Tensorflow Neural Network for Yards After Catch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notes\n",
    "\n",
    "This script was inspired by an R script written on the https://www.opensourcefootball.com/ website.\n",
    "\n",
    "**Reference:** https://www.opensourcefootball.com/posts/2020-08-19-neural-nets-using-r/\n",
    "\n",
    "\n",
    "The goal is to build a neural network to predict yards after catch for NFL Receivers. There is nothing overly fancy here given that my goal is really just to improve my `python` skills and so I decided to take elements from the `R` neural network in the above line and try and apply it to `python`. As such, this is no where near and exhaustive treatment of neural networks but rather an intro (for me) into coding in `tensorflow` in `python`. In fact, the neural network might not even be the best way to answer this question and at the end I will use linear regression to build a model and predict YAC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import preprocessing\n",
    "from sklearn.model_selection import train_test_split\n",
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get Data\n",
    "\n",
    "We will get the data from the `nflfastr`github page: https://github.com/guga31bb/nflfastR-data/tree/master/data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## set the years we are interested in obtaining\n",
    "years = [2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Write a loop to extract the data for those years\n",
    "\n",
    "pbp = pd.DataFrame()\n",
    "\n",
    "for i in years:\n",
    "        nfl_dat = pd.read_csv('https://github.com/guga31bb/nflfastR-data/blob/master/data/' \\\n",
    "                   'play_by_play_' + str(i) + '.csv.gz?raw=true',\n",
    "                  compression = 'gzip',\n",
    "                  low_memory = False)\n",
    "        \n",
    "        pbp = pbp.append(nfl_dat, sort = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>aborted_play</th>\n",
       "      <th>air_epa</th>\n",
       "      <th>air_wpa</th>\n",
       "      <th>air_yards</th>\n",
       "      <th>assist_tackle</th>\n",
       "      <th>assist_tackle_1_player_id</th>\n",
       "      <th>assist_tackle_1_player_name</th>\n",
       "      <th>assist_tackle_1_team</th>\n",
       "      <th>assist_tackle_2_player_id</th>\n",
       "      <th>assist_tackle_2_player_name</th>\n",
       "      <th>...</th>\n",
       "      <th>xyac_median_yardage</th>\n",
       "      <th>xyac_success</th>\n",
       "      <th>yac_epa</th>\n",
       "      <th>yac_wpa</th>\n",
       "      <th>yardline_100</th>\n",
       "      <th>yards_after_catch</th>\n",
       "      <th>yards_gained</th>\n",
       "      <th>ydsnet</th>\n",
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       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>6.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>78.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>10</td>\n",
       "      <td>ARI 22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1.448654</td>\n",
       "      <td>0.033835</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.998045</td>\n",
       "      <td>0.758916</td>\n",
       "      <td>0.034915</td>\n",
       "      <td>73.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>18.0</td>\n",
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       "      <td>ARI 27</td>\n",
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       "    <tr>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.053408</td>\n",
       "      <td>55.0</td>\n",
       "      <td>17.0</td>\n",
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       "      <td>53.0</td>\n",
       "      <td>10</td>\n",
       "      <td>ARI 45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 340 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   aborted_play   air_epa   air_wpa  air_yards  assist_tackle  \\\n",
       "0             0       NaN       NaN        NaN            0.0   \n",
       "1             0 -0.564643 -0.005659        0.0            0.0   \n",
       "2             0       NaN       NaN        NaN            0.0   \n",
       "3             0  1.448654  0.033835        7.0            0.0   \n",
       "4             0 -0.471865 -0.017380        0.0            0.0   \n",
       "\n",
       "  assist_tackle_1_player_id assist_tackle_1_player_name assist_tackle_1_team  \\\n",
       "0                       NaN                         NaN                  NaN   \n",
       "1                       NaN                         NaN                  NaN   \n",
       "2                       NaN                         NaN                  NaN   \n",
       "3                       NaN                         NaN                  NaN   \n",
       "4                       NaN                         NaN                  NaN   \n",
       "\n",
       "  assist_tackle_2_player_id assist_tackle_2_player_name  ...  \\\n",
       "0                       NaN                         NaN  ...   \n",
       "1                       NaN                         NaN  ...   \n",
       "2                       NaN                         NaN  ...   \n",
       "3                       NaN                         NaN  ...   \n",
       "4                       NaN                         NaN  ...   \n",
       "\n",
       "  xyac_median_yardage xyac_success   yac_epa   yac_wpa yardline_100  \\\n",
       "0                 NaN          NaN       NaN       NaN         30.0   \n",
       "1                 6.0     0.690780  0.000000  0.000000         78.0   \n",
       "2                 NaN          NaN       NaN       NaN         78.0   \n",
       "3                 1.0     0.998045  0.758916  0.034915         73.0   \n",
       "4                 6.0     0.692089  1.816268  0.053408         55.0   \n",
       "\n",
       "  yards_after_catch yards_gained ydsnet  ydstogo   yrdln  \n",
       "0               NaN          0.0   53.0        0   LA 30  \n",
       "1               0.0          0.0   53.0       10  ARI 22  \n",
       "2               NaN          5.0   53.0       10  ARI 22  \n",
       "3              11.0         18.0   53.0        5  ARI 27  \n",
       "4              17.0         17.0   53.0       10  ARI 45  \n",
       "\n",
       "[5 rows x 340 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Look at the first few rows\n",
    "\n",
    "pbp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['aborted_play',\n",
       " 'air_epa',\n",
       " 'air_wpa',\n",
       " 'air_yards',\n",
       " 'assist_tackle',\n",
       " 'assist_tackle_1_player_id',\n",
       " 'assist_tackle_1_player_name',\n",
       " 'assist_tackle_1_team',\n",
       " 'assist_tackle_2_player_id',\n",
       " 'assist_tackle_2_player_name',\n",
       " 'assist_tackle_2_team',\n",
       " 'assist_tackle_3_player_id',\n",
       " 'assist_tackle_3_player_name',\n",
       " 'assist_tackle_3_team',\n",
       " 'assist_tackle_4_player_id',\n",
       " 'assist_tackle_4_player_name',\n",
       " 'assist_tackle_4_team',\n",
       " 'away_coach',\n",
       " 'away_score',\n",
       " 'away_team',\n",
       " 'away_timeouts_remaining',\n",
       " 'away_wp',\n",
       " 'away_wp_post',\n",
       " 'blocked_player_id',\n",
       " 'blocked_player_name',\n",
       " 'comp_air_epa',\n",
       " 'comp_air_wpa',\n",
       " 'comp_yac_epa',\n",
       " 'comp_yac_wpa',\n",
       " 'complete_pass',\n",
       " 'cp',\n",
       " 'cpoe',\n",
       " 'def_wp',\n",
       " 'defensive_extra_point_attempt',\n",
       " 'defensive_extra_point_conv',\n",
       " 'defensive_two_point_attempt',\n",
       " 'defensive_two_point_conv',\n",
       " 'defteam',\n",
       " 'defteam_score',\n",
       " 'defteam_score_post',\n",
       " 'defteam_timeouts_remaining',\n",
       " 'desc',\n",
       " 'div_game',\n",
       " 'down',\n",
       " 'drive',\n",
       " 'drive_end_transition',\n",
       " 'drive_end_yard_line',\n",
       " 'drive_ended_with_score',\n",
       " 'drive_first_downs',\n",
       " 'drive_game_clock_end',\n",
       " 'drive_game_clock_start',\n",
       " 'drive_inside20',\n",
       " 'drive_play_count',\n",
       " 'drive_play_id_ended',\n",
       " 'drive_play_id_started',\n",
       " 'drive_quarter_end',\n",
       " 'drive_quarter_start',\n",
       " 'drive_real_start_time',\n",
       " 'drive_start_transition',\n",
       " 'drive_start_yard_line',\n",
       " 'drive_time_of_possession',\n",
       " 'drive_yards_penalized',\n",
       " 'end_clock_time',\n",
       " 'end_yard_line',\n",
       " 'ep',\n",
       " 'epa',\n",
       " 'extra_point_attempt',\n",
       " 'extra_point_prob',\n",
       " 'extra_point_result',\n",
       " 'fg_prob',\n",
       " 'field_goal_attempt',\n",
       " 'field_goal_result',\n",
       " 'first_down',\n",
       " 'first_down_pass',\n",
       " 'first_down_penalty',\n",
       " 'first_down_rush',\n",
       " 'fixed_drive',\n",
       " 'fixed_drive_result',\n",
       " 'forced_fumble_player_1_player_id',\n",
       " 'forced_fumble_player_1_player_name',\n",
       " 'forced_fumble_player_1_team',\n",
       " 'forced_fumble_player_2_player_id',\n",
       " 'forced_fumble_player_2_player_name',\n",
       " 'forced_fumble_player_2_team',\n",
       " 'fourth_down_converted',\n",
       " 'fourth_down_failed',\n",
       " 'fumble',\n",
       " 'fumble_forced',\n",
       " 'fumble_lost',\n",
       " 'fumble_not_forced',\n",
       " 'fumble_out_of_bounds',\n",
       " 'fumble_recovery_1_player_id',\n",
       " 'fumble_recovery_1_player_name',\n",
       " 'fumble_recovery_1_team',\n",
       " 'fumble_recovery_1_yards',\n",
       " 'fumble_recovery_2_player_id',\n",
       " 'fumble_recovery_2_player_name',\n",
       " 'fumble_recovery_2_team',\n",
       " 'fumble_recovery_2_yards',\n",
       " 'fumbled_1_player_id',\n",
       " 'fumbled_1_player_name',\n",
       " 'fumbled_1_team',\n",
       " 'fumbled_2_player_id',\n",
       " 'fumbled_2_player_name',\n",
       " 'fumbled_2_team',\n",
       " 'game_date',\n",
       " 'game_half',\n",
       " 'game_id',\n",
       " 'game_seconds_remaining',\n",
       " 'game_stadium',\n",
       " 'goal_to_go',\n",
       " 'half_seconds_remaining',\n",
       " 'home_coach',\n",
       " 'home_score',\n",
       " 'home_team',\n",
       " 'home_timeouts_remaining',\n",
       " 'home_wp',\n",
       " 'home_wp_post',\n",
       " 'id',\n",
       " 'incomplete_pass',\n",
       " 'interception',\n",
       " 'interception_player_id',\n",
       " 'interception_player_name',\n",
       " 'jersey_number',\n",
       " 'kick_distance',\n",
       " 'kicker_player_id',\n",
       " 'kicker_player_name',\n",
       " 'kickoff_attempt',\n",
       " 'kickoff_downed',\n",
       " 'kickoff_fair_catch',\n",
       " 'kickoff_in_endzone',\n",
       " 'kickoff_inside_twenty',\n",
       " 'kickoff_out_of_bounds',\n",
       " 'kickoff_returner_player_id',\n",
       " 'kickoff_returner_player_name',\n",
       " 'lateral_interception_player_id',\n",
       " 'lateral_interception_player_name',\n",
       " 'lateral_kickoff_returner_player_id',\n",
       " 'lateral_kickoff_returner_player_name',\n",
       " 'lateral_punt_returner_player_id',\n",
       " 'lateral_punt_returner_player_name',\n",
       " 'lateral_receiver_player_id',\n",
       " 'lateral_receiver_player_name',\n",
       " 'lateral_reception',\n",
       " 'lateral_recovery',\n",
       " 'lateral_return',\n",
       " 'lateral_rush',\n",
       " 'lateral_rusher_player_id',\n",
       " 'lateral_rusher_player_name',\n",
       " 'lateral_sack_player_id',\n",
       " 'lateral_sack_player_name',\n",
       " 'location',\n",
       " 'name',\n",
       " 'nfl_api_id',\n",
       " 'no_huddle',\n",
       " 'no_score_prob',\n",
       " 'old_game_id',\n",
       " 'opp_fg_prob',\n",
       " 'opp_safety_prob',\n",
       " 'opp_td_prob',\n",
       " 'order_sequence',\n",
       " 'own_kickoff_recovery',\n",
       " 'own_kickoff_recovery_player_id',\n",
       " 'own_kickoff_recovery_player_name',\n",
       " 'own_kickoff_recovery_td',\n",
       " 'pass',\n",
       " 'pass_attempt',\n",
       " 'pass_defense_1_player_id',\n",
       " 'pass_defense_1_player_name',\n",
       " 'pass_defense_2_player_id',\n",
       " 'pass_defense_2_player_name',\n",
       " 'pass_length',\n",
       " 'pass_location',\n",
       " 'pass_touchdown',\n",
       " 'passer',\n",
       " 'passer_id',\n",
       " 'passer_jersey_number',\n",
       " 'passer_player_id',\n",
       " 'passer_player_name',\n",
       " 'penalty',\n",
       " 'penalty_player_id',\n",
       " 'penalty_player_name',\n",
       " 'penalty_team',\n",
       " 'penalty_type',\n",
       " 'penalty_yards',\n",
       " 'play',\n",
       " 'play_clock',\n",
       " 'play_deleted',\n",
       " 'play_id',\n",
       " 'play_type',\n",
       " 'play_type_nfl',\n",
       " 'posteam',\n",
       " 'posteam_score',\n",
       " 'posteam_score_post',\n",
       " 'posteam_timeouts_remaining',\n",
       " 'posteam_type',\n",
       " 'punt_attempt',\n",
       " 'punt_blocked',\n",
       " 'punt_downed',\n",
       " 'punt_fair_catch',\n",
       " 'punt_in_endzone',\n",
       " 'punt_inside_twenty',\n",
       " 'punt_out_of_bounds',\n",
       " 'punt_returner_player_id',\n",
       " 'punt_returner_player_name',\n",
       " 'punter_player_id',\n",
       " 'punter_player_name',\n",
       " 'qb_dropback',\n",
       " 'qb_epa',\n",
       " 'qb_hit',\n",
       " 'qb_hit_1_player_id',\n",
       " 'qb_hit_1_player_name',\n",
       " 'qb_hit_2_player_id',\n",
       " 'qb_hit_2_player_name',\n",
       " 'qb_kneel',\n",
       " 'qb_scramble',\n",
       " 'qb_spike',\n",
       " 'qtr',\n",
       " 'quarter_end',\n",
       " 'quarter_seconds_remaining',\n",
       " 'receiver',\n",
       " 'receiver_id',\n",
       " 'receiver_jersey_number',\n",
       " 'receiver_player_id',\n",
       " 'receiver_player_name',\n",
       " 'replay_or_challenge',\n",
       " 'replay_or_challenge_result',\n",
       " 'result',\n",
       " 'return_team',\n",
       " 'return_touchdown',\n",
       " 'return_yards',\n",
       " 'roof',\n",
       " 'run_gap',\n",
       " 'run_location',\n",
       " 'rush',\n",
       " 'rush_attempt',\n",
       " 'rush_touchdown',\n",
       " 'rusher',\n",
       " 'rusher_id',\n",
       " 'rusher_jersey_number',\n",
       " 'rusher_player_id',\n",
       " 'rusher_player_name',\n",
       " 'sack',\n",
       " 'safety',\n",
       " 'safety_prob',\n",
       " 'score_differential',\n",
       " 'score_differential_post',\n",
       " 'season',\n",
       " 'season_type',\n",
       " 'series',\n",
       " 'series_result',\n",
       " 'series_success',\n",
       " 'shotgun',\n",
       " 'side_of_field',\n",
       " 'solo_tackle',\n",
       " 'solo_tackle_1_player_id',\n",
       " 'solo_tackle_1_player_name',\n",
       " 'solo_tackle_1_team',\n",
       " 'solo_tackle_2_player_id',\n",
       " 'solo_tackle_2_player_name',\n",
       " 'solo_tackle_2_team',\n",
       " 'sp',\n",
       " 'special',\n",
       " 'special_teams_play',\n",
       " 'spread_line',\n",
       " 'st_play_type',\n",
       " 'stadium',\n",
       " 'stadium_id',\n",
       " 'start_time',\n",
       " 'success',\n",
       " 'surface',\n",
       " 'tackle_for_loss_1_player_id',\n",
       " 'tackle_for_loss_1_player_name',\n",
       " 'tackle_for_loss_2_player_id',\n",
       " 'tackle_for_loss_2_player_name',\n",
       " 'tackled_for_loss',\n",
       " 'td_prob',\n",
       " 'td_team',\n",
       " 'temp',\n",
       " 'third_down_converted',\n",
       " 'third_down_failed',\n",
       " 'time',\n",
       " 'time_of_day',\n",
       " 'timeout',\n",
       " 'timeout_team',\n",
       " 'total',\n",
       " 'total_away_comp_air_epa',\n",
       " 'total_away_comp_air_wpa',\n",
       " 'total_away_comp_yac_epa',\n",
       " 'total_away_comp_yac_wpa',\n",
       " 'total_away_epa',\n",
       " 'total_away_pass_epa',\n",
       " 'total_away_pass_wpa',\n",
       " 'total_away_raw_air_epa',\n",
       " 'total_away_raw_air_wpa',\n",
       " 'total_away_raw_yac_epa',\n",
       " 'total_away_raw_yac_wpa',\n",
       " 'total_away_rush_epa',\n",
       " 'total_away_rush_wpa',\n",
       " 'total_away_score',\n",
       " 'total_home_comp_air_epa',\n",
       " 'total_home_comp_air_wpa',\n",
       " 'total_home_comp_yac_epa',\n",
       " 'total_home_comp_yac_wpa',\n",
       " 'total_home_epa',\n",
       " 'total_home_pass_epa',\n",
       " 'total_home_pass_wpa',\n",
       " 'total_home_raw_air_epa',\n",
       " 'total_home_raw_air_wpa',\n",
       " 'total_home_raw_yac_epa',\n",
       " 'total_home_raw_yac_wpa',\n",
       " 'total_home_rush_epa',\n",
       " 'total_home_rush_wpa',\n",
       " 'total_home_score',\n",
       " 'total_line',\n",
       " 'touchback',\n",
       " 'touchdown',\n",
       " 'two_point_attempt',\n",
       " 'two_point_conv_result',\n",
       " 'two_point_conversion_prob',\n",
       " 'vegas_home_wp',\n",
       " 'vegas_wp',\n",
       " 'weather',\n",
       " 'week',\n",
       " 'wind',\n",
       " 'wp',\n",
       " 'wpa',\n",
       " 'xyac_epa',\n",
       " 'xyac_fd',\n",
       " 'xyac_mean_yardage',\n",
       " 'xyac_median_yardage',\n",
       " 'xyac_success',\n",
       " 'yac_epa',\n",
       " 'yac_wpa',\n",
       " 'yardline_100',\n",
       " 'yards_after_catch',\n",
       " 'yards_gained',\n",
       " 'ydsnet',\n",
       " 'ydstogo',\n",
       " 'yrdln']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Look at the column names\n",
    "\n",
    "list(pbp.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract Passing Plays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## What are the values in the 'pass' column?\n",
    "\n",
    "pbp['pass'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values are binary with a 0 being \"no pass\" and a 1 being a \"pass\". Let's get all players where pass == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pbp[pbp['pass']== 1] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Pre-Processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make the pass location binary by specifying a \"1\" every time the pass is in the middle of the field or a \"0\" otherwise.\n",
    "\n",
    "For this, I'll use the `where()` function from the `numpy` package, which seems to behave like `case_when()` in `R`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/envs/py3-TF2.0/lib/python3.7/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "df['pass_location'] = np.where(df.pass_location == 'middle', 1, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `roof` column tells us about what type of stadium the game is being played in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['dome', 'outdoors', 'closed', 'open'], dtype=object)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['roof'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable is of `dtype = object`. In the `R` script they change this column to a factor and in `python` I believe the equivalent is a `categorical`. So we will change the data type to `categorical`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/envs/py3-TF2.0/lib/python3.7/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[dome, outdoors, closed, open]\n",
       "Categories (4, object): [dome, outdoors, closed, open]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['roof'] = df['roof'].astype('category')\n",
    "df['roof'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we will constrain the analysis to only a few key columns that we believe will influence YAC (the same columns from the above line). We will then drop NA values from the data set and reset the indexes. We will then dummy code the categorical variable, `roof`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[['yardline_100', 'down', 'ydstogo', 'shotgun', 'air_yards', 'yards_after_catch', 'qb_hit', 'pass_location', 'roof']]\n",
    "df.dropna(inplace = True)\n",
    "df.reset_index(drop = True, inplace = True)\n",
    "df = pd.get_dummies(df, columns = ['roof'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>yardline_100</th>\n",
       "      <th>down</th>\n",
       "      <th>ydstogo</th>\n",
       "      <th>shotgun</th>\n",
       "      <th>air_yards</th>\n",
       "      <th>yards_after_catch</th>\n",
       "      <th>qb_hit</th>\n",
       "      <th>pass_location</th>\n",
       "      <th>roof_closed</th>\n",
       "      <th>roof_dome</th>\n",
       "      <th>roof_open</th>\n",
       "      <th>roof_outdoors</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>78.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>73.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>36.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>12.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   yardline_100  down  ydstogo  shotgun  air_yards  yards_after_catch  qb_hit  \\\n",
       "0          78.0   1.0       10        0        0.0                0.0     0.0   \n",
       "1          73.0   3.0        5        1        7.0               11.0     0.0   \n",
       "2          55.0   1.0       10        1        0.0               17.0     0.0   \n",
       "3          36.0   2.0        8        1       12.0                0.0     0.0   \n",
       "4          32.0   1.0       10        0       13.0                0.0     0.0   \n",
       "\n",
       "   pass_location  roof_closed  roof_dome  roof_open  roof_outdoors  \n",
       "0              0            0          1          0              0  \n",
       "1              0            0          1          0              0  \n",
       "2              0            0          1          0              0  \n",
       "3              0            0          1          0              0  \n",
       "4              0            0          1          0              0  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Look at the new data set\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much data are we dealing with?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(115605, 12)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "115,605 rows and 12 columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train/Test Split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select the predictor variables, `X`, by dropping the target variable, `yards_after_catch`. Also, pre-process the `X` variables by scaling them to have a mean of 0 and variance of 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop('yards_after_catch', axis = 1)\n",
    "X = preprocessing.scale(X)\n",
    "y = df['yards_after_catch']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a train/test split with the training set representing 90% of the data and the test set the remaining 10%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_count = int(df.shape[0] * 0.9)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = sample_count, random_state=2378)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save Data in .npz format\n",
    "\n",
    "This will be a two-tuple format of inputs and targets, which we will use in `tensorflow`.\n",
    "\n",
    "**NOTE:** The data will be saved in this file format to your working directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez('yac_train', inputs = X_train, targets = y_train)\n",
    "np.savez('yac_test', inputs = X_test, targets = y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the .npz files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_npz = np.load('yac_train.npz')\n",
    "train_inputs = train_npz['inputs'].astype(np.float)\n",
    "train_targets = train_npz['targets'].astype(np.int)\n",
    "\n",
    "test_npz = np.load('yac_test.npz')\n",
    "test_inputs = test_npz['inputs'].astype(np.float)\n",
    "test_targets = test_npz['targets'].astype(np.int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Neural Netowrk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  Model input information\n",
    "1) State the number of predictors (in this case 11)\n",
    "\n",
    "2) State the number of outputs (in this case 1)\n",
    "\n",
    "3) Set the width of the hidden layers by specifying the number of units/nodes in each hidden layer (in this case I use 10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_predictors = 11\n",
    "n_outputs = 1\n",
    "hidden_layer_size = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Create the model\n",
    "\n",
    "* I'm going to specificy 4 hidden layers (each with a size of 10, as indicated above)\n",
    "* The optimizer I'll use is stochastic gradient descent\n",
    "* I'll use mean squared error as my loss function and the metrics I want to evaluate my model on are mean squared error and mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tf.keras.Sequential([  \n",
    "    tf.keras.layers.Dense(hidden_layer_size, activation = 'relu'),\n",
    "    tf.keras.layers.Dense(hidden_layer_size, activation = 'relu'),\n",
    "    tf.keras.layers.Dense(hidden_layer_size, activation = 'relu'),\n",
    "    tf.keras.layers.Dense(hidden_layer_size, activation = 'relu'),\n",
    "    tf.keras.layers.Dense(n_outputs)       \n",
    "])\n",
    "\n",
    "\n",
    "model.compile(optimizer='sgd', loss='mean_squared_error', metrics = ['mae', 'mse'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Specify the hyperparameters for batch size and epoch\n",
    "\n",
    "* Batch size will indicate the number of training samples used in a single iteration\n",
    "* Epoch will indicate the number of times the model will go through the training data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "max_epochs = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Run the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100\n",
      "116/116 - 0s - loss: 41.5853 - mae: 4.0385 - mse: 41.5853\n",
      "Epoch 2/100\n",
      "116/116 - 0s - loss: 41.9163 - mae: 4.0677 - mse: 41.9163\n",
      "Epoch 3/100\n",
      "116/116 - 0s - loss: 41.6176 - mae: 4.0381 - mse: 41.6176\n",
      "Epoch 4/100\n",
      "116/116 - 0s - loss: 41.4838 - mae: 4.0392 - mse: 41.4838\n",
      "Epoch 5/100\n",
      "116/116 - 0s - loss: 41.5506 - mae: 4.0418 - mse: 41.5506\n",
      "Epoch 6/100\n",
      "116/116 - 0s - loss: 41.6051 - mae: 4.0532 - mse: 41.6051\n",
      "Epoch 7/100\n",
      "116/116 - 0s - loss: 41.6677 - mae: 4.0523 - mse: 41.6677\n",
      "Epoch 8/100\n",
      "116/116 - 0s - loss: 41.4794 - mae: 4.0370 - mse: 41.4794\n",
      "Epoch 9/100\n",
      "116/116 - 0s - loss: 41.5663 - mae: 4.0467 - mse: 41.5663\n",
      "Epoch 10/100\n",
      "116/116 - 0s - loss: 41.4974 - mae: 4.0433 - mse: 41.4974\n",
      "Epoch 11/100\n",
      "116/116 - 0s - loss: 41.5922 - mae: 4.0515 - mse: 41.5922\n",
      "Epoch 12/100\n",
      "116/116 - 0s - loss: 41.6230 - mae: 4.0511 - mse: 41.6230\n",
      "Epoch 13/100\n",
      "116/116 - 0s - loss: 41.5722 - mae: 4.0434 - mse: 41.5722\n",
      "Epoch 14/100\n",
      "116/116 - 0s - loss: 41.4559 - mae: 4.0342 - mse: 41.4559\n",
      "Epoch 15/100\n",
      "116/116 - 0s - loss: 41.4992 - mae: 4.0503 - mse: 41.4992\n",
      "Epoch 16/100\n",
      "116/116 - 0s - loss: 41.5531 - mae: 4.0603 - mse: 41.5531\n",
      "Epoch 17/100\n",
      "116/116 - 0s - loss: 41.5513 - mae: 4.0516 - mse: 41.5513\n",
      "Epoch 18/100\n",
      "116/116 - 0s - loss: 41.6269 - mae: 4.0497 - mse: 41.6269\n",
      "Epoch 19/100\n",
      "116/116 - 0s - loss: 41.2784 - mae: 4.0428 - mse: 41.2784\n",
      "Epoch 20/100\n",
      "116/116 - 0s - loss: 41.7602 - mae: 4.0474 - mse: 41.7602\n",
      "Epoch 21/100\n",
      "116/116 - 0s - loss: 41.4768 - mae: 4.0486 - mse: 41.4768\n",
      "Epoch 22/100\n",
      "116/116 - 0s - loss: 41.5081 - mae: 4.0516 - mse: 41.5081\n",
      "Epoch 23/100\n",
      "116/116 - 0s - loss: 41.5040 - mae: 4.0316 - mse: 41.5040\n",
      "Epoch 24/100\n",
      "116/116 - 0s - loss: 41.3159 - mae: 4.0294 - mse: 41.3159\n",
      "Epoch 25/100\n",
      "116/116 - 0s - loss: 41.6381 - mae: 4.0465 - mse: 41.6381\n",
      "Epoch 26/100\n",
      "116/116 - 0s - loss: 41.5096 - mae: 4.0486 - mse: 41.5096\n",
      "Epoch 27/100\n",
      "116/116 - 0s - loss: 41.2961 - mae: 4.0252 - mse: 41.2961\n",
      "Epoch 28/100\n",
      "116/116 - 0s - loss: 41.5981 - mae: 4.0444 - mse: 41.5981\n",
      "Epoch 29/100\n",
      "116/116 - 0s - loss: 41.4773 - mae: 4.0344 - mse: 41.4773\n",
      "Epoch 30/100\n",
      "116/116 - 0s - loss: 41.4033 - mae: 4.0407 - mse: 41.4033\n",
      "Epoch 31/100\n",
      "116/116 - 0s - loss: 41.3878 - mae: 4.0552 - mse: 41.3878\n",
      "Epoch 32/100\n",
      "116/116 - 0s - loss: 41.4336 - mae: 4.0392 - mse: 41.4336\n",
      "Epoch 33/100\n",
      "116/116 - 0s - loss: 41.4247 - mae: 4.0302 - mse: 41.4247\n",
      "Epoch 34/100\n",
      "116/116 - 0s - loss: 41.3417 - mae: 4.0342 - mse: 41.3417\n",
      "Epoch 35/100\n",
      "116/116 - 0s - loss: 41.5442 - mae: 4.0421 - mse: 41.5442\n",
      "Epoch 36/100\n",
      "116/116 - 0s - loss: 41.3597 - mae: 4.0462 - mse: 41.3597\n",
      "Epoch 37/100\n",
      "116/116 - 0s - loss: 41.5896 - mae: 4.0537 - mse: 41.5896\n",
      "Epoch 38/100\n",
      "116/116 - 0s - loss: 41.3461 - mae: 4.0355 - mse: 41.3461\n",
      "Epoch 39/100\n",
      "116/116 - 0s - loss: 41.4600 - mae: 4.0479 - mse: 41.4600\n",
      "Epoch 40/100\n",
      "116/116 - 0s - loss: 41.3987 - mae: 4.0412 - mse: 41.3987\n",
      "Epoch 41/100\n",
      "116/116 - 0s - loss: 41.4780 - mae: 4.0440 - mse: 41.4780\n",
      "Epoch 42/100\n",
      "116/116 - 0s - loss: 41.3917 - mae: 4.0436 - mse: 41.3917\n",
      "Epoch 43/100\n",
      "116/116 - 0s - loss: 41.3637 - mae: 4.0346 - mse: 41.3637\n",
      "Epoch 44/100\n",
      "116/116 - 0s - loss: 41.6891 - mae: 4.0538 - mse: 41.6891\n",
      "Epoch 45/100\n",
      "116/116 - 0s - loss: 41.5190 - mae: 4.0414 - mse: 41.5190\n",
      "Epoch 46/100\n",
      "116/116 - 0s - loss: 41.3537 - mae: 4.0379 - mse: 41.3537\n",
      "Epoch 47/100\n",
      "116/116 - 0s - loss: 41.5754 - mae: 4.0635 - mse: 41.5754\n",
      "Epoch 48/100\n",
      "116/116 - 0s - loss: 41.4986 - mae: 4.0549 - mse: 41.4986\n",
      "Epoch 49/100\n",
      "116/116 - 0s - loss: 41.3092 - mae: 4.0316 - mse: 41.3092\n",
      "Epoch 50/100\n",
      "116/116 - 0s - loss: 41.6039 - mae: 4.0504 - mse: 41.6039\n",
      "Epoch 51/100\n",
      "116/116 - 0s - loss: 41.3890 - mae: 4.0437 - mse: 41.3890\n",
      "Epoch 52/100\n",
      "116/116 - 0s - loss: 41.7307 - mae: 4.0589 - mse: 41.7307\n",
      "Epoch 53/100\n",
      "116/116 - 0s - loss: 41.4416 - mae: 4.0482 - mse: 41.4416\n",
      "Epoch 54/100\n",
      "116/116 - 0s - loss: 41.5006 - mae: 4.0447 - mse: 41.5006\n",
      "Epoch 55/100\n",
      "116/116 - 0s - loss: 41.3139 - mae: 4.0474 - mse: 41.3139\n",
      "Epoch 56/100\n",
      "116/116 - 0s - loss: 41.6071 - mae: 4.0537 - mse: 41.6071\n",
      "Epoch 57/100\n",
      "116/116 - 0s - loss: 41.3188 - mae: 4.0319 - mse: 41.3188\n",
      "Epoch 58/100\n",
      "116/116 - 0s - loss: 41.0929 - mae: 4.0405 - mse: 41.0929\n",
      "Epoch 59/100\n",
      "116/116 - 0s - loss: 41.7017 - mae: 4.0628 - mse: 41.7017\n",
      "Epoch 60/100\n",
      "116/116 - 0s - loss: 41.4671 - mae: 4.0361 - mse: 41.4671\n",
      "Epoch 61/100\n",
      "116/116 - 0s - loss: 41.4314 - mae: 4.0504 - mse: 41.4314\n",
      "Epoch 62/100\n",
      "116/116 - 0s - loss: 41.3674 - mae: 4.0363 - mse: 41.3674\n",
      "Epoch 63/100\n",
      "116/116 - 0s - loss: 41.6109 - mae: 4.0498 - mse: 41.6109\n",
      "Epoch 64/100\n",
      "116/116 - 0s - loss: 41.6349 - mae: 4.0577 - mse: 41.6349\n",
      "Epoch 65/100\n",
      "116/116 - 0s - loss: 41.4153 - mae: 4.0383 - mse: 41.4153\n",
      "Epoch 66/100\n",
      "116/116 - 0s - loss: 41.2213 - mae: 4.0393 - mse: 41.2213\n",
      "Epoch 67/100\n",
      "116/116 - 0s - loss: 41.4381 - mae: 4.0555 - mse: 41.4381\n",
      "Epoch 68/100\n",
      "116/116 - 0s - loss: 41.2278 - mae: 4.0347 - mse: 41.2278\n",
      "Epoch 69/100\n",
      "116/116 - 0s - loss: 41.3776 - mae: 4.0497 - mse: 41.3776\n",
      "Epoch 70/100\n",
      "116/116 - 0s - loss: 41.2303 - mae: 4.0248 - mse: 41.2303\n",
      "Epoch 71/100\n",
      "116/116 - 0s - loss: 41.2976 - mae: 4.0419 - mse: 41.2976\n",
      "Epoch 72/100\n",
      "116/116 - 0s - loss: 41.4841 - mae: 4.0409 - mse: 41.4841\n",
      "Epoch 73/100\n",
      "116/116 - 0s - loss: 41.5264 - mae: 4.0533 - mse: 41.5264\n",
      "Epoch 74/100\n",
      "116/116 - 0s - loss: 41.3568 - mae: 4.0336 - mse: 41.3568\n",
      "Epoch 75/100\n",
      "116/116 - 0s - loss: 41.3899 - mae: 4.0516 - mse: 41.3899\n",
      "Epoch 76/100\n",
      "116/116 - 0s - loss: 41.4994 - mae: 4.0448 - mse: 41.4994\n",
      "Epoch 77/100\n",
      "116/116 - 0s - loss: 41.3258 - mae: 4.0271 - mse: 41.3258\n",
      "Epoch 78/100\n",
      "116/116 - 0s - loss: 41.2565 - mae: 4.0210 - mse: 41.2565\n",
      "Epoch 79/100\n",
      "116/116 - 0s - loss: 41.2874 - mae: 4.0409 - mse: 41.2874\n",
      "Epoch 80/100\n",
      "116/116 - 0s - loss: 41.3340 - mae: 4.0275 - mse: 41.3340\n",
      "Epoch 81/100\n",
      "116/116 - 0s - loss: 41.3797 - mae: 4.0432 - mse: 41.3797\n",
      "Epoch 82/100\n",
      "116/116 - 0s - loss: 41.2152 - mae: 4.0291 - mse: 41.2152\n",
      "Epoch 83/100\n",
      "116/116 - 0s - loss: 41.5380 - mae: 4.0377 - mse: 41.5380\n",
      "Epoch 84/100\n",
      "116/116 - 0s - loss: 41.3656 - mae: 4.0451 - mse: 41.3656\n",
      "Epoch 85/100\n",
      "116/116 - 0s - loss: 41.4950 - mae: 4.0511 - mse: 41.4950\n",
      "Epoch 86/100\n",
      "116/116 - 0s - loss: 41.2891 - mae: 4.0342 - mse: 41.2891\n",
      "Epoch 87/100\n",
      "116/116 - 0s - loss: 41.2477 - mae: 4.0326 - mse: 41.2477\n",
      "Epoch 88/100\n",
      "116/116 - 0s - loss: 41.3066 - mae: 4.0438 - mse: 41.3066\n",
      "Epoch 89/100\n",
      "116/116 - 0s - loss: 41.2096 - mae: 4.0327 - mse: 41.2096\n",
      "Epoch 90/100\n",
      "116/116 - 0s - loss: 41.4934 - mae: 4.0435 - mse: 41.4934\n",
      "Epoch 91/100\n",
      "116/116 - 0s - loss: 41.5894 - mae: 4.0491 - mse: 41.5894\n",
      "Epoch 92/100\n",
      "116/116 - 0s - loss: 41.3582 - mae: 4.0451 - mse: 41.3582\n",
      "Epoch 93/100\n",
      "116/116 - 0s - loss: 41.3260 - mae: 4.0484 - mse: 41.3260\n",
      "Epoch 94/100\n",
      "116/116 - 0s - loss: 41.3184 - mae: 4.0429 - mse: 41.3184\n",
      "Epoch 95/100\n",
      "116/116 - 0s - loss: 41.3258 - mae: 4.0518 - mse: 41.3258\n",
      "Epoch 96/100\n",
      "116/116 - 0s - loss: 41.4148 - mae: 4.0479 - mse: 41.4148\n",
      "Epoch 97/100\n",
      "116/116 - 0s - loss: 41.1540 - mae: 4.0471 - mse: 41.1540\n",
      "Epoch 98/100\n",
      "116/116 - 0s - loss: 41.3485 - mae: 4.0302 - mse: 41.3485\n",
      "Epoch 99/100\n",
      "116/116 - 0s - loss: 41.5178 - mae: 4.0495 - mse: 41.5178\n",
      "Epoch 100/100\n",
      "116/116 - 0s - loss: 41.4034 - mae: 4.0453 - mse: 41.4034\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x148bb9510>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(train_inputs,\n",
    "         train_targets,\n",
    "         batch_size = batch_size,\n",
    "         epochs = max_epochs,\n",
    "         verbose = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the final iteration, we see a mean absolute error of 4.0453 and a mean squared error of 41.4034."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First get the model predictions on the test data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.933353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.350162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.171444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.393558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.684061</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Pred\n",
       "0  3.933353\n",
       "1  5.350162\n",
       "2  3.171444\n",
       "3  4.393558\n",
       "4  3.684061"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_YAC = model.predict(test_inputs)\n",
    "pred_YAC = pd.DataFrame(pred_YAC, columns = ['Pred'])\n",
    "pred_YAC.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert the predictions from a data frame into a string\n",
    "\n",
    "predictions = pred_YAC['Pred']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now get the actual values of YAC observed in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_YAC = pd.DataFrame(test_targets, columns = ['Obs_YAC'])\n",
    "actual = test_YAC['Obs_YAC']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calulate the residual between observed and predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid = actual - predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Residuals')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(resid)\n",
    "plt.title('Histogram of Residuals', size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean absolute error on the test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.158478421594513"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae = resid.abs().mean()\n",
    "mae"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean squared error on the test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44.9336538832123"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_resid = resid ** 2\n",
    "mse = sq_resid.mean()\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results on the test data seem competitive with (though slightly worse than) the results in the final iteration of the training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I said at the start, the exercise of writing the neural network was to work on improving my `python` skills (as I mainly work in `R` and have done so for the last 8 years). Thus, I didn't believe that a neural network was the best tool for this analysis (though it is the most fancy). As such, I'll now build a linear regression model and see what type of results I can get.\n",
    "\n",
    "I'll buld the regression model in both the `sklearn` and `statsmodels` packages. I do this because, while the former seems to be the most preferred approach for `python` coders, it frustrates me because I have a hard time getting the output about the model that I would like (though this may be more on me given my lack of understanding of a lot of `python`). Conversely, the latter provides a nice model output so that you can understand what went on under the hood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression in sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model as lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that we have already created our train and test splits above, so I will simply use those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First create a linear regression instance\n",
    "lm.model = lm.LinearRegression()\n",
    "\n",
    "# Now create the linear model\n",
    "fit_sklearn = lm.model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the model coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.1565691970456955,\n",
       " array([ 0.00000000e+00,  7.98104832e-01,  1.02404253e-01,  3.77836187e-01,\n",
       "        -2.34585021e-01, -9.50577574e-01,  3.46594785e-02, -1.31089643e-01,\n",
       "        -2.92473726e+12, -3.06674584e+12, -1.10461171e+12, -3.98163106e+12]))"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_sklearn.intercept_, fit_sklearn.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is useless as there are no varibale names. Let's just look at the coefficients with their column names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>yardline_100</th>\n",
       "      <td>7.978854e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>down</th>\n",
       "      <td>1.014954e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ydstogo</th>\n",
       "      <td>3.761414e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>shotgun</th>\n",
       "      <td>-2.364584e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>air_yards</th>\n",
       "      <td>-9.484371e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>qb_hit</th>\n",
       "      <td>3.368871e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pass_location</th>\n",
       "      <td>-1.298373e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>roof_closed</th>\n",
       "      <td>8.850522e+12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>roof_dome</th>\n",
       "      <td>9.280253e+12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>roof_open</th>\n",
       "      <td>3.342656e+12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>roof_outdoors</th>\n",
       "      <td>1.204878e+13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          0\n",
       "yardline_100   7.978854e-01\n",
       "down           1.014954e-01\n",
       "ydstogo        3.761414e-01\n",
       "shotgun       -2.364584e-01\n",
       "air_yards     -9.484371e-01\n",
       "qb_hit         3.368871e-02\n",
       "pass_location -1.298373e-01\n",
       "roof_closed    8.850522e+12\n",
       "roof_dome      9.280253e+12\n",
       "roof_open      3.342656e+12\n",
       "roof_outdoors  1.204878e+13"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "value = fit_sklearn.coef_\n",
    "coef = ['yardline_100', 'down', 'ydstogo', 'shotgun', 'air_yards', 'qb_hit', 'pass_location', 'roof_closed', 'roof_dome', 'roof_open', 'roof_outdoors']\n",
    "pd.DataFrame(value, coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make Predictions on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = fit_sklearn.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid = y_test - preds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Residuals')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(resid)\n",
    "plt.title(\"Histogram of Residuals\", size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.542613084974376"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae = resid.abs().mean()\n",
    "mae"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.097402620785836"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_resid = resid ** 2\n",
    "mse = sq_resid.mean()\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the regression performed slightly worse than the neural network did. The absolute error for the neural network on the test set was 4.2 while the absolute error for the linear regression was 4.5. Not a massive difference for a much simpoler and easier to interpret model! But as they say....*\"It's a game of inches!\"*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression in statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I'll build the same regression model on the training set in the `statsmodels1` package. As you will see, the output of the regression model is much easier to look at than the array of coefficients that `sklearn` kicks out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before building the model we need to add a `constant` term to the `X_train` data set. This will ensure that `statsmodels` includes an intercept in our model as it doesn't automatically add one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = smf.add_constant(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build the regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "fit_statsmodels = smf.OLS(y_train, X_train).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the nice looking summary of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>yards_after_catch</td> <th>  R-squared:         </th> <td>   0.036</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.035</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>   <th>  F-statistic:       </th> <td>   42.81</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 27 Aug 2020</td>  <th>  Prob (F-statistic):</th> <td>4.03e-84</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:36:32</td>      <th>  Log-Likelihood:    </th> <td> -38720.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 11561</td>       <th>  AIC:               </th> <td>7.746e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 11550</td>       <th>  BIC:               </th> <td>7.754e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    10</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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    5.1635</td> <td>    0.064</td> <td>   80.514</td> <td> 0.000</td> <td>    5.038</td> <td>    5.289</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.7979</td> <td>    0.065</td> <td>   12.226</td> <td> 0.000</td> <td>    0.670</td> <td>    0.926</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td>    0.1015</td> <td>    0.069</td> <td>    1.463</td> <td> 0.144</td> <td>   -0.035</td> <td>    0.238</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>    0.3769</td> <td>    0.068</td> <td>    5.527</td> <td> 0.000</td> <td>    0.243</td> <td>    0.511</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>   -0.2357</td> <td>    0.067</td> <td>   -3.505</td> <td> 0.000</td> <td>   -0.368</td> <td>   -0.104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td>   -0.9492</td> <td>    0.065</td> <td>  -14.616</td> <td> 0.000</td> <td>   -1.076</td> <td>   -0.822</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>    0.0353</td> <td>    0.065</td> <td>    0.547</td> <td> 0.584</td> <td>   -0.091</td> <td>    0.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td>   -0.1303</td> <td>    0.065</td> <td>   -2.011</td> <td> 0.044</td> <td>   -0.257</td> <td>   -0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td>    0.0575</td> <td>    0.049</td> <td>    1.162</td> <td> 0.245</td> <td>   -0.039</td> <td>    0.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td>   -0.0139</td> <td>    0.048</td> <td>   -0.290</td> <td> 0.772</td> <td>   -0.108</td> <td>    0.080</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   -0.0528</td> <td>    0.062</td> <td>   -0.851</td> <td> 0.395</td> <td>   -0.174</td> <td>    0.069</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>   -0.0169</td> <td>    0.035</td> <td>   -0.482</td> <td> 0.629</td> <td>   -0.086</td> <td>    0.052</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>8846.156</td> <th>  Durbin-Watson:     </th>  <td>   2.017</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>233664.633</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 3.471</td>  <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>23.902</td>  <th>  Cond. No.          </th>  <td>3.13e+15</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 2.17e-27. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:      yards_after_catch   R-squared:                       0.036\n",
       "Model:                            OLS   Adj. R-squared:                  0.035\n",
       "Method:                 Least Squares   F-statistic:                     42.81\n",
       "Date:                Thu, 27 Aug 2020   Prob (F-statistic):           4.03e-84\n",
       "Time:                        17:36:32   Log-Likelihood:                -38720.\n",
       "No. Observations:               11561   AIC:                         7.746e+04\n",
       "Df Residuals:                   11550   BIC:                         7.754e+04\n",
       "Df Model:                          10                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          5.1635      0.064     80.514      0.000       5.038       5.289\n",
       "x1             0.7979      0.065     12.226      0.000       0.670       0.926\n",
       "x2             0.1015      0.069      1.463      0.144      -0.035       0.238\n",
       "x3             0.3769      0.068      5.527      0.000       0.243       0.511\n",
       "x4            -0.2357      0.067     -3.505      0.000      -0.368      -0.104\n",
       "x5            -0.9492      0.065    -14.616      0.000      -1.076      -0.822\n",
       "x6             0.0353      0.065      0.547      0.584      -0.091       0.162\n",
       "x7            -0.1303      0.065     -2.011      0.044      -0.257      -0.003\n",
       "x8             0.0575      0.049      1.162      0.245      -0.039       0.155\n",
       "x9            -0.0139      0.048     -0.290      0.772      -0.108       0.080\n",
       "x10           -0.0528      0.062     -0.851      0.395      -0.174       0.069\n",
       "x11           -0.0169      0.035     -0.482      0.629      -0.086       0.052\n",
       "==============================================================================\n",
       "Omnibus:                     8846.156   Durbin-Watson:                   2.017\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           233664.633\n",
       "Skew:                           3.471   Prob(JB):                         0.00\n",
       "Kurtosis:                      23.902   Cond. No.                     3.13e+15\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 2.17e-27. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_statsmodels.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make Prededictions on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "## set an intercept/constant\n",
    "X_test = smf.add_constant(X_test)\n",
    "\n",
    "## make predictions\n",
    "preds = fit_statsmodels.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid = y_test - preds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of Residuals')"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(resid)\n",
    "plt.title(\"Histogram of Residuals\", size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate mean absolute error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5361872627598965"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae = resid.abs().mean()\n",
    "mae"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.098360483784845"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_resid = resid ** 2\n",
    "mse = sq_resid.mean()\n",
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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