05-intersection-char-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intersection Crash Analysis Using Only Intersection Characteristics\n",
    "\n",
    "Linear regression analysis of factors affecting red light crashes\n",
    "\n",
    "This data is created by me. It is from dictionary contained in this repository under the file 'int_chars.py'.\n",
    "\n",
    "To create this file, I went through all 180+ intersections with red light cameras. I cross referenced it with a map at https://data.cityofchicago.org/Transportation/Average-Daily-Traffic-Counts-Map/pf56-35rv and google maps to compile the following data.\n",
    "\n",
    "- roads (list): of road segments as identified in average-daily-traffic-counts db in link above. Used to determine volume of traffic.\n",
    "- protected_turn (int): How any of the left turns are protected (left turn arrow).\n",
    "- total_lanes (int): Count of total lanes. If a road has one lane for all directions N/E/S/W bound traffic, that counts as 4. Rangees from 3 to 14 lanes.\n",
    "- medians (int): Count of physical median barriers that extend up to intersection.\n",
    "- exit (int): 0 if no exit. 1 if exit on/off ramp within 100m of center of intersection. Traffic flow is affected by proximity to exit.\n",
    "- split (int): 1 if it is a divided boulevard (common in Chicago) where divided lanes are split by traffic signals in median. Look at examples on google map.\n",
    "- way (int): directions of traffic flow. A 4 way intersection might be NESW.\n",
    "- underpass (int): number of ways that have an underpass extending up to the intersection. These are notoriously bad intersections in Chicago.\n",
    "- no_left (int): number of no left turn signs. Usually with smaller streets onto larger roads or high volumne intersections.\n",
    "- angled (int): 1 if angle between two 2way roads is greater than 30 degrees (used 1/2/sqrt(3) rule to measure.\n",
    "- triangle (int): 1 if three 2way roads meet intersect or form a triangle where all 3 roads <50m\n",
    "- one_way (int): number of 1 way directions.\n",
    "- turn_lanes (int): how many directions have physical and identified turn lanes for left hand turns.\n",
    "- lat (float): latitude of center of inersection.\n",
    "- long (float): longitude\n",
    "- rlc (int): 1 for red light camera is present\n",
    "- intersection (str): name of intersection as defined in signal_crashes table in db\n",
    "- daily_traffic (int): volume of daily traffic through intersection. Sum of incoming roads from roads list.\n",
    "\n",
    "The primary purpose of the data was to get lat/long for center of intersection to assign crash data more accurately than cam location which is often 20m or more away from center.   \n",
    "The secondary purpose is to see what characteristics lead to more crashes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n",
    "from modules.myfuncs import *\n",
    "import numpy as np\n",
    "import sqlite3\n",
    "import seaborn as sns\n",
    "\n",
    "import sklearn\n",
    "from sklearn.model_selection import train_test_split, cross_val_score, KFold, GridSearchCV\n",
    "from sklearn.preprocessing import MinMaxScaler, PolynomialFeatures, scale, StandardScaler\n",
    "from sklearn.feature_selection import RFE\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn import metrics\n",
    "\n",
    "# import libraries\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import scipy.stats as stats\n",
    "import statsmodels.stats.api as sms\n",
    "\n",
    "pd.options.display.max_rows = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sqlite3 version: 2.6.0\n",
      "connected to database/rlc.db\n"
     ]
    }
   ],
   "source": [
    "conn = create_connection('database/rlc.db')  # function from myfuncs file\n",
    "c = conn.cursor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('cam_locations',), ('cam_startend',), ('daily_violations',), ('all_crashes',), ('hourly_congestion',), ('hourly_weather',), ('region_data',), ('intersection_cams',), ('all_hours',), ('int_startend',), ('intersection_chars',), ('signal_crashes',), ('daily_covid',), ('holidays',), ('rlc_all_hours',)]\n"
     ]
    }
   ],
   "source": [
    "print(sql_fetch_tables(c, conn))\n",
    "#table_info(c, conn)  # use if you need to see columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Query our data\n",
    "I would like to get hourly intersection data with the following columns:\n",
    "\n",
    "\n",
    "signal_crashes\n",
    "\t-crash_date\n",
    "\t-posted_speed_limit\n",
    "\t-device_condition\n",
    "\t-weather_condition\n",
    "\t-lighting_condition\n",
    "\t-first_crash_type\n",
    "\t-trafficway_type\n",
    "\t-alignment\n",
    "\t-roadway_surface_cond\n",
    "\t-road_defect\n",
    "\t-report_type\n",
    "\t-crash_type\n",
    "\t-damage\n",
    "\t-prim_contributory_cause\n",
    "\t-sec_contributory_cause\n",
    "\t-street_no\n",
    "\t-street_direction\n",
    "\t-street_name\n",
    "\t-most_severe_injury\n",
    "\t-injuries_total\n",
    "\t-injuries_fatal\n",
    "\t-injuries_incapacitating\n",
    "\t-injuries_non_incapacitating\n",
    "\t-injuries_reported_not_evident\n",
    "\t-injuries_no_indication\n",
    "\t-injuries_unknown\n",
    "\t-latitude\n",
    "\t-longitude\n",
    "\t-lane_cnt\n",
    "\t-work_zone_i\n",
    "\t-work_zone_type\n",
    "\t-workers_present_i\n",
    "\t-intersection\n",
    "\t-year\n",
    "\t-month\n",
    "\t-day\n",
    "\t-hour\n",
    "\t-region_id\n",
    "\t-time\n",
    "\t-weekday\n",
    "\n",
    "hourly_weather\n",
    "\t-temp\n",
    "\t-rain_1h\n",
    "\t-rain_3h\n",
    "\t-snow_1h\n",
    "\t-snow_3h\n",
    "\t-time\n",
    "\t-year\n",
    "\t-month\n",
    "\t-day\n",
    "\t-hour\n",
    "\t-weekday\n",
    "\n",
    "hourly_congestion\n",
    "\t-year\n",
    "\t-month\n",
    "\t-day\n",
    "\t-hour\n",
    "\t-region_id\n",
    "\t-bus_count\n",
    "\t-num_reads\n",
    "\t-speed\n",
    "\t-weekday\n",
    "    \n",
    "Tables will be queried to JOIN on year, month, day, hour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "WHAT I REALLY NEED HERE\n",
    "A single dataset with the following:\n",
    "- daily intersection chars (all the stuff I entered)\n",
    "- daily intersection crashes (injuries, deaths, number etc)\n",
    "- daily wx (temp, precip mainly)\n",
    "- daily congestion (might not need this)\n",
    "- daily violations (already in the format)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cam_locations\n",
      "\t-camera_id\n",
      "\t-intersection\n",
      "\t-address\n",
      "\t-violation_date\n",
      "\t-violations\n",
      "\t-latitude\n",
      "\t-longitude\n",
      "\t-month\n",
      "\t-day\n",
      "\t-weekday\n",
      "\t-year\n",
      "\n",
      "cam_startend\n",
      "\t-camera_id\n",
      "\t-start\n",
      "\t-end\n",
      "\n",
      "daily_violations\n",
      "\t-intersection\n",
      "\t-camera_id\n",
      "\t-address\n",
      "\t-violation_date\n",
      "\t-violations\n",
      "\t-latitude\n",
      "\t-longitude\n",
      "\t-month\n",
      "\t-day\n",
      "\t-weekday\n",
      "\t-year\n",
      "\n",
      "all_crashes\n",
      "\t-crash_record_id\n",
      "\t-rd_no\n",
      "\t-crash_date\n",
      "\t-posted_speed_limit\n",
      "\t-traffic_control_device\n",
      "\t-device_condition\n",
      "\t-weather_condition\n",
      "\t-lighting_condition\n",
      "\t-first_crash_type\n",
      "\t-trafficway_type\n",
      "\t-alignment\n",
      "\t-roadway_surface_cond\n",
      "\t-road_defect\n",
      "\t-report_type\n",
      "\t-crash_type\n",
      "\t-damage\n",
      "\t-prim_contributory_cause\n",
      "\t-sec_contributory_cause\n",
      "\t-street_no\n",
      "\t-street_direction\n",
      "\t-street_name\n",
      "\t-beat_of_occurrence\n",
      "\t-num_units\n",
      "\t-most_severe_injury\n",
      "\t-injuries_total\n",
      "\t-injuries_fatal\n",
      "\t-injuries_incapacitating\n",
      "\t-injuries_non_incapacitating\n",
      "\t-injuries_reported_not_evident\n",
      "\t-injuries_no_indication\n",
      "\t-injuries_unknown\n",
      "\t-crash_hour\n",
      "\t-crash_day_of_week\n",
      "\t-crash_month\n",
      "\t-latitude\n",
      "\t-longitude\n",
      "\t-lane_cnt\n",
      "\t-intersection_related_i\n",
      "\t-hit_and_run_i\n",
      "\t-crash_date_est_i\n",
      "\t-work_zone_i\n",
      "\t-work_zone_type\n",
      "\t-workers_present_i\n",
      "\n",
      "hourly_congestion\n",
      "\t-year\n",
      "\t-month\n",
      "\t-day\n",
      "\t-hour\n",
      "\t-region_id\n",
      "\t-bus_count\n",
      "\t-num_reads\n",
      "\t-speed\n",
      "\t-weekday\n",
      "\t-quantile_speed\n",
      "\n",
      "hourly_weather\n",
      "\t-temp\n",
      "\t-rain_1h\n",
      "\t-rain_3h\n",
      "\t-snow_1h\n",
      "\t-snow_3h\n",
      "\t-weather_main\n",
      "\t-time\n",
      "\t-year\n",
      "\t-month\n",
      "\t-day\n",
      "\t-hour\n",
      "\t-weekday\n",
      "\n",
      "region_data\n",
      "\t-region_id\n",
      "\t-region\n",
      "\t-description\n",
      "\t-north\n",
      "\t-south\n",
      "\t-east\n",
      "\t-west\n",
      "\n",
      "intersection_cams\n",
      "\t-intersection\n",
      "\t-latitude\n",
      "\t-longitude\n",
      "\t-cam1\n",
      "\t-cam2\n",
      "\t-cam3\n",
      "\t-region_id\n",
      "\n",
      "all_hours\n",
      "\t-datetime\n",
      "\t-day\n",
      "\t-hour\n",
      "\t-intersection\n",
      "\t-month\n",
      "\t-year\n",
      "\n",
      "int_startend\n",
      "\t-intersection\n",
      "\t-start\n",
      "\t-end\n",
      "\n",
      "intersection_chars\n",
      "\t-protected_turn\n",
      "\t-total_lanes\n",
      "\t-medians\n",
      "\t-exit\n",
      "\t-split\n",
      "\t-way\n",
      "\t-underpass\n",
      "\t-no_left\n",
      "\t-angled\n",
      "\t-triangle\n",
      "\t-one_way\n",
      "\t-turn_lanes\n",
      "\t-lat\n",
      "\t-long\n",
      "\t-rlc\n",
      "\t-intersection\n",
      "\t-daily_traffic\n",
      "\t-speed\n",
      "\n",
      "signal_crashes\n",
      "\t-crash_record_id\n",
      "\t-rd_no\n",
      "\t-crash_date\n",
      "\t-posted_speed_limit\n",
      "\t-traffic_control_device\n",
      "\t-device_condition\n",
      "\t-weather_condition\n",
      "\t-lighting_condition\n",
      "\t-first_crash_type\n",
      "\t-trafficway_type\n",
      "\t-alignment\n",
      "\t-roadway_surface_cond\n",
      "\t-road_defect\n",
      "\t-report_type\n",
      "\t-crash_type\n",
      "\t-damage\n",
      "\t-prim_contributory_cause\n",
      "\t-sec_contributory_cause\n",
      "\t-street_no\n",
      "\t-street_direction\n",
      "\t-street_name\n",
      "\t-beat_of_occurrence\n",
      "\t-num_units\n",
      "\t-most_severe_injury\n",
      "\t-injuries_total\n",
      "\t-injuries_fatal\n",
      "\t-injuries_incapacitating\n",
      "\t-injuries_non_incapacitating\n",
      "\t-injuries_reported_not_evident\n",
      "\t-injuries_no_indication\n",
      "\t-injuries_unknown\n",
      "\t-crash_hour\n",
      "\t-crash_day_of_week\n",
      "\t-crash_month\n",
      "\t-latitude\n",
      "\t-longitude\n",
      "\t-lane_cnt\n",
      "\t-intersection_related_i\n",
      "\t-hit_and_run_i\n",
      "\t-crash_date_est_i\n",
      "\t-work_zone_i\n",
      "\t-work_zone_type\n",
      "\t-workers_present_i\n",
      "\t-intersection\n",
      "\t-year\n",
      "\t-month\n",
      "\t-day\n",
      "\t-hour\n",
      "\t-region_id\n",
      "\t-time\n",
      "\t-weekday\n",
      "\t-start\n",
      "\t-end\n",
      "\t-rlc_state\n",
      "\n",
      "daily_covid\n",
      "\t-lab_report_date\n",
      "\t-cases_total\n",
      "\t-deaths_total\n",
      "\t-cases_age_0_17\n",
      "\t-cases_age_18_29\n",
      "\t-cases_age_30_39\n",
      "\t-cases_age_40_49\n",
      "\t-cases_age_50_59\n",
      "\t-cases_age_60_69\n",
      "\t-cases_age_70_79\n",
      "\t-cases_age_80_\n",
      "\t-cases_age_unknown\n",
      "\t-cases_female\n",
      "\t-cases_male\n",
      "\t-cases_unknown_gender\n",
      "\t-cases_latinx\n",
      "\t-cases_asian_non_latinx\n",
      "\t-cases_black_non_latinx\n",
      "\t-cases_white_non_latinx\n",
      "\t-cases_other_non_latinx\n",
      "\t-cases_unknown_race_eth\n",
      "\t-deaths_0_17_yrs\n",
      "\t-deaths_18_29_yrs\n",
      "\t-deaths_30_39_yrs\n",
      "\t-deaths_40_49_yrs\n",
      "\t-deaths_50_59_yrs\n",
      "\t-deaths_60_69_yrs\n",
      "\t-deaths_70_79_yrs\n",
      "\t-deaths_80_yrs\n",
      "\t-deaths_unknown_age\n",
      "\t-deaths_female\n",
      "\t-deaths_male\n",
      "\t-deaths_unknown_gender\n",
      "\t-deaths_latinx\n",
      "\t-deaths_asian_non_latinx\n",
      "\t-deaths_black_non_latinx\n",
      "\t-deaths_white_non_latinx\n",
      "\t-deaths_other_non_latinx\n",
      "\t-deaths_unknown_race_eth\n",
      "\t-hospitalizations_total\n",
      "\t-hospitalizations_age_0_17\n",
      "\t-hospitalizations_age_18_29\n",
      "\t-hospitalizations_age_30_39\n",
      "\t-hospitalizations_age_40_49\n",
      "\t-hospitalizations_age_50_59\n",
      "\t-hospitalizations_age_60_69\n",
      "\t-hospitalizations_age_70_79\n",
      "\t-hospitalizations_age_80_\n",
      "\t-hospitalizations_age_unknown\n",
      "\t-hospitalizations_female\n",
      "\t-hospitalizations_male\n",
      "\t-hospitalizations_unknown_gender\n",
      "\t-hospitalizations_latinx\n",
      "\t-hospitalizations_asian_non_latinx\n",
      "\t-hospitalizations_black_non_latinx\n",
      "\t-hospitalizations_white_non_latinx\n",
      "\t-hospitalizations_other_race_non_latinx\n",
      "\t-hospitalizations_unknown_race_ethnicity\n",
      "\n",
      "holidays\n",
      "\t-index\n",
      "\t-date\n",
      "\t-holiday\n",
      "\t-year\n",
      "\t-month\n",
      "\t-day\n",
      "\n",
      "rlc_all_hours\n",
      "\t-datetime\n",
      "\t-day\n",
      "\t-hour\n",
      "\t-intersection\n",
      "\t-month\n",
      "\t-year\n",
      "\t-rlc_state\n",
      "\n"
     ]
    }
   ],
   "source": [
    "table_info(c, conn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>injuries_per_year</th>\n",
       "      <th>crash_per_year</th>\n",
       "      <th>rear_end_per_year</th>\n",
       "      <th>n_crash</th>\n",
       "      <th>injuries</th>\n",
       "      <th>traffic_per_lane</th>\n",
       "      <th>protected_ratio</th>\n",
       "      <th>daily_traffic</th>\n",
       "      <th>million_cars_per_year</th>\n",
       "      <th>avg_violations</th>\n",
       "      <th>...</th>\n",
       "      <th>one_way</th>\n",
       "      <th>turn_lanes</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>rlc</th>\n",
       "      <th>intersection</th>\n",
       "      <th>daily_traffic</th>\n",
       "      <th>speed</th>\n",
       "      <th>lanes_per_direction</th>\n",
       "      <th>region_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>10.461538</td>\n",
       "      <td>13.846154</td>\n",
       "      <td>3.384615</td>\n",
       "      <td>45.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>7183.0</td>\n",
       "      <td>0</td>\n",
       "      <td>43100</td>\n",
       "      <td>15.7315</td>\n",
       "      <td>6.180218</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>41.692362</td>\n",
       "      <td>-87.642423</td>\n",
       "      <td>1</td>\n",
       "      <td>111TH AND HALSTED</td>\n",
       "      <td>43100</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.307692</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7083.0</td>\n",
       "      <td>1</td>\n",
       "      <td>42500</td>\n",
       "      <td>15.5125</td>\n",
       "      <td>6.321429</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>41.685089</td>\n",
       "      <td>-87.642094</td>\n",
       "      <td>1</td>\n",
       "      <td>115TH AND HALSTED</td>\n",
       "      <td>42500</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>6.769231</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>1.846154</td>\n",
       "      <td>39.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>6966.0</td>\n",
       "      <td>1</td>\n",
       "      <td>41800</td>\n",
       "      <td>15.2570</td>\n",
       "      <td>6.405021</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>41.677774</td>\n",
       "      <td>-87.641930</td>\n",
       "      <td>1</td>\n",
       "      <td>119TH AND HALSTED</td>\n",
       "      <td>41800</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>5.846154</td>\n",
       "      <td>13.538462</td>\n",
       "      <td>2.461538</td>\n",
       "      <td>44.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>3650.0</td>\n",
       "      <td>0</td>\n",
       "      <td>36500</td>\n",
       "      <td>13.3225</td>\n",
       "      <td>8.567300</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>41.838441</td>\n",
       "      <td>-87.617338</td>\n",
       "      <td>1</td>\n",
       "      <td>31ST ST AND MARTIN LUTHER KING DRIVE</td>\n",
       "      <td>36500</td>\n",
       "      <td>35</td>\n",
       "      <td>2.5</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5.846154</td>\n",
       "      <td>22.461538</td>\n",
       "      <td>4.923077</td>\n",
       "      <td>73.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>5300.0</td>\n",
       "      <td>0</td>\n",
       "      <td>42400</td>\n",
       "      <td>15.4760</td>\n",
       "      <td>3.211443</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>41.830281</td>\n",
       "      <td>-87.684775</td>\n",
       "      <td>1</td>\n",
       "      <td>35TH AND WESTERN</td>\n",
       "      <td>42400</td>\n",
       "      <td>35</td>\n",
       "      <td>2.0</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   injuries_per_year  crash_per_year  rear_end_per_year  n_crash  injuries  \\\n",
       "0          10.461538       13.846154           3.384615     45.0      34.0   \n",
       "1           0.000000        0.307692           0.000000      1.0       0.0   \n",
       "2           6.769231       12.000000           1.846154     39.0      22.0   \n",
       "3           5.846154       13.538462           2.461538     44.0      19.0   \n",
       "4           5.846154       22.461538           4.923077     73.0      19.0   \n",
       "\n",
       "   traffic_per_lane  protected_ratio  daily_traffic  million_cars_per_year  \\\n",
       "0            7183.0                0          43100                15.7315   \n",
       "1            7083.0                1          42500                15.5125   \n",
       "2            6966.0                1          41800                15.2570   \n",
       "3            3650.0                0          36500                13.3225   \n",
       "4            5300.0                0          42400                15.4760   \n",
       "\n",
       "   avg_violations  ...  one_way  turn_lanes        lat       long  rlc  \\\n",
       "0        6.180218  ...        0           2  41.692362 -87.642423    1   \n",
       "1        6.321429  ...        0           4  41.685089 -87.642094    1   \n",
       "2        6.405021  ...        0           4  41.677774 -87.641930    1   \n",
       "3        8.567300  ...        0           0  41.838441 -87.617338    1   \n",
       "4        3.211443  ...        0           2  41.830281 -87.684775    1   \n",
       "\n",
       "                           intersection  daily_traffic  speed  \\\n",
       "0                     111TH AND HALSTED          43100     35   \n",
       "1                     115TH AND HALSTED          42500     35   \n",
       "2                     119TH AND HALSTED          41800     35   \n",
       "3  31ST ST AND MARTIN LUTHER KING DRIVE          36500     35   \n",
       "4                      35TH AND WESTERN          42400     35   \n",
       "\n",
       "   lanes_per_direction  region_id  \n",
       "0                  1.5         26  \n",
       "1                  1.5         26  \n",
       "2                  1.5         26  \n",
       "3                  2.5         16  \n",
       "4                  2.0         15  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#create my db\n",
    "crash_df = pd.read_sql_query('''\n",
    "WITH v AS(SELECT violations,\n",
    "                 intersection,\n",
    "                 year,\n",
    "                 month,\n",
    "                 day\n",
    "        FROM daily_violations\n",
    "        WHERE violation_date >= \\'2017-09-01\\' AND violation_date <= \\'2020-12-31\\'\n",
    "        GROUP BY year, month, day, intersection\n",
    "        ),\n",
    "    ic AS(SELECT *\n",
    "         FROM intersection_chars\n",
    "        ),\n",
    "    cr AS(SELECT COUNT(crash_record_id) as n_crash,\n",
    "                 SUM(injuries_total) as injuries,\n",
    "                 intersection,\n",
    "                 year,\n",
    "                 month,\n",
    "                 day,\n",
    "                SUM(first_crash_type = 'REAR END') as rear_end\n",
    "         FROM signal_crashes \n",
    "        WHERE crash_date >= \\'2017-09-01\\' AND crash_date <= \\'2020-12-31\\'\n",
    "         GROUP BY year, month, day, intersection\n",
    "        ),\n",
    "    \n",
    "    ah AS(SELECT intersection, \n",
    "                COUNT(year) as n_cams,\n",
    "                year,\n",
    "                month,\n",
    "                day\n",
    "            FROM rlc_all_hours \n",
    "            WHERE rlc_state=1 \n",
    "            GROUP BY year, month, day, intersection\n",
    "            ),\n",
    "    \n",
    "    rg AS(SELECT region_id, intersection \n",
    "        FROM intersection_cams\n",
    "        GROUP BY intersection)\n",
    "    \n",
    "\n",
    "SELECT \n",
    "    (CAST(SUM(cr.injuries) AS FLOAT) / 3.25) as injuries_per_year,\n",
    "    (CAST(SUM(cr.n_crash) AS FLOAT)/ 3.25) as crash_per_year,\n",
    "    (CAST(SUM(cr.rear_end) AS FLOAT)/ 3.25) as rear_end_per_year,\n",
    "    SUM(cr.n_crash) as n_crash,\n",
    "    SUM(cr.injuries) as injuries,\n",
    "    \n",
    "    (CAST((ic.daily_traffic/ic.total_lanes) AS FLOAT)) as traffic_per_lane,\n",
    "    ic.protected_turn/ic.way as protected_ratio,\n",
    "    \n",
    "    ic.daily_traffic,\n",
    "    (ic.daily_traffic * 365) /1e6 AS million_cars_per_year,\n",
    "    \n",
    "    AVG(v.violations) as avg_violations,\n",
    "    \n",
    "    (ic.exit + ic.triangle + ic.angled + ic.underpass + way/4 - 1) as complexity,\n",
    "\n",
    "    ic.*,\n",
    "\n",
    "    (CAST(ic.total_lanes AS FLOAT)/ic.way) AS lanes_per_direction,  \n",
    "    \n",
    "    rg.region_id\n",
    "\n",
    "FROM ah\n",
    "LEFT JOIN v\n",
    "    ON v.year = ah.year\n",
    "    AND v.month = ah.month\n",
    "    AND v.day = ah.day\n",
    "    AND v.intersection = ah.intersection\n",
    "LEFT JOIN cr\n",
    "    ON cr.year = ah.year\n",
    "    AND cr.month = ah.month\n",
    "    AND cr.day = ah.day\n",
    "    AND cr.intersection = ah.intersection\n",
    "LEFT JOIN ic\n",
    "    ON ic.intersection = ah.intersection\n",
    "LEFT JOIN rg\n",
    "    ON rg.intersection = ah.intersection\n",
    "    \n",
    "GROUP BY ah.intersection\n",
    "ORDER BY ah.intersection\n",
    "                                    ''', conn)\n",
    "\n",
    "crash_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "crash_df.describe()\n",
    "crash_df.isna().sum()\n",
    "crash_df.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>injuries_per_year</th>\n",
       "      <th>crash_per_year</th>\n",
       "      <th>rear_end_per_year</th>\n",
       "      <th>n_crash</th>\n",
       "      <th>injuries</th>\n",
       "      <th>traffic_per_lane</th>\n",
       "      <th>protected_ratio</th>\n",
       "      <th>daily_traffic</th>\n",
       "      <th>million_cars_per_year</th>\n",
       "      <th>avg_violations</th>\n",
       "      <th>...</th>\n",
       "      <th>no_left</th>\n",
       "      <th>angled</th>\n",
       "      <th>triangle</th>\n",
       "      <th>one_way</th>\n",
       "      <th>turn_lanes</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>rlc</th>\n",
       "      <th>speed</th>\n",
       "      <th>lanes_per_direction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.0</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>4.664615</td>\n",
       "      <td>12.038974</td>\n",
       "      <td>3.128205</td>\n",
       "      <td>39.126667</td>\n",
       "      <td>15.160000</td>\n",
       "      <td>8077.553333</td>\n",
       "      <td>0.346667</td>\n",
       "      <td>51010.666667</td>\n",
       "      <td>18.618893</td>\n",
       "      <td>5.457007</td>\n",
       "      <td>...</td>\n",
       "      <td>0.246667</td>\n",
       "      <td>0.146667</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.206667</td>\n",
       "      <td>3.280000</td>\n",
       "      <td>41.882333</td>\n",
       "      <td>-87.698173</td>\n",
       "      <td>1.0</td>\n",
       "      <td>35.700000</td>\n",
       "      <td>1.600333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>3.689395</td>\n",
       "      <td>7.603059</td>\n",
       "      <td>2.123817</td>\n",
       "      <td>24.709941</td>\n",
       "      <td>11.990533</td>\n",
       "      <td>2210.363882</td>\n",
       "      <td>0.477503</td>\n",
       "      <td>14445.993600</td>\n",
       "      <td>5.272788</td>\n",
       "      <td>4.428081</td>\n",
       "      <td>...</td>\n",
       "      <td>0.633904</td>\n",
       "      <td>0.373388</td>\n",
       "      <td>0.373927</td>\n",
       "      <td>0.571078</td>\n",
       "      <td>1.295941</td>\n",
       "      <td>0.083481</td>\n",
       "      <td>0.050689</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.572358</td>\n",
       "      <td>0.427832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.307692</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3011.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>21600.000000</td>\n",
       "      <td>7.884000</td>\n",
       "      <td>1.575975</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>41.677774</td>\n",
       "      <td>-87.812226</td>\n",
       "      <td>1.0</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>2.461538</td>\n",
       "      <td>7.461538</td>\n",
       "      <td>1.846154</td>\n",
       "      <td>24.250000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>6585.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>41875.000000</td>\n",
       "      <td>15.284375</td>\n",
       "      <td>2.948526</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>41.810519</td>\n",
       "      <td>-87.735973</td>\n",
       "      <td>1.0</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>3.692308</td>\n",
       "      <td>10.461538</td>\n",
       "      <td>2.769231</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>8062.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>49200.000000</td>\n",
       "      <td>17.958000</td>\n",
       "      <td>3.908946</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>41.903494</td>\n",
       "      <td>-87.698817</td>\n",
       "      <td>1.0</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>5.846154</td>\n",
       "      <td>15.384615</td>\n",
       "      <td>3.923077</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>9650.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>58150.000000</td>\n",
       "      <td>21.224750</td>\n",
       "      <td>6.286126</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>41.945854</td>\n",
       "      <td>-87.662371</td>\n",
       "      <td>1.0</td>\n",
       "      <td>35.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>30.461538</td>\n",
       "      <td>69.538462</td>\n",
       "      <td>16.615385</td>\n",
       "      <td>226.000000</td>\n",
       "      <td>99.000000</td>\n",
       "      <td>13925.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>105500.000000</td>\n",
       "      <td>38.507500</td>\n",
       "      <td>27.870066</td>\n",
       "      <td>...</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>42.012234</td>\n",
       "      <td>-87.575373</td>\n",
       "      <td>1.0</td>\n",
       "      <td>65.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 28 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       injuries_per_year  crash_per_year  rear_end_per_year     n_crash  \\\n",
       "count         150.000000      150.000000         150.000000  150.000000   \n",
       "mean            4.664615       12.038974           3.128205   39.126667   \n",
       "std             3.689395        7.603059           2.123817   24.709941   \n",
       "min             0.000000        0.307692           0.000000    1.000000   \n",
       "25%             2.461538        7.461538           1.846154   24.250000   \n",
       "50%             3.692308       10.461538           2.769231   34.000000   \n",
       "75%             5.846154       15.384615           3.923077   50.000000   \n",
       "max            30.461538       69.538462          16.615385  226.000000   \n",
       "\n",
       "         injuries  traffic_per_lane  protected_ratio  daily_traffic  \\\n",
       "count  150.000000        150.000000       150.000000     150.000000   \n",
       "mean    15.160000       8077.553333         0.346667   51010.666667   \n",
       "std     11.990533       2210.363882         0.477503   14445.993600   \n",
       "min      0.000000       3011.000000         0.000000   21600.000000   \n",
       "25%      8.000000       6585.500000         0.000000   41875.000000   \n",
       "50%     12.000000       8062.500000         0.000000   49200.000000   \n",
       "75%     19.000000       9650.000000         1.000000   58150.000000   \n",
       "max     99.000000      13925.000000         1.000000  105500.000000   \n",
       "\n",
       "       million_cars_per_year  avg_violations  ...     no_left      angled  \\\n",
       "count             150.000000      150.000000  ...  150.000000  150.000000   \n",
       "mean               18.618893        5.457007  ...    0.246667    0.146667   \n",
       "std                 5.272788        4.428081  ...    0.633904    0.373388   \n",
       "min                 7.884000        1.575975  ...    0.000000    0.000000   \n",
       "25%                15.284375        2.948526  ...    0.000000    0.000000   \n",
       "50%                17.958000        3.908946  ...    0.000000    0.000000   \n",
       "75%                21.224750        6.286126  ...    0.000000    0.000000   \n",
       "max                38.507500       27.870066  ...    3.000000    2.000000   \n",
       "\n",
       "         triangle     one_way  turn_lanes         lat        long    rlc  \\\n",
       "count  150.000000  150.000000  150.000000  150.000000  150.000000  150.0   \n",
       "mean     0.166667    0.206667    3.280000   41.882333  -87.698173    1.0   \n",
       "std      0.373927    0.571078    1.295941    0.083481    0.050689    0.0   \n",
       "min      0.000000    0.000000    0.000000   41.677774  -87.812226    1.0   \n",
       "25%      0.000000    0.000000    2.000000   41.810519  -87.735973    1.0   \n",
       "50%      0.000000    0.000000    4.000000   41.903494  -87.698817    1.0   \n",
       "75%      0.000000    0.000000    4.000000   41.945854  -87.662371    1.0   \n",
       "max      1.000000    3.000000    6.000000   42.012234  -87.575373    1.0   \n",
       "\n",
       "            speed  lanes_per_direction  \n",
       "count  150.000000           150.000000  \n",
       "mean    35.700000             1.600333  \n",
       "std      3.572358             0.427832  \n",
       "min     30.000000             1.000000  \n",
       "25%     35.000000             1.500000  \n",
       "50%     35.000000             1.500000  \n",
       "75%     35.000000             2.000000  \n",
       "max     65.000000             3.000000  \n",
       "\n",
       "[8 rows x 28 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crash_df.drop_duplicates(inplace=True)\n",
    "crash_df = crash_df.loc[:,~crash_df.columns.duplicated()]  # had a single dupe column preventing modeling\n",
    "crash_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['injuries_per_year', 'crash_per_year', 'rear_end_per_year', 'n_crash',\n",
       "       'injuries', 'traffic_per_lane', 'protected_ratio', 'daily_traffic',\n",
       "       'million_cars_per_year', 'avg_violations', 'complexity',\n",
       "       'protected_turn', 'total_lanes', 'medians', 'exit', 'split', 'way',\n",
       "       'underpass', 'no_left', 'angled', 'triangle', 'one_way', 'turn_lanes',\n",
       "       'lat', 'long', 'rlc', 'intersection', 'speed', 'lanes_per_direction',\n",
       "       'region_id'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crash_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['crash_record_id']\n"
     ]
    }
   ],
   "source": [
    "# need to drop all of the rows I don't have data for\n",
    "try:\n",
    "    crash_df.dropna(subset=['crash_record_id'], inplace=True)\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now drop out the rows that do not have daily violations. Should cure all our nans\n",
    "# Some of these cams were only running before our query.\n",
    "crash_df.dropna(subset=['avg_violations'], inplace=True)\n",
    "crash_df.dropna(subset=['intersection'], inplace=True)\n",
    "crash_df = crash_df.loc[:,~crash_df.columns.duplicated()]  # had a dupe column preventing modeling\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a pretty solid dataframe to do analysis on the red light intersections.\n",
    "\n",
    "We would like to know what factors affect the target (danger)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['injuries_per_year', 'crash_per_year', 'rear_end_per_year', 'n_crash',\n",
      "       'injuries', 'traffic_per_lane', 'protected_ratio', 'daily_traffic',\n",
      "       'million_cars_per_year', 'avg_violations', 'complexity',\n",
      "       'protected_turn', 'total_lanes', 'medians', 'exit', 'split', 'way',\n",
      "       'underpass', 'no_left', 'angled', 'triangle', 'one_way', 'turn_lanes',\n",
      "       'lat', 'long', 'rlc', 'intersection', 'speed', 'lanes_per_direction',\n",
      "       'region_id'],\n",
      "      dtype='object')\n"
     ]
    },
    {
     "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>injuries_per_year</th>\n",
       "      <th>crash_per_year</th>\n",
       "      <th>rear_end_per_year</th>\n",
       "      <th>n_crash</th>\n",
       "      <th>injuries</th>\n",
       "      <th>traffic_per_lane</th>\n",
       "      <th>protected_ratio</th>\n",
       "      <th>daily_traffic</th>\n",
       "      <th>million_cars_per_year</th>\n",
       "      <th>avg_violations</th>\n",
       "      <th>...</th>\n",
       "      <th>triangle</th>\n",
       "      <th>one_way</th>\n",
       "      <th>turn_lanes</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>rlc</th>\n",
       "      <th>intersection</th>\n",
       "      <th>speed</th>\n",
       "      <th>lanes_per_direction</th>\n",
       "      <th>region_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>10.461538</td>\n",
       "      <td>13.846154</td>\n",
       "      <td>3.384615</td>\n",
       "      <td>45.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>7183.0</td>\n",
       "      <td>0</td>\n",
       "      <td>43100</td>\n",
       "      <td>15.7315</td>\n",
       "      <td>6.180218</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>41.692362</td>\n",
       "      <td>-87.642423</td>\n",
       "      <td>1</td>\n",
       "      <td>111TH AND HALSTED</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.307692</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7083.0</td>\n",
       "      <td>1</td>\n",
       "      <td>42500</td>\n",
       "      <td>15.5125</td>\n",
       "      <td>6.321429</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>41.685089</td>\n",
       "      <td>-87.642094</td>\n",
       "      <td>1</td>\n",
       "      <td>115TH AND HALSTED</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>6.769231</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>1.846154</td>\n",
       "      <td>39.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>6966.0</td>\n",
       "      <td>1</td>\n",
       "      <td>41800</td>\n",
       "      <td>15.2570</td>\n",
       "      <td>6.405021</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>41.677774</td>\n",
       "      <td>-87.641930</td>\n",
       "      <td>1</td>\n",
       "      <td>119TH AND HALSTED</td>\n",
       "      <td>35</td>\n",
       "      <td>1.5</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>5.846154</td>\n",
       "      <td>13.538462</td>\n",
       "      <td>2.461538</td>\n",
       "      <td>44.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>3650.0</td>\n",
       "      <td>0</td>\n",
       "      <td>36500</td>\n",
       "      <td>13.3225</td>\n",
       "      <td>8.567300</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>41.838441</td>\n",
       "      <td>-87.617338</td>\n",
       "      <td>1</td>\n",
       "      <td>31ST ST AND MARTIN LUTHER KING DRIVE</td>\n",
       "      <td>35</td>\n",
       "      <td>2.5</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5.846154</td>\n",
       "      <td>22.461538</td>\n",
       "      <td>4.923077</td>\n",
       "      <td>73.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>5300.0</td>\n",
       "      <td>0</td>\n",
       "      <td>42400</td>\n",
       "      <td>15.4760</td>\n",
       "      <td>3.211443</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>41.830281</td>\n",
       "      <td>-87.684775</td>\n",
       "      <td>1</td>\n",
       "      <td>35TH AND WESTERN</td>\n",
       "      <td>35</td>\n",
       "      <td>2.0</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   injuries_per_year  crash_per_year  rear_end_per_year  n_crash  injuries  \\\n",
       "0          10.461538       13.846154           3.384615     45.0      34.0   \n",
       "1           0.000000        0.307692           0.000000      1.0       0.0   \n",
       "2           6.769231       12.000000           1.846154     39.0      22.0   \n",
       "3           5.846154       13.538462           2.461538     44.0      19.0   \n",
       "4           5.846154       22.461538           4.923077     73.0      19.0   \n",
       "\n",
       "   traffic_per_lane  protected_ratio  daily_traffic  million_cars_per_year  \\\n",
       "0            7183.0                0          43100                15.7315   \n",
       "1            7083.0                1          42500                15.5125   \n",
       "2            6966.0                1          41800                15.2570   \n",
       "3            3650.0                0          36500                13.3225   \n",
       "4            5300.0                0          42400                15.4760   \n",
       "\n",
       "   avg_violations  ...  triangle  one_way  turn_lanes        lat       long  \\\n",
       "0        6.180218  ...         0        0           2  41.692362 -87.642423   \n",
       "1        6.321429  ...         0        0           4  41.685089 -87.642094   \n",
       "2        6.405021  ...         0        0           4  41.677774 -87.641930   \n",
       "3        8.567300  ...         0        0           0  41.838441 -87.617338   \n",
       "4        3.211443  ...         0        0           2  41.830281 -87.684775   \n",
       "\n",
       "   rlc                          intersection  speed  lanes_per_direction  \\\n",
       "0    1                     111TH AND HALSTED     35                  1.5   \n",
       "1    1                     115TH AND HALSTED     35                  1.5   \n",
       "2    1                     119TH AND HALSTED     35                  1.5   \n",
       "3    1  31ST ST AND MARTIN LUTHER KING DRIVE     35                  2.5   \n",
       "4    1                      35TH AND WESTERN     35                  2.0   \n",
       "\n",
       "   region_id  \n",
       "0         26  \n",
       "1         26  \n",
       "2         26  \n",
       "3         16  \n",
       "4         15  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_final = crash_df.copy()  # so I don't change my dataset\n",
    "print(df_final.columns)\n",
    "df_final.head()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single variable regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CRASH_PER_YEAR **** CRASH_PER_YEAR **** CRASH_PER_YEAR **** CRASH_PER_YEAR **** CRASH_PER_YEAR **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 6.110e+32\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):               0.00\n",
      "Time:                        16:01:10   Log-Likelihood:                 4770.5\n",
      "No. Observations:                 150   AIC:                            -9537.\n",
      "Df Residuals:                     148   BIC:                            -9531.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept       3.997e-15   5.75e-16      6.945      0.000    2.86e-15    5.13e-15\n",
      "crash_per_year     1.0000   4.05e-17   2.47e+16      0.000       1.000       1.000\n",
      "==============================================================================\n",
      "Omnibus:                       91.160   Durbin-Watson:                   0.047\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4474.867\n",
      "Skew:                          -1.318   Prob(JB):                         0.00\n",
      "Kurtosis:                      29.628   Cond. No.                         26.8\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "AVG_VIOLATIONS **** AVG_VIOLATIONS **** AVG_VIOLATIONS **** AVG_VIOLATIONS **** AVG_VIOLATIONS **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.076\n",
      "Model:                            OLS   Adj. R-squared:                  0.069\n",
      "Method:                 Least Squares   F-statistic:                     12.09\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           0.000665\n",
      "Time:                        16:01:10   Log-Likelihood:                -510.73\n",
      "No. Observations:                 150   AIC:                             1025.\n",
      "Df Residuals:                     148   BIC:                             1031.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept          9.4637      0.952      9.937      0.000       7.582      11.346\n",
      "avg_violations     0.4719      0.136      3.478      0.001       0.204       0.740\n",
      "==============================================================================\n",
      "Omnibus:                      161.345   Durbin-Watson:                   1.810\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4831.082\n",
      "Skew:                           3.846   Prob(JB):                         0.00\n",
      "Kurtosis:                      29.717   Cond. No.                         11.3\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "TOTAL_LANES **** TOTAL_LANES **** TOTAL_LANES **** TOTAL_LANES **** TOTAL_LANES **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.323\n",
      "Model:                            OLS   Adj. R-squared:                  0.319\n",
      "Method:                 Least Squares   F-statistic:                     70.72\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           3.18e-14\n",
      "Time:                        16:01:10   Log-Likelihood:                -487.33\n",
      "No. Observations:                 150   AIC:                             978.7\n",
      "Df Residuals:                     148   BIC:                             984.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept      -3.0879      1.870     -1.651      0.101      -6.784       0.608\n",
      "total_lanes     2.3036      0.274      8.410      0.000       1.762       2.845\n",
      "==============================================================================\n",
      "Omnibus:                       62.949   Durbin-Watson:                   1.841\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              311.568\n",
      "Skew:                           1.431   Prob(JB):                     2.21e-68\n",
      "Kurtosis:                       9.454   Cond. No.                         25.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "MEDIANS **** MEDIANS **** MEDIANS **** MEDIANS **** MEDIANS **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.104\n",
      "Model:                            OLS   Adj. R-squared:                  0.098\n",
      "Method:                 Least Squares   F-statistic:                     17.10\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           5.92e-05\n",
      "Time:                        16:01:10   Log-Likelihood:                -508.42\n",
      "No. Observations:                 150   AIC:                             1021.\n",
      "Df Residuals:                     148   BIC:                             1027.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     10.6561      0.678     15.718      0.000       9.316      11.996\n",
      "medians        3.0960      0.749      4.135      0.000       1.617       4.576\n",
      "==============================================================================\n",
      "Omnibus:                      126.695   Durbin-Watson:                   1.908\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2263.250\n",
      "Skew:                           2.812   Prob(JB):                         0.00\n",
      "Kurtosis:                      21.179   Cond. No.                         1.73\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "WAY **** WAY **** WAY **** WAY **** WAY **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.124\n",
      "Model:                            OLS   Adj. R-squared:                  0.118\n",
      "Method:                 Least Squares   F-statistic:                     20.91\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           1.01e-05\n",
      "Time:                        16:01:10   Log-Likelihood:                -506.71\n",
      "No. Observations:                 150   AIC:                             1017.\n",
      "Df Residuals:                     148   BIC:                             1023.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -8.2811      4.481     -1.848      0.067     -17.137       0.575\n",
      "way            4.9321      1.078      4.573      0.000       2.801       7.063\n",
      "==============================================================================\n",
      "Omnibus:                       68.598   Durbin-Watson:                   1.611\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              287.259\n",
      "Skew:                           1.668   Prob(JB):                     4.19e-63\n",
      "Kurtosis:                       8.902   Cond. No.                         33.8\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "SPEED **** SPEED **** SPEED **** SPEED **** SPEED **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.113\n",
      "Model:                            OLS   Adj. R-squared:                  0.107\n",
      "Method:                 Least Squares   F-statistic:                     18.81\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           2.66e-05\n",
      "Time:                        16:01:10   Log-Likelihood:                -507.65\n",
      "No. Observations:                 150   AIC:                             1019.\n",
      "Df Residuals:                     148   BIC:                             1025.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept    -13.4755      5.912     -2.279      0.024     -25.158      -1.793\n",
      "speed          0.7147      0.165      4.337      0.000       0.389       1.040\n",
      "==============================================================================\n",
      "Omnibus:                      122.210   Durbin-Watson:                   1.767\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1928.816\n",
      "Skew:                           2.718   Prob(JB):                         0.00\n",
      "Kurtosis:                      19.705   Cond. No.                         362.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "\n",
      "MILLION_CARS_PER_YEAR **** MILLION_CARS_PER_YEAR **** MILLION_CARS_PER_YEAR **** MILLION_CARS_PER_YEAR **** MILLION_CARS_PER_YEAR **** \n",
      "Red Light Camera Crash - Injuries\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         crash_per_year   R-squared:                       0.101\n",
      "Model:                            OLS   Adj. R-squared:                  0.095\n",
      "Method:                 Least Squares   F-statistic:                     16.56\n",
      "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           7.63e-05\n",
      "Time:                        16:01:10   Log-Likelihood:                -508.67\n",
      "No. Observations:                 150   AIC:                             1021.\n",
      "Df Residuals:                     148   BIC:                             1027.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=========================================================================================\n",
      "                            coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------\n",
      "Intercept                 3.5217      2.175      1.619      0.107      -0.776       7.819\n",
      "million_cars_per_year     0.4575      0.112      4.070      0.000       0.235       0.680\n",
      "==============================================================================\n",
      "Omnibus:                      117.398   Durbin-Watson:                   1.744\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1299.536\n",
      "Skew:                           2.731   Prob(JB):                    6.45e-283\n",
      "Kurtosis:                      16.345   Cond. No.                         71.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "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>ind_var</th>\n",
       "      <th>r_squared</th>\n",
       "      <th>intercept</th>\n",
       "      <th>slope</th>\n",
       "      <th>p-value</th>\n",
       "      <th>normality (JB)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>avg_violations</td>\n",
       "      <td>0.075541</td>\n",
       "      <td>9.463724e+00</td>\n",
       "      <td>0.471916</td>\n",
       "      <td>6.645041e-04</td>\n",
       "      <td>4831.082017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>million_cars_per_year</td>\n",
       "      <td>0.100645</td>\n",
       "      <td>3.521731e+00</td>\n",
       "      <td>0.457452</td>\n",
       "      <td>7.633114e-05</td>\n",
       "      <td>1299.535500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>medians</td>\n",
       "      <td>0.103579</td>\n",
       "      <td>1.065608e+01</td>\n",
       "      <td>3.096031</td>\n",
       "      <td>5.916961e-05</td>\n",
       "      <td>2263.249572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>speed</td>\n",
       "      <td>0.112764</td>\n",
       "      <td>-1.347549e+01</td>\n",
       "      <td>0.714691</td>\n",
       "      <td>2.657669e-05</td>\n",
       "      <td>1928.815942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>way</td>\n",
       "      <td>0.123812</td>\n",
       "      <td>-8.281115e+00</td>\n",
       "      <td>4.932061</td>\n",
       "      <td>1.007750e-05</td>\n",
       "      <td>287.258885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>total_lanes</td>\n",
       "      <td>0.323344</td>\n",
       "      <td>-3.087859e+00</td>\n",
       "      <td>2.303579</td>\n",
       "      <td>3.181382e-14</td>\n",
       "      <td>311.568432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>crash_per_year</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.996803e-15</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>4474.867162</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 ind_var  r_squared     intercept     slope       p-value  \\\n",
       "1         avg_violations   0.075541  9.463724e+00  0.471916  6.645041e-04   \n",
       "6  million_cars_per_year   0.100645  3.521731e+00  0.457452  7.633114e-05   \n",
       "3                medians   0.103579  1.065608e+01  3.096031  5.916961e-05   \n",
       "5                  speed   0.112764 -1.347549e+01  0.714691  2.657669e-05   \n",
       "4                    way   0.123812 -8.281115e+00  4.932061  1.007750e-05   \n",
       "2            total_lanes   0.323344 -3.087859e+00  2.303579  3.181382e-14   \n",
       "0         crash_per_year   1.000000  3.996803e-15  1.000000  0.000000e+00   \n",
       "\n",
       "   normality (JB)  \n",
       "1     4831.082017  \n",
       "6     1299.535500  \n",
       "3     2263.249572  \n",
       "5     1928.815942  \n",
       "4      287.258885  \n",
       "2      311.568432  \n",
       "0     4474.867162  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets look at some regressions for all of my chosen columns\n",
    "\n",
    "# import libraries\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import scipy.stats as stats\n",
    "import statsmodels.stats.api as sms\n",
    "\n",
    "# I don't need to see regression analysis for all of my variables\n",
    "target = 'crash_per_year'\n",
    "\n",
    "\n",
    "continuous = [target, 'avg_violations', 'total_lanes', 'medians', 'way', 'speed', 'million_cars_per_year']\n",
    "\n",
    "\n",
    "categoricals = ['exit', 'split', 'underpass', 'angled', 'triangle', 'no_left', 'region_id']\n",
    "\n",
    "\n",
    "\n",
    "df_cont = df_final[continuous]\n",
    "\n",
    "\n",
    "\n",
    "results = []\n",
    "\n",
    "for idx, column in enumerate(df_cont.columns):\n",
    "    print()\n",
    "    print((column.upper() + \" **** \") * 5)\n",
    "    print (\"Red Light Camera Crash - Injuries\")\n",
    "    \n",
    "    f = '{}~{}'.format(target, column)  # create my model formula\n",
    "    model = smf.ols(formula=f, data=df_cont).fit()  # fit the model\n",
    "    print(model.summary())\n",
    "    \n",
    "#     fig, axes = plt.subplots(figsize=(12,10))\n",
    "#     fig = sm.graphics.plot_regress_exog(model, column, fig=fig)\n",
    "#     fig = sm.graphics.qqplot(model.resid, dist=stats.norm, line='45', fit=True)\n",
    "#     fig.tight_layout()\n",
    "#     plt.show()\n",
    "        \n",
    "    results.append([column, model.rsquared, model.params[0], model.params[1], model.pvalues[1], sms.jarque_bera(model.resid)[0]])\n",
    "\n",
    "result_df = pd.DataFrame(results, columns=['ind_var', 'r_squared', 'intercept', 'slope', 'p-value', 'normality (JB)' ])\n",
    "result_df.sort_values(by='r_squared')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['injuries_per_year', 'crash_per_year', 'rear_end_per_year', 'n_crash',\n",
       "       'injuries', 'traffic_per_lane', 'protected_ratio', 'daily_traffic',\n",
       "       'million_cars_per_year', 'avg_violations', 'complexity',\n",
       "       'protected_turn', 'total_lanes', 'medians', 'exit', 'split', 'way',\n",
       "       'underpass', 'no_left', 'angled', 'triangle', 'one_way', 'turn_lanes',\n",
       "       'lat', 'long', 'rlc', 'intersection', 'speed', 'lanes_per_direction',\n",
       "       'region_id'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crash_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "# create correlation matrix\n",
    "plt.figure(figsize = (10,8))\n",
    "sns.heatmap(df_cont.corr(), center=0.4, cmap = \"cool\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One Hot Encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get rid of categories that have high correlation and others.\n",
    "\n",
    "df_continuous = df_cont.copy()\n",
    "#df_ohe = crash_df[categoricals] # defined earlier\n",
    "df_ohe = df_final[categoricals] # defined earlier\n",
    "df_ohe[categoricals] = df_ohe[categoricals].astype(str)\n",
    "\n",
    "# One hot encoding   \n",
    "#df_ohe = pd.get_dummies(df_ohe, columns=['way'], drop_first=True)\n",
    "df_final2 = pd.concat([df_continuous, df_ohe], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "crash_per_year           0\n",
       "avg_violations           0\n",
       "total_lanes              0\n",
       "medians                  0\n",
       "way                      0\n",
       "speed                    0\n",
       "million_cars_per_year    0\n",
       "exit                     0\n",
       "split                    0\n",
       "underpass                0\n",
       "angled                   0\n",
       "triangle                 0\n",
       "no_left                  0\n",
       "region_id                0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_final2 = df_final2.dropna()  # one intersection without crash_per_year (mislabeled)\n",
    "df_final2.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "X_ = df_final2.drop(target, axis=1)  # drop my potential targets\n",
    "\n",
    "y = df_final2[target]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "### FEATURE SELECTION\n",
    "\n",
    "#from sklearn.datasets import make_friedman1\n",
    "from sklearn.feature_selection import RFE\n",
    "from sklearn.linear_model import LinearRegression, Ridge\n",
    "\n",
    "linreg = LinearRegression()\n",
    "selector = RFE(linreg, step=1, n_features_to_select=15)\n",
    "selector = selector.fit(X_, y)\n",
    "X_transformed = selector.transform(X_)\n",
    "\n",
    "rfe_df = pd.DataFrame(list(zip(X_.columns, selector.support_, selector.ranking_, selector.estimator_.coef_)),\n",
    "                  columns=['feature', 'support', 'rank', 'coef', ])\n",
    "\n",
    "\n",
    "keepers = rfe_df.sort_values(by=['support', 'rank'], ascending=False)\n",
    "keepers.head(10)\n",
    "\n",
    "keepers.head(20)\n",
    "\n",
    "manual_keep = ['total_lanes', 'way', 'speed', 'exit', 'split', \n",
    "               'underpass', 'triangle', 'million_cars_per_year']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply my feature selection to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#X_ = X.iloc[:,selector.support_] \n",
    "# Chose not to keep n_cams because I consider it a mitigation put in place, not inherent to intersection\n",
    "X = X_[manual_keep]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_sum = '+'.join(X.columns)\n",
    "formula = target + '~' + pred_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>     <td>crash_per_year</td>  <th>  R-squared:         </th> <td>   0.500</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.468</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   15.54</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 14 Mar 2021</td> <th>  Prob (F-statistic):</th> <td>2.25e-17</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:01:31</td>     <th>  Log-Likelihood:    </th> <td> -464.68</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   150</td>      <th>  AIC:               </th> <td>   949.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   140</td>      <th>  BIC:               </th> <td>   979.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     9</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td>  -14.5614</td> <td>    6.013</td> <td>   -2.422</td> <td> 0.017</td> <td>  -26.450</td> <td>   -2.673</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>exit[T.1]</th>             <td>    5.0483</td> <td>    1.500</td> <td>    3.366</td> <td> 0.001</td> <td>    2.083</td> <td>    8.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>split[T.1]</th>            <td>   10.9146</td> <td>    2.502</td> <td>    4.362</td> <td> 0.000</td> <td>    5.968</td> <td>   15.861</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>underpass[T.1]</th>        <td>    3.0185</td> <td>    2.235</td> <td>    1.350</td> <td> 0.179</td> <td>   -1.401</td> <td>    7.438</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>underpass[T.2]</th>        <td>    0.8426</td> <td>    2.427</td> <td>    0.347</td> <td> 0.729</td> <td>   -3.957</td> <td>    5.642</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>triangle[T.1]</th>         <td>    1.2937</td> <td>    1.405</td> <td>    0.921</td> <td> 0.359</td> <td>   -1.483</td> <td>    4.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>total_lanes</th>           <td>    0.9155</td> <td>    0.345</td> <td>    2.655</td> <td> 0.009</td> <td>    0.234</td> <td>    1.597</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>way</th>                   <td>    1.4879</td> <td>    1.036</td> <td>    1.436</td> <td> 0.153</td> <td>   -0.561</td> <td>    3.537</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>speed</th>                 <td>    0.3128</td> <td>    0.137</td> <td>    2.286</td> <td> 0.024</td> <td>    0.042</td> <td>    0.583</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>million_cars_per_year</th> <td>    0.0949</td> <td>    0.108</td> <td>    0.881</td> <td> 0.380</td> <td>   -0.118</td> <td>    0.308</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>10.494</td> <th>  Durbin-Watson:     </th> <td>   1.911</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.005</td> <th>  Jarque-Bera (JB):  </th> <td>  13.840</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.426</td> <th>  Prob(JB):          </th> <td>0.000988</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.220</td> <th>  Cond. No.          </th> <td>    557.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:         crash_per_year   R-squared:                       0.500\n",
       "Model:                            OLS   Adj. R-squared:                  0.468\n",
       "Method:                 Least Squares   F-statistic:                     15.54\n",
       "Date:                Sun, 14 Mar 2021   Prob (F-statistic):           2.25e-17\n",
       "Time:                        16:01:31   Log-Likelihood:                -464.68\n",
       "No. Observations:                 150   AIC:                             949.4\n",
       "Df Residuals:                     140   BIC:                             979.5\n",
       "Df Model:                           9                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept               -14.5614      6.013     -2.422      0.017     -26.450      -2.673\n",
       "exit[T.1]                 5.0483      1.500      3.366      0.001       2.083       8.014\n",
       "split[T.1]               10.9146      2.502      4.362      0.000       5.968      15.861\n",
       "underpass[T.1]            3.0185      2.235      1.350      0.179      -1.401       7.438\n",
       "underpass[T.2]            0.8426      2.427      0.347      0.729      -3.957       5.642\n",
       "triangle[T.1]             1.2937      1.405      0.921      0.359      -1.483       4.071\n",
       "total_lanes               0.9155      0.345      2.655      0.009       0.234       1.597\n",
       "way                       1.4879      1.036      1.436      0.153      -0.561       3.537\n",
       "speed                     0.3128      0.137      2.286      0.024       0.042       0.583\n",
       "million_cars_per_year     0.0949      0.108      0.881      0.380      -0.118       0.308\n",
       "==============================================================================\n",
       "Omnibus:                       10.494   Durbin-Watson:                   1.911\n",
       "Prob(Omnibus):                  0.005   Jarque-Bera (JB):               13.840\n",
       "Skew:                           0.426   Prob(JB):                     0.000988\n",
       "Kurtosis:                       4.220   Cond. No.                         557.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula=formula, data=pd.concat([X, y], axis=1)).fit()\n",
    "model.summary()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bad:\n",
    "Large JB is troubling.  Errors are not normally distributed.\n",
    "This is the lowest I could get the BIC and AIC.\n",
    "\n",
    "\n",
    "The good\n",
    "F-statistic looks okay with low pval.\n",
    "Low skew value is good to see."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cross_val(model, X, y):\n",
    "    # return a cross val score for my models\n",
    "    pred = cross_val_score(model, X, y, cv=5, scoring='r2')\n",
    "    return -pred.mean()\n",
    "\n",
    "def print_evaluate(true, predicted):  \n",
    "    # print out all of my stats for the model\n",
    "    mae, mse, rmse, r2 = evaluate(true, predicted)\n",
    "    print('MAE: {:.2f}'.format(mae))\n",
    "    print('MSE: {:.2f}'.format(mse))\n",
    "    print('RMSE: {:.2f}'.format(rmse))\n",
    "    print('R2: {:.2f}'.format(r2))\n",
    "    \n",
    "def evaluate(true, predicted):\n",
    "    # get multiple stats on my model predictions\n",
    "    mae = metrics.mean_absolute_error(true, predicted)\n",
    "    mse = metrics.mean_squared_error(true, predicted)\n",
    "    rmse = np.sqrt(metrics.mean_squared_error(true, predicted))\n",
    "    r2 = metrics.r2_score(true, predicted)\n",
    "    return mae, mse, rmse, r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = LinearRegression()\n",
    "reg.fit(X, y)  # my regression object\n",
    "\n",
    "pred = reg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fee018a8860>"
      ]
     },
     "execution_count": 26,
     "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": [
    "sns.regplot(y, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "sns.distplot((y - pred), bins=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean crash per year: 12.0\n",
      "Standard Dev crash per year: 7.6\n",
      "\n",
      "Linear Regression Results:\n",
      "=========================\n",
      "Test set:\n",
      "MAE: 3.98\n",
      "MSE: 28.95\n",
      "RMSE: 5.38\n",
      "R2: 0.50\n"
     ]
    }
   ],
   "source": [
    "print('Mean crash per year: {:.1f}'.format(y.mean()))\n",
    "print('Standard Dev crash per year: {:.1f}'.format(y.std()))\n",
    "\n",
    "print()\n",
    "\n",
    "print(\"Linear Regression Results:\")\n",
    "print('=========================')\n",
    "print('Test set:')\n",
    "print_evaluate(y, pred)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " total_lanes: 0.9919558621287965\n",
      "         way: 1.6232230437238457\n",
      "       speed: 0.32002302448937886\n",
      "        exit: 5.2445779558039645\n",
      "       split: 10.690637829006642\n",
      "   underpass: 0.976819319504212\n",
      "    triangle: 0.9991731927151153\n",
      "million_cars_per_year: 0.09867557626389543\n"
     ]
    },
    {
     "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>feature</th>\n",
       "      <th>coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>total_lanes</td>\n",
       "      <td>0.991956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>way</td>\n",
       "      <td>1.623223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>speed</td>\n",
       "      <td>0.320023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>exit</td>\n",
       "      <td>5.244578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>split</td>\n",
       "      <td>10.690638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>underpass</td>\n",
       "      <td>0.976819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>triangle</td>\n",
       "      <td>0.999173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>million_cars_per_year</td>\n",
       "      <td>0.098676</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 feature  coefficient\n",
       "0            total_lanes     0.991956\n",
       "1                    way     1.623223\n",
       "2                  speed     0.320023\n",
       "3                   exit     5.244578\n",
       "4                  split    10.690638\n",
       "5              underpass     0.976819\n",
       "6               triangle     0.999173\n",
       "7  million_cars_per_year     0.098676"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficients = dict(zip(X.columns,list(reg.coef_)))\n",
    "for var in coefficients:\n",
    "    print('{:>12}: {}'.format(var, coefficients[var]))\n",
    "\n",
    "coefs_df = pd.DataFrame()\n",
    "coefs_df['feature'] = list(X.columns)\n",
    "coefs_df['coefficient'] = list(reg.coef_)\n",
    "\n",
    "\n",
    "coefs_df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>Model</th>\n",
       "      <th>MAE</th>\n",
       "      <th>MSE</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>R2</th>\n",
       "      <th>Cross Validation Score (r2)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Linear Regression</td>\n",
       "      <td>3.975806</td>\n",
       "      <td>28.951023</td>\n",
       "      <td>5.380615</td>\n",
       "      <td>0.495812</td>\n",
       "      <td>0.094537</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Model       MAE        MSE      RMSE        R2  \\\n",
       "0  Linear Regression  3.975806  28.951023  5.380615  0.495812   \n",
       "\n",
       "   Cross Validation Score (r2)  \n",
       "0                     0.094537  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_df = pd.DataFrame(data=[[\"Linear Regression\", *evaluate(y, pred) , cross_val(reg, X, y)]], \n",
    "                          columns=['Model', 'MAE', 'MSE', 'RMSE', 'R2', \"Cross Validation Score (r2)\"])\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ridge Regression Results:\n",
      "=========================\n",
      "MAE: 4.00\n",
      "MSE: 29.07\n",
      "RMSE: 5.39\n",
      "R2: 0.49\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge, RidgeCV\n",
    "\n",
    "model = Ridge()\n",
    "model.fit(X, y)\n",
    "pred = model.predict(X)\n",
    "\n",
    "\n",
    "print(\"Ridge Regression Results:\")\n",
    "print('=========================')\n",
    "print_evaluate(y, pred)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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>Model</th>\n",
       "      <th>MAE</th>\n",
       "      <th>MSE</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>R2</th>\n",
       "      <th>Cross Validation Score (r2)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Linear Regression</td>\n",
       "      <td>3.975806</td>\n",
       "      <td>28.951023</td>\n",
       "      <td>5.380615</td>\n",
       "      <td>0.495812</td>\n",
       "      <td>0.094537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Ridge Regression</td>\n",
       "      <td>3.998220</td>\n",
       "      <td>29.067657</td>\n",
       "      <td>5.391443</td>\n",
       "      <td>0.493781</td>\n",
       "      <td>0.094621</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Model       MAE        MSE      RMSE        R2  \\\n",
       "0  Linear Regression  3.975806  28.951023  5.380615  0.495812   \n",
       "0   Ridge Regression  3.998220  29.067657  5.391443  0.493781   \n",
       "\n",
       "   Cross Validation Score (r2)  \n",
       "0                     0.094537  \n",
       "0                     0.094621  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge = pd.DataFrame(data=[[\"Ridge Regression\", *evaluate(y, pred) , cross_val(model, X, y)]], \n",
    "                          columns=['Model', 'MAE', 'MSE', 'RMSE', 'R2', \"Cross Validation Score (r2)\"])\n",
    "results_df.append(ridge)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "forest_cont = ['total_lanes', 'exit', 'split', 'way',\n",
    "       'angled', 'triangle', 'one_way', 'turn_lanes',\n",
    "        'million_cars_per_year', 'speed', 'underpass', 'medians']\n",
    "\n",
    "forest_cat = ['region_id']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['crash_per_year',\n",
       " 'avg_violations',\n",
       " 'total_lanes',\n",
       " 'medians',\n",
       " 'way',\n",
       " 'speed',\n",
       " 'million_cars_per_year']"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "continuous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_continuous = crash_df[forest_cont]  # ended up using same as linreg\n",
    "#df_continuous.drop(columns=[target], inplace=True)\n",
    "\n",
    "df_ohe = crash_df[forest_cat].astype(str)\n",
    "df_ohe = pd.get_dummies(df_ohe, columns=forest_cat, drop_first=True)\n",
    "\n",
    "df_final = pd.concat([df_continuous, df_ohe], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = df_final\n",
    "y = crash_df[target]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.2893754020802852"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "base = RandomForestRegressor(random_state = 42)\n",
    "base.fit(X_train, y_train)\n",
    "\n",
    "base.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 48 candidates, totalling 240 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  33 tasks      | elapsed:   10.7s\n",
      "[Parallel(n_jobs=-1)]: Done 154 tasks      | elapsed:   35.6s\n",
      "[Parallel(n_jobs=-1)]: Done 240 out of 240 | elapsed:   56.0s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, error_score='raise-deprecating',\n",
       "             estimator=RandomForestRegressor(bootstrap=True, criterion='mse',\n",
       "                                             max_depth=None,\n",
       "                                             max_features='auto',\n",
       "                                             max_leaf_nodes=None,\n",
       "                                             min_impurity_decrease=0.0,\n",
       "                                             min_impurity_split=None,\n",
       "                                             min_samples_leaf=1,\n",
       "                                             min_samples_split=2,\n",
       "                                             min_weight_fraction_leaf=0.0,\n",
       "                                             n_estimators='warn', n_jobs=None,\n",
       "                                             oob_score=False, random_state=None,\n",
       "                                             verbose=0, warm_start=False),\n",
       "             iid='warn', n_jobs=-1,\n",
       "             param_grid={'bootstrap': [True], 'max_depth': [10, 20, 30, 40],\n",
       "                         'max_features': [5, 10, 15, 20],\n",
       "                         'min_samples_leaf': [5], 'min_samples_split': [2],\n",
       "                         'n_estimators': [200, 300, 1000]},\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring=None, verbose=2)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "# Create the parameter grid based on the results of random search \n",
    "param_grid = {\n",
    "    'bootstrap': [True],\n",
    "    'max_depth': [10, 20, 30, 40],\n",
    "    'max_features': [5, 10, 15, 20],\n",
    "    'min_samples_leaf': [5],\n",
    "    'min_samples_split': [2],\n",
    "    'n_estimators': [200, 300, 1000]\n",
    "}\n",
    "\n",
    "# Create a based model\n",
    "forest = RandomForestRegressor()\n",
    "# Instantiate the grid search model\n",
    "grid_search = GridSearchCV(estimator=forest, param_grid=param_grid, cv=5, n_jobs=-1, verbose=2)\n",
    "\n",
    "grid_search.fit(X_train, y_train)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=20,\n",
       "                      max_features=20, max_leaf_nodes=None,\n",
       "                      min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "                      min_samples_leaf=5, min_samples_split=2,\n",
       "                      min_weight_fraction_leaf=0.0, n_estimators=200,\n",
       "                      n_jobs=None, oob_score=False, random_state=None,\n",
       "                      verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10546887649903647"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "forest = RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=30,\n",
    "                      max_features=10, max_leaf_nodes=None,\n",
    "                      min_impurity_decrease=0.0, min_impurity_split=None,\n",
    "                      min_samples_leaf=5, min_samples_split=2,\n",
    "                      min_weight_fraction_leaf=0.0, n_estimators=300,\n",
    "                      n_jobs=None, oob_score=False, random_state=None,\n",
    "                      verbose=0, warm_start=False)\n",
    "\n",
    "forest.fit(X_train, y_train)\n",
    "forest.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "#y_pred = forest.predict(X_test)\n",
    "y_pred = forest.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "# # Visualising the Random Forest Regression Results  \n",
    "plt.figure(figsize=[5,5])\n",
    "plt.scatter(y, y_pred, color='red')\n",
    "plt.plot([0,60], [0, 60])\n",
    "plt.title('Random Forest Regression')\n",
    "plt.xlabel('actual')\n",
    "plt.ylabel('predicted')\n",
    "plt.xlim(0,65)\n",
    "plt.ylim(0,65)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obvious outlier is a very complex intersection (Stoney Island and 79th)\n",
    "https://www.google.com/maps/place/S+South+Chicago+Ave,+Chicago,+IL+60649/@41.7517208,-87.5866419,18z/data=!3m1!4b1!4m5!3m4!1s0x880e288c47aa2dff:0x8bf4bcdffdf5f588!8m2!3d41.7517208!4d-87.5857653"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.10546887649903647\n"
     ]
    },
    {
     "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>feature</th>\n",
       "      <th>importance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>total_lanes</td>\n",
       "      <td>0.174438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>million_cars_per_year</td>\n",
       "      <td>0.154131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>speed</td>\n",
       "      <td>0.139006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>medians</td>\n",
       "      <td>0.136847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>split</td>\n",
       "      <td>0.095798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>exit</td>\n",
       "      <td>0.088499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>turn_lanes</td>\n",
       "      <td>0.065920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>underpass</td>\n",
       "      <td>0.062923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>triangle</td>\n",
       "      <td>0.018434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>33</td>\n",
       "      <td>region_id_5</td>\n",
       "      <td>0.016889</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  feature  importance\n",
       "0             total_lanes    0.174438\n",
       "8   million_cars_per_year    0.154131\n",
       "9                   speed    0.139006\n",
       "11                medians    0.136847\n",
       "2                   split    0.095798\n",
       "1                    exit    0.088499\n",
       "7              turn_lanes    0.065920\n",
       "10              underpass    0.062923\n",
       "5                triangle    0.018434\n",
       "33            region_id_5    0.016889"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(forest.score(X_test, y_test)) # r2\n",
    "df = pd.DataFrame(list(zip(X_test.columns, forest.feature_importances_)), columns=['feature', 'importance'])\n",
    "df.sort_values(by='importance', ascending=False)[:10]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Series([], Name: intersection, dtype: object)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this intersection throws almost needs it's own category.  It's insane\n",
    "crash_df[crash_df.n_crash==200]['intersection']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average crashes per year (per intersection): 12.0\n",
      "Max crashes per year: 69.5\n",
      "Min crashes per year: 0.3\n",
      "Std dev crashes per year: 7.6\n",
      "\n",
      "Model on X_test set:\n",
      "MAE: 3.36\n",
      "MSE: 16.53\n",
      "RMSE: 4.07\n",
      "R2: 0.11\n",
      "\n",
      "Model on X set:\n",
      "MAE: 3.92\n",
      "MSE: 36.67\n",
      "RMSE: 6.06\n",
      "R2: 0.36\n"
     ]
    },
    {
     "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": [
    "# Get mae to compare it\n",
    "sns.distplot(y)\n",
    "print('Average crashes per year (per intersection): {:.1f}'.format(y.mean()))\n",
    "print('Max crashes per year: {:.1f}'.format(y.max()))\n",
    "print('Min crashes per year: {:.1f}'.format(y.min()))\n",
    "print('Std dev crashes per year: {:.1f}'.format(y.std()))\n",
    "\n",
    "\n",
    "print()\n",
    "\n",
    "print(\"Model on X_test set:\")\n",
    "pred = forest.predict(X_test)\n",
    "print_evaluate(y_test, pred)\n",
    "\n",
    "print()\n",
    "pred= forest.predict(X)\n",
    "print('Model on X set:')\n",
    "print_evaluate(y, pred)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not a great result for the random forest.  It did not fare much better than the regressions.  I cold tune the hyperparameters, but will stick with Ridge regression for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results of intersection characteristic analysis\n",
    "Linear Regression gave the better results.  I kept it because of the better cross validation and the ability to interpret the results.  The r2 value is not as meaningful since we trained and scored on the same set. \n",
    "\n",
    "The random forest explained approximately 38% of the test set, but appears to be overfitting to the training set.\n",
    "\n",
    "Characteristics used : 'traffic', 'total_lanes', 'medians', 'speed', 'violations_per_year', 'n_cams'\n",
    "Most important characteristics (by rank): 'total_lanes', 'cams'\n",
    "\n",
    "These characteristics accounted for about half of the crashes by r-square value.  Adding in more characteristics improves performance, but the individual p_vals do not support their inclusion, and would risk overfitting on a small dataset.\n",
    "\n",
    "From our linear regression coefficients:\n",
    "Every 50 violations is one more accident per year. (this is the best predictor we have)\n",
    "A 6 way intersection will have about 5 more accidents per year. (2.5 per way)\n",
    "Each additional lane adds about one accident per year.\n",
    "An intersection with 10mph higher speed limit has one more accident per year.\n",
    "\n",
    "\n",
    "Only a handful of the gathered characteristics meaningfully informed the model.\n",
    "One possible hypothesis: dangerous intersections have had characteristics changed to mitigate the accidents.  Medians, no turns, protected turns, no left, cameras etc. were installed to make the intersection safer.  Perhaps they only occur at the more dangerous intersections, and their presence is the result rather than the cause of the accidents and should not be considered.  For this reason, I chose to only keep variables that were inherent to the intersection, and could not be mitigated (lanes, ways, traffic, violations, split, triangles, overpasses, exits).\n",
    "\n",
    "\n",
    "The random forest model produced a higher score (MSE) than the linear model.  It used similar features (violations, lanes, and traffic added the most predictive value to the model)"
   ]
  }
 ],
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   "language": "python",
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