "0          320                  357          2  \n",
       "1          357                  320          3  \n",
       "2          259                  281          4  \n",
       "3          281                  259          0  \n",
       "4          302                  307          0  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the csv file into a pandas DataFrame\n",
    "nfl = pd.read_csv('data/nfl.csv')\n",
    "nfl.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['3d%', '3d%_allowed', 'TOP', 'date', 'first_downs',\n",
       "       'first_downs_allowed', 'ha', 'margin', 'opp', 'pass_yards',\n",
       "       'pass_yards_allowed', 'penalty_yards', 'plays', 'points',\n",
       "       'points_allowed', 'result', 'rush_yards', 'rush_yards_allowed',\n",
       "       'sacked', 'sacks', 'takeaways', 'team', 'total_points', 'total_yards',\n",
       "       'total_yards_allowed', 'turnovers'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nfl.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4806, 2) (4806, 1)\n"
     ]
    }
   ],
   "source": [
    "# Assign X and y\n",
    "\n",
    "X = nfl[[\"pass_yards\", \"rush_yards\"]]\n",
    "y = nfl[\"points\"].values.reshape(-1, 1)\n",
    "print(X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#plt.scatter(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 Score: 0.2583722760234307\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "\n",
    "# Fitting our model with all of our features in X\n",
    "model.fit(X, y)\n",
    "\n",
    "score = model.score(X, y)\n",
    "print(f\"R2 Score: {score}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rt7AxfOtiltuGRl0fLIKQVphL95ObcKGbtLjT9sEdB2C/7WYZyjBrI2vw690n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\nwRcEQWgRxOALgiC0CP8fANEdlwZqbxIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2849e5095c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = model.predict(X)\n",
    "# Plot Residuals\n",
    "plt.scatter(predictions, predictions - y)\n",
    "plt.hlines(y=0, xmin=predictions.min(), xmax=predictions.max())\n",
    "plt.show()"
   ]
  },
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