analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e68dbe95",
   "metadata": {},
   "source": [
    "## Gathering BGG Data\n",
    "\n",
    "This notebook gives the web scraping pipeline to get data for each board game on BGG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c359b49",
   "metadata": {},
   "outputs": [],
   "source": [
    "import requests, bs4\n",
    "from bs4 import BeautifulSoup as bs\n",
    "import pandas as pd\n",
    "import re\n",
    "import time, os\n",
    "import ast\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import HuberRegressor\n",
    "from scipy import stats\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cab04946",
   "metadata": {},
   "outputs": [],
   "source": [
    "from selenium import webdriver\n",
    "from selenium.webdriver.common.keys import Keys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "035277b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#url = \"https://boardgamegeek.com/boardgame/586/front/stats\"\n",
    "\n",
    "#response = requests.get(url)\n",
    "#status = response.status_code\n",
    "#if status == 200:\n",
    "#  page = response.text\n",
    "#  soup = bs(page)\n",
    "#else:\n",
    "#  print(f\"Oops! Received status code {status}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6d44f29",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "575791aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-153-3ed8d520c4d8>:4: DeprecationWarning: executable_path has been deprecated, please pass in a Service object\n",
      "  driver = webdriver.Chrome(chromedriver)\n"
     ]
    }
   ],
   "source": [
    "chromedriver = \"/Applications/chromedriver\" # path to the chromedriver executable\n",
    "os.environ[\"webdriver.chrome.driver\"] = chromedriver\n",
    "\n",
    "driver = webdriver.Chrome(chromedriver)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3309d70c",
   "metadata": {},
   "source": [
    "## Stats Page\n",
    "\n",
    "We'll begin by exploring the stats page for one game. From here, we should be able to get\n",
    "\n",
    "* Number owned\n",
    "* Average rating\n",
    "* Weight\n",
    "* Recommended age\n",
    "* Min, max estimated time\n",
    "* Min, max player count\n",
    "* Community min, max and best player counts\n",
    "\n",
    "Other features to consider:\n",
    "\n",
    "* \\# of ratings\n",
    "* Std deviation of ratings\n",
    "* \\# of comments\n",
    "* \\# of plays\n",
    "* \\# of fans\n",
    "* \\# of page views\n",
    "* Prev. owned\n",
    "* Wishlist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "399b0a52",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "driver.get(\"https://boardgamegeek.com/boardgame/122691/magnum-opus/stats\")\n",
    "\n",
    "soup = bs(driver.page_source,'html5lib')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45b67168",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "2113d60c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'316'"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soup.find_all(href=re.compile(\"status=own\"))[0].text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "4b8d175a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'6.967'"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soup.find(text=re.compile(\"Avg. Rating\")).next.next.text.strip()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fe7237aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_num_owned(soup):\n",
    "    try:\n",
    "        num_str = soup.find(href=re.compile(\"status=own\")).text\n",
    "        num = int(num_str.replace(\",\",\"\"))\n",
    "        return num\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "31804ed2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "316"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_num_owned(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "10231bc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_rating(soup):\n",
    "    try:\n",
    "        return float(soup.find(text=re.compile(\"Avg. Rating\")).next.next.text.strip())\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "817788df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.967"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_rating(soup)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba60bf4f",
   "metadata": {},
   "source": [
    "### Gameplay items\n",
    "\n",
    "The gameplay item class contains 4 relevant pieces of information for us.\n",
    "\n",
    "* Player count\n",
    "* Play time\n",
    "* Player age\n",
    "* Weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "1269637e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[' \\t\\t\\t\\t \\t\\t\\t\\t\\t     2–4  \\t\\t\\t\\t\\tPlayers \\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\tCommunity: \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t\\t(no votes) \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t\\t3–4 \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t\\t— \\t\\t\\t\\t\\t\\t\\t\\tBest: 4 \\t\\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t', ' \\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t     60  Min \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\tPlaying Time \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t', ' \\t\\t\\t\\t \\t\\t\\t\\t\\tAge: \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t12+ \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\tCommunity: 12+ \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t', \" \\t\\t\\t\\t \\t\\t\\t\\t\\tWeight: \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t–– \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t2.54 \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t/ 5 Complexity Rating \\t\\t\\t\\t\\t  \\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t\\t'Complexity' Rating Results \\t\\t\\t\\t\\t\\t \\t\\t\\t\\t\\t  \\t\\t\\t\\t\\t \\t\\t\\t\\t\\t\\t Learn more about complexity ratings \\t\\t\\t\\t\\t \\t\\t\\t\\t \\t\\t\\t\"]\n"
     ]
    }
   ],
   "source": [
    "gameplay_list = soup.find_all(class_=\"gameplay-item\")\n",
    "\n",
    "print([x.text for x in gameplay_list])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c1be9c7",
   "metadata": {},
   "source": [
    "Game weight and player age are fairly straight forward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "ed749989",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.54"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(gameplay_list[3].find(text=re.compile(\"/ 5\")).previous.strip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e8188acd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_weight(soup):\n",
    "    try:\n",
    "        gameplay_list = soup.find_all(class_=\"gameplay-item\")\n",
    "\n",
    "        return float(gameplay_list[3].find(text=re.compile(\"/ 5\")).previous.strip())\n",
    "    \n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "ffa31ee3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.54"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_weight(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6212b548",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Fix this, so not dependant on +\n",
    "def get_age(soup):\n",
    "    try:\n",
    "        gameplay_list = soup.find_all(class_=\"gameplay-item\")\n",
    "        return int(gameplay_list[2].find(text=re.compile(\"\\+\")).strip().replace(\"+\",\"\"))\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "20b228df",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = get_age(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "2f2f6c54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cae10bd",
   "metadata": {},
   "source": [
    "Note this is only the age \"on the box\". There is also a community recommended age, which I am not scraping at this time. (Something to look at later)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bc6d7db",
   "metadata": {},
   "source": [
    "Play time and player counts are trickier. The way the html is structured changes based on if the minimum and maximum values are the same. For example the player count may appear as \n",
    "\n",
    "2 Players\n",
    "\n",
    "OR\n",
    "\n",
    "2 - 6 Players\n",
    "\n",
    "So we have to deal with those cases here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "10cf2656",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<span class=\"ng-binding ng-scope\" ng-if=\"min &gt; 0\">60</span>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gameplay_list[1].find_all(class_=re.compile(\"ng-binding ng-scope\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26ef858c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7e1cac87",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_minmax_time(soup):\n",
    "    try:\n",
    "        gameplay_list = soup.find_all(class_=\"gameplay-item\")\n",
    "        time_values = gameplay_list[1].find_all(class_=re.compile(\"ng-binding ng-scope\"))\n",
    "        if len(time_values) == 3:\n",
    "            return int(time_values[0].text), int(time_values[1].text.replace(\"–\",\"\"))\n",
    "        else:\n",
    "            #If only one value, same min and max time\n",
    "            value = int(time_values[0].text)\n",
    "            return value,value\n",
    "    except:\n",
    "        return None, None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "79e7c213",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60, 60)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_minmax_time(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "99d6f0e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<span class=\"ng-binding ng-scope\" ng-if=\"min &gt; 0\">2</span>,\n",
       " <span class=\"ng-binding ng-scope\" ng-if=\"max&gt;0 &amp;&amp; min != max\"><!-- ngIf: min>0 --><span class=\"ng-binding ng-scope\" ng-if=\"min&gt;0\">–</span><!-- end ngIf: min>0 -->3</span>,\n",
       " <span class=\"ng-binding ng-scope\" ng-if=\"min&gt;0\">–</span>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gameplay_list[0].find_all(class_=re.compile(\"ng-binding ng-scope\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "82355ca2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_minmax_players(soup):\n",
    "    try:\n",
    "        gameplay_list = soup.find_all(class_=\"gameplay-item\")\n",
    "        players_values = gameplay_list[0].find_all(class_=re.compile(\"ng-binding ng-scope\"))\n",
    "        if len(players_values) == 3:\n",
    "            return int(players_values[0].text), int(players_values[1].text.replace(\"–\",\"\"))\n",
    "        else:\n",
    "            #If only one player count, min and max are the same\n",
    "            value = int(players_values[0].text)\n",
    "            return value, value\n",
    "    except:\n",
    "        return None, None\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3eb02386",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2bb2940c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_minmax_players(soup)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "548fa9e5",
   "metadata": {},
   "source": [
    "There is also community recommended number of players (a min, max and best count). This is again something to look at later."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29beeb55",
   "metadata": {},
   "source": [
    "## Credits Page\n",
    "\n",
    "Like we did for the stats page, we'll now try to collect the data for one credits page. Features we are looking to scrape are:\n",
    "\n",
    "* Designer(s)\n",
    "* Publisher(s)\n",
    "* Categories\n",
    "* Mechanisms\n",
    "\n",
    "The should all be fairly similar, but note that each of these may have more than one entry. A slight challenge to account for."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e077e826",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "driver.get(\"https://boardgamegeek.com/boardgame/122691/magnum-opus/credits\")\n",
    "\n",
    "soup = bs(driver.page_source,'html5lib')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5fbe396d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_publishers(soup):\n",
    "    try:\n",
    "        pubs = soup.find(attrs={\"name\":\"boardgamepublisher\"}).find_next(\"div\").find_all(\"a\")\n",
    "        pubs = [x.text.strip() for x in pubs]\n",
    "        return pubs\n",
    "    except:\n",
    "        return None\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "b43b351a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Clever Mojo Games', 'Game Salute']"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_publishers(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "18669a8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_designers(soup):\n",
    "    try:\n",
    "        designers = soup.find(attrs={\"name\":\"boardgamedesigner\"}).find_next(\"div\").find_all(\"a\")\n",
    "        designers = [x.text.strip() for x in designers]\n",
    "        return designers\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "c2f82f28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Ian Stedman']"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_designers(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0e4f1994",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_categories(soup):\n",
    "    try:\n",
    "        cats = soup.find(attrs={\"name\":\"boardgamecategory\"}).find_next(\"div\").find_all(\"a\")\n",
    "        cats = [x.text.strip() for x in cats]\n",
    "        return cats\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "cf25267f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Card Game', 'Fantasy', 'Medieval', 'Mythology']"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_categories(soup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "dfb2a686",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mechanics(soup):\n",
    "    try:\n",
    "        mechs = soup.find(attrs={\"name\":\"boardgamemechanic\"}).find_next(\"div\").find_all(\"a\")\n",
    "        mechs = [x.text.strip() for x in mechs]\n",
    "        return mechs\n",
    "    except:\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "15cbc187",
   "metadata": {},
   "outputs": [],
   "source": [
    "get_mechanics(soup)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6162bbf3",
   "metadata": {},
   "source": [
    "## URL Collections\n",
    "\n",
    "Now let's collect the name, url, and year for all the games.\n",
    "\n",
    "We'll start by creating an empty dataframe to fill in with the information as we get it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "731f1f2c",
   "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>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [name, url, year, num_owned, rating, weight, player_age, min_players, max_players, min_time, max_time, designers, publishers, categories, mechanics]\n",
       "Index: []"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_names = [\"name\",\"url\",\"year\", \"num_owned\", \"rating\", \"weight\", \"player_age\", \"min_players\",\"max_players\",\n",
    "               \"min_time\",\"max_time\",\"designers\",\"publishers\",\"categories\",\"mechanics\"]\n",
    "\n",
    "df = pd.DataFrame(columns = column_names)\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "537b9d90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9389671361502347 % pages read, 2 in total\n",
      "5.633802816901409 % pages read, 12 in total\n",
      "10.328638497652582 % pages read, 22 in total\n",
      "15.023474178403756 % pages read, 32 in total\n",
      "19.718309859154928 % pages read, 42 in total\n",
      "24.413145539906104 % pages read, 52 in total\n",
      "29.107981220657276 % pages read, 62 in total\n",
      "33.80281690140845 % pages read, 72 in total\n",
      "38.497652582159624 % pages read, 82 in total\n",
      "43.1924882629108 % pages read, 92 in total\n",
      "47.88732394366197 % pages read, 102 in total\n",
      "52.58215962441315 % pages read, 112 in total\n",
      "57.27699530516433 % pages read, 122 in total\n",
      "61.97183098591549 % pages read, 132 in total\n",
      "66.66666666666666 % pages read, 142 in total\n",
      "71.36150234741784 % pages read, 152 in total\n",
      "76.05633802816901 % pages read, 162 in total\n",
      "80.75117370892019 % pages read, 172 in total\n",
      "85.44600938967136 % pages read, 182 in total\n",
      "90.14084507042254 % pages read, 192 in total\n",
      "94.83568075117371 % pages read, 202 in total\n",
      "99.53051643192488 % pages read, 212 in total\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "base_url = \"https://boardgamegeek.com/browse/boardgame/page/\"\n",
    "start = 1\n",
    "stop = 214\n",
    "\n",
    "for i in range(start, stop+1):\n",
    "    if  (i - start) % 10 == 2:\n",
    "        print((i-start)/(stop-start)*100, \"% pages read,\", (i-start), \"in total\")\n",
    "        df.to_csv(\"games.csv\", index=False)\n",
    "    url = base_url + str(i)\n",
    "    driver.get(url)\n",
    "    soup = bs(driver.page_source,'html5lib')\n",
    "    rows = []\n",
    "    for x in soup.find_all(\"div\", attrs={\"id\":re.compile(\"results_objectname\")}):\n",
    "        try:\n",
    "            game_url = x.find(\"a\")[\"href\"]\n",
    "        except:\n",
    "            game_url = None\n",
    "        try:\n",
    "            game_name = x.find(\"a\").text\n",
    "        except:\n",
    "            game_name = None\n",
    "        try:\n",
    "            game_year = int(x.find(class_=\"smallerfont dull\").text.replace(\"(\",\"\").replace(\")\",\"\"))\n",
    "        except:\n",
    "            game_year = None\n",
    "        rows.append([game_name,game_url, game_year])\n",
    "    df_temp = pd.DataFrame(rows, columns = [\"name\",\"url\",\"year\"])\n",
    "    df = pd.concat([df,df_temp])\n",
    "    time.sleep(5)\n",
    "\n",
    "df.to_csv(\"games.csv\", index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "17abd2c5",
   "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>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Gloomhaven</td>\n",
       "      <td>/boardgame/174430/gloomhaven</td>\n",
       "      <td>2017</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Pandemic Legacy: Season 1</td>\n",
       "      <td>/boardgame/161936/pandemic-legacy-season-1</td>\n",
       "      <td>2015</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Brass: Birmingham</td>\n",
       "      <td>/boardgame/224517/brass-birmingham</td>\n",
       "      <td>2018</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Terraforming Mars</td>\n",
       "      <td>/boardgame/167791/terraforming-mars</td>\n",
       "      <td>2016</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Gloomhaven: Jaws of the Lion</td>\n",
       "      <td>/boardgame/291457/gloomhaven-jaws-lion</td>\n",
       "      <td>2020</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>Labyrinth</td>\n",
       "      <td>/boardgame/6546/labyrinth</td>\n",
       "      <td>1940.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>Dirty Minds: The Game of Naughty Clues</td>\n",
       "      <td>/boardgame/2956/dirty-minds-game-naughty-clues</td>\n",
       "      <td>1990.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>MindTrap</td>\n",
       "      <td>/boardgame/1923/mindtrap</td>\n",
       "      <td>1991.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>Phase 10</td>\n",
       "      <td>/boardgame/1258/phase-10</td>\n",
       "      <td>1982.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>The Ungame</td>\n",
       "      <td>/boardgame/6283/ungame</td>\n",
       "      <td>1973.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>21400 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                      name  \\\n",
       "0                               Gloomhaven   \n",
       "1                Pandemic Legacy: Season 1   \n",
       "2                        Brass: Birmingham   \n",
       "3                        Terraforming Mars   \n",
       "4             Gloomhaven: Jaws of the Lion   \n",
       "..                                     ...   \n",
       "95                               Labyrinth   \n",
       "96  Dirty Minds: The Game of Naughty Clues   \n",
       "97                                MindTrap   \n",
       "98                                Phase 10   \n",
       "99                              The Ungame   \n",
       "\n",
       "                                               url    year num_owned rating  \\\n",
       "0                     /boardgame/174430/gloomhaven    2017      None   None   \n",
       "1       /boardgame/161936/pandemic-legacy-season-1    2015      None   None   \n",
       "2               /boardgame/224517/brass-birmingham    2018      None   None   \n",
       "3              /boardgame/167791/terraforming-mars    2016      None   None   \n",
       "4           /boardgame/291457/gloomhaven-jaws-lion    2020      None   None   \n",
       "..                                             ...     ...       ...    ...   \n",
       "95                       /boardgame/6546/labyrinth  1940.0      None   None   \n",
       "96  /boardgame/2956/dirty-minds-game-naughty-clues  1990.0      None   None   \n",
       "97                        /boardgame/1923/mindtrap  1991.0      None   None   \n",
       "98                        /boardgame/1258/phase-10  1982.0      None   None   \n",
       "99                          /boardgame/6283/ungame  1973.0      None   None   \n",
       "\n",
       "   weight player_age min_players max_players min_time max_time designers  \\\n",
       "0    None       None        None        None     None     None      None   \n",
       "1    None       None        None        None     None     None      None   \n",
       "2    None       None        None        None     None     None      None   \n",
       "3    None       None        None        None     None     None      None   \n",
       "4    None       None        None        None     None     None      None   \n",
       "..    ...        ...         ...         ...      ...      ...       ...   \n",
       "95   None       None        None        None     None     None      None   \n",
       "96   None       None        None        None     None     None      None   \n",
       "97   None       None        None        None     None     None      None   \n",
       "98   None       None        None        None     None     None      None   \n",
       "99   None       None        None        None     None     None      None   \n",
       "\n",
       "   publishers categories mechanics  \n",
       "0        None       None      None  \n",
       "1        None       None      None  \n",
       "2        None       None      None  \n",
       "3        None       None      None  \n",
       "4        None       None      None  \n",
       "..        ...        ...       ...  \n",
       "95       None       None      None  \n",
       "96       None       None      None  \n",
       "97       None       None      None  \n",
       "98       None       None      None  \n",
       "99       None       None      None  \n",
       "\n",
       "[21400 rows x 15 columns]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "f770afc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\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>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>The Piggyback Brigade</td>\n",
       "      <td>/boardgame/1806/piggyback-brigade</td>\n",
       "      <td>2000</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Skräll</td>\n",
       "      <td>/boardgame/31421/skrall</td>\n",
       "      <td>2007.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Descent on Crete: May 1941</td>\n",
       "      <td>/boardgame/5860/descent-crete-may-1941</td>\n",
       "      <td>1978.0</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Castro</td>\n",
       "      <td>/boardgame/149863/castro</td>\n",
       "      <td>2013</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1655: Habemus Papam</td>\n",
       "      <td>/boardgame/82955/1655-habemus-papam</td>\n",
       "      <td>2010</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         name                                     url    year  \\\n",
       "0       The Piggyback Brigade       /boardgame/1806/piggyback-brigade    2000   \n",
       "1                      Skräll                 /boardgame/31421/skrall  2007.0   \n",
       "2  Descent on Crete: May 1941  /boardgame/5860/descent-crete-may-1941  1978.0   \n",
       "3                      Castro                /boardgame/149863/castro    2013   \n",
       "4         1655: Habemus Papam     /boardgame/82955/1655-habemus-papam    2010   \n",
       "\n",
       "  num_owned rating weight player_age min_players max_players min_time  \\\n",
       "0      None   None   None       None        None        None     None   \n",
       "1      None   None   None       None        None        None     None   \n",
       "2      None   None   None       None        None        None     None   \n",
       "3      None   None   None       None        None        None     None   \n",
       "4      None   None   None       None        None        None     None   \n",
       "\n",
       "  max_time designers publishers categories mechanics  \n",
       "0     None      None       None       None      None  \n",
       "1     None      None       None       None      None  \n",
       "2     None      None       None       None      None  \n",
       "3     None      None       None       None      None  \n",
       "4     None      None       None       None      None  "
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df.sample(frac=1)\n",
    "df2.reset_index(inplace=True,drop=True)\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "828dc6f7",
   "metadata": {},
   "source": [
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b971d5e4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "98353c95",
   "metadata": {},
   "source": [
    "Now let's scrape all the pages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b734a4e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-19-dbdefea6d783>:4: DeprecationWarning: executable_path has been deprecated, please pass in a Service object\n",
      "  driver = webdriver.Chrome(chromedriver)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21380 games scraped 99.90654205607477 %\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rsolava/opt/anaconda3/lib/python3.8/site-packages/pandas/core/generic.py:5494: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self[name] = value\n"
     ]
    }
   ],
   "source": [
    "chromedriver = \"/Applications/chromedriver\" # path to the chromedriver executable\n",
    "os.environ[\"webdriver.chrome.driver\"] = chromedriver\n",
    "\n",
    "driver = webdriver.Chrome(chromedriver)\n",
    "\n",
    "df2 = pickle.load(open(\"df2.p\",\"rb\"))\n",
    "\n",
    "for ind in df2.index:\n",
    "    #Check if we've seen this row already\n",
    "    if df2.iloc[ind].notna().sum() > 3:\n",
    "        continue\n",
    "        \n",
    "    \n",
    "    if ind % 20 == 0:\n",
    "        print(ind, \"games scraped\", ind/df2.shape[0]*100, \"%\")\n",
    "        df2.to_csv(\"games2.csv\", index=False)\n",
    "        pickle.dump(df2, open(\"df2.p\",\"wb\"))\n",
    "        \n",
    "        \n",
    "    url = \"https://boardgamegeek.com/\" + df2.iloc[ind].url\n",
    "    \n",
    "    driver.get(url + \"/stats\")\n",
    "    stats_soup = bs(driver.page_source,'html5lib')\n",
    "    \n",
    "    df2.iloc[ind].num_owned = get_num_owned(stats_soup)\n",
    "    df2.iloc[ind].rating = get_rating(stats_soup)\n",
    "    df2.iloc[ind].weight = get_weight(stats_soup)\n",
    "    df2.iloc[ind].player_age = get_age(stats_soup)\n",
    "    df2.iloc[ind].min_time,df2.iloc[ind].max_time= get_minmax_time(stats_soup)\n",
    "    df2.iloc[ind].min_players,df2.iloc[ind].max_players= get_minmax_players(stats_soup)\n",
    "    \n",
    "    time.sleep(5)\n",
    "    \n",
    "    driver.get(url + \"/credits\")\n",
    "    credits_soup = bs(driver.page_source,'html5lib')\n",
    "    \n",
    "    df2.iloc[ind].designers = get_designers(credits_soup)\n",
    "    df2.iloc[ind].publishers = get_publishers(credits_soup)\n",
    "    df2.iloc[ind].categories = get_categories(credits_soup)\n",
    "    df2.iloc[ind].mechanics = get_mechanics(credits_soup)\n",
    "    \n",
    "    \n",
    "    \n",
    "    time.sleep(5)\n",
    "    \n",
    "\n",
    "df2.to_csv(\"games2.csv\", index=False)\n",
    "pickle.dump(df2, open(\"df2.p\",\"wb\"))  \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "35e8e05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Read in df2 from csv or pickle\n",
    "#def string_to_list(x):\n",
    "#    try:\n",
    "#        return ast.literal_eval(x)\n",
    "#    except:\n",
    "#        return None\n",
    "#df2 = pd.read_csv(\"games2.csv\")\n",
    "\n",
    "#df2.publishers = df2.publishers.apply(string_to_list)    \n",
    "#df2.categories = df2.categories.apply(string_to_list)    \n",
    "#df2.designers = df2.designers.apply(string_to_list)    \n",
    "#df2.mechanics = df2.mechanics.apply(string_to_list)\n",
    "\n",
    "df2 = pickle.load(open(\"df2.p\",\"rb\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "77101861",
   "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>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>The Piggyback Brigade</td>\n",
       "      <td>/boardgame/1806/piggyback-brigade</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>679.0</td>\n",
       "      <td>6.101</td>\n",
       "      <td>1.05</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>[Alex Randolph]</td>\n",
       "      <td>[Devir, Drei Magier Spiele, G3, Korea Boardgam...</td>\n",
       "      <td>[Action / Dexterity, Children's Game, Dice, Ra...</td>\n",
       "      <td>[Dice Rolling]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Skräll</td>\n",
       "      <td>/boardgame/31421/skrall</td>\n",
       "      <td>2007.0</td>\n",
       "      <td>75.0</td>\n",
       "      <td>5.709</td>\n",
       "      <td>1.75</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>[Anthony Pendleton, Paul Smith]</td>\n",
       "      <td>[Strategic Retreat]</td>\n",
       "      <td>[Science Fiction, Space Exploration, Wargame]</td>\n",
       "      <td>[Dice Rolling, Modular Board, Variable Player ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Descent on Crete: May 1941</td>\n",
       "      <td>/boardgame/5860/descent-crete-may-1941</td>\n",
       "      <td>1978.0</td>\n",
       "      <td>249.0</td>\n",
       "      <td>5.961</td>\n",
       "      <td>3.91</td>\n",
       "      <td>14.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>[Eric Goldberg]</td>\n",
       "      <td>[SPI (Simulations Publications, Inc.)]</td>\n",
       "      <td>[Wargame, World War II]</td>\n",
       "      <td>[Dice Rolling, Hexagon Grid, Simulation]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Castro</td>\n",
       "      <td>/boardgame/149863/castro</td>\n",
       "      <td>2013.0</td>\n",
       "      <td>287.0</td>\n",
       "      <td>6.515</td>\n",
       "      <td>1.41</td>\n",
       "      <td>8.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>[Jürgen P. Grunau]</td>\n",
       "      <td>[Noris Spiele]</td>\n",
       "      <td>[Dice]</td>\n",
       "      <td>[Dice Rolling, Pattern Building, Push Your Luck]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1655: Habemus Papam</td>\n",
       "      <td>/boardgame/82955/1655-habemus-papam</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>738.0</td>\n",
       "      <td>6.453</td>\n",
       "      <td>2.16</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>[Christoph Bauer]</td>\n",
       "      <td>[999 Games, DDD Verlag GmbH]</td>\n",
       "      <td>[Card Game, Pike and Shot, Religious]</td>\n",
       "      <td>[Auction/Bidding, Set Collection]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         name                                     url    year  \\\n",
       "0       The Piggyback Brigade       /boardgame/1806/piggyback-brigade  2000.0   \n",
       "1                      Skräll                 /boardgame/31421/skrall  2007.0   \n",
       "2  Descent on Crete: May 1941  /boardgame/5860/descent-crete-may-1941  1978.0   \n",
       "3                      Castro                /boardgame/149863/castro  2013.0   \n",
       "4         1655: Habemus Papam     /boardgame/82955/1655-habemus-papam  2010.0   \n",
       "\n",
       "   num_owned  rating  weight  player_age  min_players  max_players  min_time  \\\n",
       "0      679.0   6.101    1.05         4.0          2.0          7.0      15.0   \n",
       "1       75.0   5.709    1.75         NaN          2.0          6.0      60.0   \n",
       "2      249.0   5.961    3.91        14.0          2.0          2.0     240.0   \n",
       "3      287.0   6.515    1.41         8.0          2.0          4.0      20.0   \n",
       "4      738.0   6.453    2.16        10.0          3.0          4.0      30.0   \n",
       "\n",
       "   max_time                        designers  \\\n",
       "0      25.0                  [Alex Randolph]   \n",
       "1      60.0  [Anthony Pendleton, Paul Smith]   \n",
       "2     240.0                  [Eric Goldberg]   \n",
       "3      20.0               [Jürgen P. Grunau]   \n",
       "4      30.0                [Christoph Bauer]   \n",
       "\n",
       "                                          publishers  \\\n",
       "0  [Devir, Drei Magier Spiele, G3, Korea Boardgam...   \n",
       "1                                [Strategic Retreat]   \n",
       "2             [SPI (Simulations Publications, Inc.)]   \n",
       "3                                     [Noris Spiele]   \n",
       "4                       [999 Games, DDD Verlag GmbH]   \n",
       "\n",
       "                                          categories  \\\n",
       "0  [Action / Dexterity, Children's Game, Dice, Ra...   \n",
       "1      [Science Fiction, Space Exploration, Wargame]   \n",
       "2                            [Wargame, World War II]   \n",
       "3                                             [Dice]   \n",
       "4              [Card Game, Pike and Shot, Religious]   \n",
       "\n",
       "                                           mechanics  \n",
       "0                                     [Dice Rolling]  \n",
       "1  [Dice Rolling, Modular Board, Variable Player ...  \n",
       "2           [Dice Rolling, Hexagon Grid, Simulation]  \n",
       "3   [Dice Rolling, Pattern Building, Push Your Luck]  \n",
       "4                  [Auction/Bidding, Set Collection]  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "36869dd0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 21379 entries, 0 to 21379\n",
      "Data columns (total 15 columns):\n",
      " #   Column       Non-Null Count  Dtype  \n",
      "---  ------       --------------  -----  \n",
      " 0   name         21379 non-null  object \n",
      " 1   url          21379 non-null  object \n",
      " 2   year         21195 non-null  float64\n",
      " 3   num_owned    21379 non-null  float64\n",
      " 4   rating       21377 non-null  float64\n",
      " 5   weight       21379 non-null  float64\n",
      " 6   player_age   20951 non-null  float64\n",
      " 7   min_players  21345 non-null  float64\n",
      " 8   max_players  21345 non-null  float64\n",
      " 9   min_time     20763 non-null  float64\n",
      " 10  max_time     20763 non-null  float64\n",
      " 11  designers    21369 non-null  object \n",
      " 12  publishers   21369 non-null  object \n",
      " 13  categories   21369 non-null  object \n",
      " 14  mechanics    21369 non-null  object \n",
      "dtypes: float64(9), object(6)\n",
      "memory usage: 2.6+ MB\n"
     ]
    }
   ],
   "source": [
    "game_df = df2[df2.num_owned.notna()]\n",
    "game_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "7a27e0c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rsolava/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:1676: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self._setitem_single_column(ilocs[0], value, pi)\n"
     ]
    }
   ],
   "source": [
    "game_df.loc[:,\"num_owned\"] = game_df.num_owned.astype(int, errors=\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "0bd66edd",
   "metadata": {},
   "outputs": [],
   "source": [
    "game_df.loc[:,\"rating\"] = game_df.rating.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"year\"] = game_df.year.astype(float,errors=\"ignore\")\n",
    "game_df.loc[:,\"weight\"] = game_df.weight.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"player_age\"] = game_df.player_age.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"min_players\"] = game_df.min_players.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"max_players\"] = game_df.max_players.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"min_time\"] = game_df.min_time.astype(float, errors=\"ignore\")\n",
    "game_df.loc[:,\"max_time\"] = game_df.max_time.astype(float, errors=\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "1e445a8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name            object\n",
       "url             object\n",
       "year           float64\n",
       "num_owned        int64\n",
       "rating         float64\n",
       "weight         float64\n",
       "player_age     float64\n",
       "min_players    float64\n",
       "max_players    float64\n",
       "min_time       float64\n",
       "max_time       float64\n",
       "designers       object\n",
       "publishers      object\n",
       "categories      object\n",
       "mechanics       object\n",
       "dtype: object"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3ba1e457",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rsolava/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:1597: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self.obj[key] = value\n",
      "/Users/rsolava/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:1676: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self._setitem_single_column(ilocs[0], value, pi)\n"
     ]
    }
   ],
   "source": [
    "game_df.loc[:,\"log_owned\"] = np.log10(game_df.num_owned)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2d11165",
   "metadata": {},
   "source": [
    "Dealing with missing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d830a28b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "year missing: 184, mean: 2003.4703467799009, median: 2011.0\n",
      "num_owned missing: 0, mean: 1448.448664577389, median: 313.0\n",
      "rating missing: 2, mean: 6.421054076811534, median: 6.446\n",
      "weight missing: 0, mean: 1.9855779035502084, median: 1.97\n",
      "player_age missing: 428, mean: 10.292682926829269, median: 10.0\n",
      "min_players missing: 34, mean: 2.014523307566175, median: 2.0\n",
      "max_players missing: 34, mean: 5.688779573670649, median: 4.0\n",
      "min_time missing: 616, mean: 66.01001782016087, median: 30.0\n",
      "max_time missing: 616, mean: 93.40148340798535, median: 45.0\n",
      "log_owned missing: 0, mean: 2.600123341696565, median: 2.4955443375464483\n"
     ]
    }
   ],
   "source": [
    "for col in game_df.select_dtypes(include=np.number).columns:\n",
    "    print(col, \"missing: {}, mean: {}, median: {}\".format(\n",
    "        game_df[col].isna().sum(), game_df[col].mean(), game_df[col].median()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ecda34b",
   "metadata": {},
   "source": [
    "We'll impute all missing values with the median.\n",
    "\n",
    "For each feature, either the mean and median seem very close, or the mean is highly effected by outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "baa316d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-7-822852be40f3>:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  game_df[col] = game_df[col].fillna(value=game_df[col].median())\n"
     ]
    }
   ],
   "source": [
    "for col in game_df.select_dtypes(include=np.number).columns:\n",
    "    game_df[col] = game_df[col].fillna(value=game_df[col].median())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d7ebefe7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 21379 entries, 0 to 21379\n",
      "Data columns (total 16 columns):\n",
      " #   Column       Non-Null Count  Dtype  \n",
      "---  ------       --------------  -----  \n",
      " 0   name         21379 non-null  object \n",
      " 1   url          21379 non-null  object \n",
      " 2   year         21379 non-null  float64\n",
      " 3   num_owned    21379 non-null  float64\n",
      " 4   rating       21379 non-null  float64\n",
      " 5   weight       21379 non-null  float64\n",
      " 6   player_age   21379 non-null  float64\n",
      " 7   min_players  21379 non-null  float64\n",
      " 8   max_players  21379 non-null  float64\n",
      " 9   min_time     21379 non-null  float64\n",
      " 10  max_time     21379 non-null  float64\n",
      " 11  designers    21369 non-null  object \n",
      " 12  publishers   21369 non-null  object \n",
      " 13  categories   21369 non-null  object \n",
      " 14  mechanics    21369 non-null  object \n",
      " 15  log_owned    21379 non-null  float64\n",
      "dtypes: float64(10), object(6)\n",
      "memory usage: 2.8+ MB\n"
     ]
    }
   ],
   "source": [
    "game_df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30116370",
   "metadata": {},
   "source": [
    "## Remove outliers in year\n",
    "\n",
    "We want to remove all 2020 and later games, since these games may not be released yet or have been out for a much shorter time.\n",
    "\n",
    "We'll also remove all games from before 1980."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d91f44a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1979.5 2039.5\n"
     ]
    }
   ],
   "source": [
    "Q1 = game_df.year.quantile(0.25)\n",
    "Q3 = game_df.year.quantile(0.75)\n",
    "IQR = Q3-Q1\n",
    "\n",
    "print(Q1-1.5*IQR,Q3+1.5*IQR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "24600848",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18678, 16)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df = game_df[(game_df.year < 2020) & (game_df.year >=1980)]\n",
    "\n",
    "game_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2c53e5d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6cd51208",
   "metadata": {},
   "source": [
    "Remove outliers in terms of log_owned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "d24d9eda",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q1 = game_df.log_owned.quantile(0.25)\n",
    "Q3 = game_df.log_owned.quantile(0.75)\n",
    "IQR = Q3-Q1\n",
    "\n",
    "\n",
    "game_df = game_df[~((game_df.log_owned < (Q1 - 1.5 * IQR)) |(game_df.log_owned > (Q3 + 1.5 * IQR)))]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b4afab57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18678, 16)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f9f1d00a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#game_df = game_df.dropna()\n",
    "#game_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "98e947cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>num_owned</td>    <th>  R-squared:         </th> <td>   0.081</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.081</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   274.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Nov 2021</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:28:16</td>     <th>  Log-Likelihood:    </th> <td> -31843.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 18678</td>      <th>  AIC:               </th> <td>6.370e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 18671</td>      <th>  BIC:               </th> <td>6.375e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>       <td>  -23.9607</td> <td>    2.022</td> <td>  -11.850</td> <td> 0.000</td> <td>  -27.924</td> <td>  -19.997</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>year</th>        <td>    0.0141</td> <td>    0.001</td> <td>   14.038</td> <td> 0.000</td> <td>    0.012</td> <td>    0.016</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th>      <td>    0.9284</td> <td>    0.046</td> <td>   20.265</td> <td> 0.000</td> <td>    0.839</td> <td>    1.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>player_age</th>  <td>    0.0375</td> <td>    0.004</td> <td>    9.422</td> <td> 0.000</td> <td>    0.030</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight_sq</th>   <td>   -0.1343</td> <td>    0.010</td> <td>  -13.029</td> <td> 0.000</td> <td>   -0.154</td> <td>   -0.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>avg_time</th>    <td>-3.337e-05</td> <td> 4.56e-05</td> <td>   -0.731</td> <td> 0.465</td> <td>   -0.000</td> <td> 5.61e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>avg_players</th> <td>    0.0030</td> <td>    0.001</td> <td>    2.386</td> <td> 0.017</td> <td>    0.001</td> <td>    0.005</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>1641.101</td> <th>  Durbin-Watson:     </th> <td>   1.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>2222.362</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.736</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 3.828</td>  <th>  Cond. No.          </th> <td>4.17e+05</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 4.17e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              num_owned   R-squared:                       0.081\n",
       "Model:                            OLS   Adj. R-squared:                  0.081\n",
       "Method:                 Least Squares   F-statistic:                     274.8\n",
       "Date:                Tue, 09 Nov 2021   Prob (F-statistic):               0.00\n",
       "Time:                        17:28:16   Log-Likelihood:                -31843.\n",
       "No. Observations:               18678   AIC:                         6.370e+04\n",
       "Df Residuals:                   18671   BIC:                         6.375e+04\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "const         -23.9607      2.022    -11.850      0.000     -27.924     -19.997\n",
       "year            0.0141      0.001     14.038      0.000       0.012       0.016\n",
       "weight          0.9284      0.046     20.265      0.000       0.839       1.018\n",
       "player_age      0.0375      0.004      9.422      0.000       0.030       0.045\n",
       "weight_sq      -0.1343      0.010    -13.029      0.000      -0.154      -0.114\n",
       "avg_time    -3.337e-05   4.56e-05     -0.731      0.465      -0.000    5.61e-05\n",
       "avg_players     0.0030      0.001      2.386      0.017       0.001       0.005\n",
       "==============================================================================\n",
       "Omnibus:                     1641.101   Durbin-Watson:                   1.985\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2222.362\n",
       "Skew:                           0.736   Prob(JB):                         0.00\n",
       "Kurtosis:                       3.828   Cond. No.                     4.17e+05\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 4.17e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X =game_df.drop(columns =[\"name\",\"url\",\"rating\",\"num_owned\",\"designers\",\"publishers\",\"categories\",\"mechanics\",\"log_owned\"])\n",
    "X[\"weight_sq\"] = X.weight*X.weight\n",
    "X[\"avg_time\"] = (X.min_time + X.max_time)/2\n",
    "X = X.drop(columns=[\"min_time\",\"max_time\"])\n",
    "X[\"avg_players\"] = (X.min_players + X.max_players)/2\n",
    "X = X.drop(columns=[\"min_players\",\"max_players\"])\n",
    "y = game_df.num_owned\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(np.log(y),X)\n",
    "game_model = model.fit()\n",
    "\n",
    "game_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0bac8117",
   "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": [
    "x = np.arange(0, 6)\n",
    "\n",
    "# scatter-plot data\n",
    "ax = game_df.plot(x='rating', y='num_owned', kind='scatter',logy=True)\n",
    "\n",
    "# plot regression line on the same axes, set x-axis limits\n",
    "#ax.plot(x, np.exp(game_model.params.const + game_model.params.weight * x), color = \"red\")\n",
    "\n",
    "#plt.savefig(\"weight_reg.png\", bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d5aa242e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const         -23.960716\n",
       "year            0.014125\n",
       "weight          0.928388\n",
       "player_age      0.037509\n",
       "weight_sq      -0.134270\n",
       "avg_time       -0.000033\n",
       "avg_players     0.002951\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_model.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4e2cecbc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8657cdda",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a6ec354d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(max_depth=25)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = game_df.log_owned\n",
    "X = game_df.drop(columns =[\"name\",\"url\",\"rating\",\"num_owned\",\"designers\",\"publishers\",\"categories\",\"mechanics\",\"log_owned\"])\n",
    "\n",
    "X, X_test, y, y_test = train_test_split(X,y, test_size=0.3)\n",
    "\n",
    "reg_tree = RandomForestRegressor(max_depth=25)\n",
    "reg_tree.fit(X, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f6879919",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.17904096, 0.41098997, 0.09746151, 0.04117842, 0.09616024,\n",
       "       0.08312252, 0.09204639])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_tree.feature_importances_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4eea9a12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2990270117788939"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_tree.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "41a554f4",
   "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>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "      <th>log_owned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>The Piggyback Brigade</td>\n",
       "      <td>/boardgame/1806/piggyback-brigade</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>679</td>\n",
       "      <td>6.101</td>\n",
       "      <td>1.05</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>[Alex Randolph]</td>\n",
       "      <td>[Devir, Drei Magier Spiele, G3, Korea Boardgam...</td>\n",
       "      <td>[Action / Dexterity, Children's Game, Dice, Ra...</td>\n",
       "      <td>[Dice Rolling]</td>\n",
       "      <td>2.831870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Skräll</td>\n",
       "      <td>/boardgame/31421/skrall</td>\n",
       "      <td>2007.0</td>\n",
       "      <td>75</td>\n",
       "      <td>5.709</td>\n",
       "      <td>1.75</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>[Anthony Pendleton, Paul Smith]</td>\n",
       "      <td>[Strategic Retreat]</td>\n",
       "      <td>[Science Fiction, Space Exploration, Wargame]</td>\n",
       "      <td>[Dice Rolling, Modular Board, Variable Player ...</td>\n",
       "      <td>1.875061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Castro</td>\n",
       "      <td>/boardgame/149863/castro</td>\n",
       "      <td>2013.0</td>\n",
       "      <td>287</td>\n",
       "      <td>6.515</td>\n",
       "      <td>1.41</td>\n",
       "      <td>8.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>[Jürgen P. Grunau]</td>\n",
       "      <td>[Noris Spiele]</td>\n",
       "      <td>[Dice]</td>\n",
       "      <td>[Dice Rolling, Pattern Building, Push Your Luck]</td>\n",
       "      <td>2.457882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1655: Habemus Papam</td>\n",
       "      <td>/boardgame/82955/1655-habemus-papam</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>738</td>\n",
       "      <td>6.453</td>\n",
       "      <td>2.16</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>[Christoph Bauer]</td>\n",
       "      <td>[999 Games, DDD Verlag GmbH]</td>\n",
       "      <td>[Card Game, Pike and Shot, Religious]</td>\n",
       "      <td>[Auction/Bidding, Set Collection]</td>\n",
       "      <td>2.868056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Kreus</td>\n",
       "      <td>/boardgame/198110/kreus</td>\n",
       "      <td>2016.0</td>\n",
       "      <td>826</td>\n",
       "      <td>6.696</td>\n",
       "      <td>2.00</td>\n",
       "      <td>10.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>[Julien Prothière]</td>\n",
       "      <td>[2Tomatoes Games, CMON Global Limited, Sweet G...</td>\n",
       "      <td>[Card Game, Deduction, Mythology]</td>\n",
       "      <td>[Communication Limits, Cooperative Game]</td>\n",
       "      <td>2.916980</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    name                                  url    year  \\\n",
       "0  The Piggyback Brigade    /boardgame/1806/piggyback-brigade  2000.0   \n",
       "1                 Skräll              /boardgame/31421/skrall  2007.0   \n",
       "3                 Castro             /boardgame/149863/castro  2013.0   \n",
       "4    1655: Habemus Papam  /boardgame/82955/1655-habemus-papam  2010.0   \n",
       "5                  Kreus              /boardgame/198110/kreus  2016.0   \n",
       "\n",
       "   num_owned  rating  weight  player_age  min_players  max_players  min_time  \\\n",
       "0        679   6.101    1.05         4.0          2.0          7.0      15.0   \n",
       "1         75   5.709    1.75        10.0          2.0          6.0      60.0   \n",
       "3        287   6.515    1.41         8.0          2.0          4.0      20.0   \n",
       "4        738   6.453    2.16        10.0          3.0          4.0      30.0   \n",
       "5        826   6.696    2.00        10.0          3.0          6.0      20.0   \n",
       "\n",
       "   max_time                        designers  \\\n",
       "0      25.0                  [Alex Randolph]   \n",
       "1      60.0  [Anthony Pendleton, Paul Smith]   \n",
       "3      20.0               [Jürgen P. Grunau]   \n",
       "4      30.0                [Christoph Bauer]   \n",
       "5      30.0               [Julien Prothière]   \n",
       "\n",
       "                                          publishers  \\\n",
       "0  [Devir, Drei Magier Spiele, G3, Korea Boardgam...   \n",
       "1                                [Strategic Retreat]   \n",
       "3                                     [Noris Spiele]   \n",
       "4                       [999 Games, DDD Verlag GmbH]   \n",
       "5  [2Tomatoes Games, CMON Global Limited, Sweet G...   \n",
       "\n",
       "                                          categories  \\\n",
       "0  [Action / Dexterity, Children's Game, Dice, Ra...   \n",
       "1      [Science Fiction, Space Exploration, Wargame]   \n",
       "3                                             [Dice]   \n",
       "4              [Card Game, Pike and Shot, Religious]   \n",
       "5                  [Card Game, Deduction, Mythology]   \n",
       "\n",
       "                                           mechanics  log_owned  \n",
       "0                                     [Dice Rolling]   2.831870  \n",
       "1  [Dice Rolling, Modular Board, Variable Player ...   1.875061  \n",
       "3   [Dice Rolling, Pattern Building, Push Your Luck]   2.457882  \n",
       "4                  [Auction/Bidding, Set Collection]   2.868056  \n",
       "5           [Communication Limits, Cooperative Game]   2.916980  "
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae25c728",
   "metadata": {},
   "source": [
    "## Are games sold and number owned correlated?\n",
    "\n",
    "We're using number of users who own the game as a proxy for number of games sold, since unfortunately the number of games sold is just not public information. It seems reasonable that these things would be correlated, but are they really? Luckily, one publisher did share their sales data, so we'll use this limited information to see if this assumption is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cef4be19",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_sold = [[\"Twilight Struggle\", 100000], [\"Battle Line\",40000],[\"Dominant Species\",25000],\n",
    "            [\"Commands & Colors: Ancients\", 20000],[\"Paths of Glory\",16000],[\"Combat Commander: Europe\",13000],\n",
    "            [\"Wilderness War\",11000], [\"Labyrinth: The War on Terror, 2001 – ?\",11000],\n",
    "            [\"Thunder Alley\", 9500], [\"Formula Motor Racing\",9000], [\"Ivanhoe\",9000],\n",
    "            [\"Commands & Colors: Napoleonics\",9000], [\"Washington's War\", 9000],[\"Here I Stand\", 8500]]\n",
    "\n",
    "num_sold_df = pd.DataFrame(num_sold, columns = [\"name\",\"num_sold\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "db846867",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "      <th>log_owned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>15694</th>\n",
       "      <td>Washington's War</td>\n",
       "      <td>/boardgame/38996/washingtons-war</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>4499.0</td>\n",
       "      <td>7.636</td>\n",
       "      <td>2.84</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>[Mark Herman]</td>\n",
       "      <td>[GMT Games, Spielworxx]</td>\n",
       "      <td>[Age of Reason, American Revolutionary War, Wa...</td>\n",
       "      <td>[Area Majority / Influence, Campaign / Battle ...</td>\n",
       "      <td>3.653116</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   name                               url    year  num_owned  \\\n",
       "15694  Washington's War  /boardgame/38996/washingtons-war  2010.0     4499.0   \n",
       "\n",
       "       rating  weight  player_age  min_players  max_players  min_time  \\\n",
       "15694   7.636    2.84        12.0          2.0          2.0      90.0   \n",
       "\n",
       "       max_time      designers               publishers  \\\n",
       "15694      90.0  [Mark Herman]  [GMT Games, Spielworxx]   \n",
       "\n",
       "                                              categories  \\\n",
       "15694  [Age of Reason, American Revolutionary War, Wa...   \n",
       "\n",
       "                                               mechanics  log_owned  \n",
       "15694  [Area Majority / Influence, Campaign / Battle ...   3.653116  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df[(game_df.name == \"Washington's War\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7b802d83",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>num_sold</th>\n",
       "      <th>url</th>\n",
       "      <th>year</th>\n",
       "      <th>num_owned</th>\n",
       "      <th>rating</th>\n",
       "      <th>weight</th>\n",
       "      <th>player_age</th>\n",
       "      <th>min_players</th>\n",
       "      <th>max_players</th>\n",
       "      <th>min_time</th>\n",
       "      <th>max_time</th>\n",
       "      <th>designers</th>\n",
       "      <th>publishers</th>\n",
       "      <th>categories</th>\n",
       "      <th>mechanics</th>\n",
       "      <th>log_owned</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Battle Line</th>\n",
       "      <td>40000</td>\n",
       "      <td>/boardgame/760/battle-line</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>19632.0</td>\n",
       "      <td>7.414</td>\n",
       "      <td>1.90</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>[Reiner Knizia]</td>\n",
       "      <td>[GMT Games, Chrononauts Games, Lavka Games, Ne...</td>\n",
       "      <td>[Ancient, Card Game, Deduction]</td>\n",
       "      <td>[Card Play Conflict Resolution, Hand Managemen...</td>\n",
       "      <td>4.292965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Combat Commander: Europe</th>\n",
       "      <td>13000</td>\n",
       "      <td>/boardgame/21050/combat-commander-europe</td>\n",
       "      <td>2006.0</td>\n",
       "      <td>8296.0</td>\n",
       "      <td>7.946</td>\n",
       "      <td>3.25</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>[Chad Jensen]</td>\n",
       "      <td>[GMT Games, Devir]</td>\n",
       "      <td>[Wargame, World War II]</td>\n",
       "      <td>[Advantage Token, Campaign / Battle Card Drive...</td>\n",
       "      <td>3.918869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Commands &amp; Colors: Ancients</th>\n",
       "      <td>20000</td>\n",
       "      <td>/boardgame/14105/commands-colors-ancients</td>\n",
       "      <td>2006.0</td>\n",
       "      <td>10626.0</td>\n",
       "      <td>7.776</td>\n",
       "      <td>2.69</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>[Richard Borg]</td>\n",
       "      <td>[GMT Games, Wargames Club Publishing]</td>\n",
       "      <td>[Ancient, Wargame]</td>\n",
       "      <td>[Campaign / Battle Card Driven, Command Cards,...</td>\n",
       "      <td>4.026370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Commands &amp; Colors: Napoleonics</th>\n",
       "      <td>9000</td>\n",
       "      <td>/boardgame/62222/commands-colors-napoleonics</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>5073.0</td>\n",
       "      <td>8.009</td>\n",
       "      <td>2.74</td>\n",
       "      <td>14.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>[Richard Borg]</td>\n",
       "      <td>[GMT Games]</td>\n",
       "      <td>[Napoleonic, Wargame]</td>\n",
       "      <td>[Campaign / Battle Card Driven, Command Cards,...</td>\n",
       "      <td>3.705265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dominant Species</th>\n",
       "      <td>25000</td>\n",
       "      <td>/boardgame/62219/dominant-species</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>20123.0</td>\n",
       "      <td>7.841</td>\n",
       "      <td>4.04</td>\n",
       "      <td>14.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>[Chad Jensen]</td>\n",
       "      <td>[GMT Games, Asmodee, Asterion Press, Filosofia...</td>\n",
       "      <td>[Animals, Environmental, Prehistoric]</td>\n",
       "      <td>[Action Queue, Area Majority / Influence, Card...</td>\n",
       "      <td>4.303693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Formula Motor Racing</th>\n",
       "      <td>9000</td>\n",
       "      <td>/boardgame/635/formula-motor-racing</td>\n",
       "      <td>1995.0</td>\n",
       "      <td>2320.0</td>\n",
       "      <td>6.408</td>\n",
       "      <td>1.18</td>\n",
       "      <td>8.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>[Reiner Knizia]</td>\n",
       "      <td>[Egmont Polska, Gibsons, GMT Games, Die Spiege...</td>\n",
       "      <td>[Card Game, Racing, Sports]</td>\n",
       "      <td>[Dice Rolling, Hand Management, Relative Movem...</td>\n",
       "      <td>3.365488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Here I Stand</th>\n",
       "      <td>8500</td>\n",
       "      <td>/boardgame/17392/here-i-stand</td>\n",
       "      <td>2006.0</td>\n",
       "      <td>5161.0</td>\n",
       "      <td>7.911</td>\n",
       "      <td>4.17</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>360.0</td>\n",
       "      <td>[Ed Beach]</td>\n",
       "      <td>[GMT Games, Banana Games, Devir, Udo Grebe Gam...</td>\n",
       "      <td>[Negotiation, Pike and Shot, Political, Religi...</td>\n",
       "      <td>[Campaign / Battle Card Driven, Dice Rolling, ...</td>\n",
       "      <td>3.712734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ivanhoe</th>\n",
       "      <td>9000</td>\n",
       "      <td>/boardgame/883/ivanhoe</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>2562.0</td>\n",
       "      <td>6.539</td>\n",
       "      <td>1.61</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>[Reiner Knizia, Andy Lewis]</td>\n",
       "      <td>[Asmodee, GMT Games, Maldón]</td>\n",
       "      <td>[Card Game, Fighting, Medieval]</td>\n",
       "      <td>[Auction/Bidding, Hand Management, Set Collect...</td>\n",
       "      <td>3.408579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Labyrinth: The War on Terror, 2001 – ?</th>\n",
       "      <td>11000</td>\n",
       "      <td>/boardgame/62227/labyrinth-war-terror-2001</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>8964.0</td>\n",
       "      <td>7.595</td>\n",
       "      <td>3.63</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>[Volko Ruhnke]</td>\n",
       "      <td>[GMT Games, Asterion Press, Bard Centrum Gier,...</td>\n",
       "      <td>[Arabian, Modern Warfare, Political, Wargame]</td>\n",
       "      <td>[Action Points, Action/Event, Area Majority / ...</td>\n",
       "      <td>3.952502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Paths of Glory</th>\n",
       "      <td>16000</td>\n",
       "      <td>/boardgame/91/paths-glory</td>\n",
       "      <td>1999.0</td>\n",
       "      <td>8850.0</td>\n",
       "      <td>8.057</td>\n",
       "      <td>3.84</td>\n",
       "      <td>14.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>480.0</td>\n",
       "      <td>480.0</td>\n",
       "      <td>[Ted Raicer]</td>\n",
       "      <td>[GMT Games, Devir, DiceTree Games, Udo Grebe G...</td>\n",
       "      <td>[Wargame, World War I]</td>\n",
       "      <td>[Campaign / Battle Card Driven, Dice Rolling, ...</td>\n",
       "      <td>3.946943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Thunder Alley</th>\n",
       "      <td>9500</td>\n",
       "      <td>/boardgame/108906/thunder-alley</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>4169.0</td>\n",
       "      <td>7.321</td>\n",
       "      <td>2.38</td>\n",
       "      <td>10.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>[Jeff Horger, Carla Horger]</td>\n",
       "      <td>[GMT Games]</td>\n",
       "      <td>[Racing, Sports]</td>\n",
       "      <td>[Hand Management, Race]</td>\n",
       "      <td>3.620032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Twilight Struggle</th>\n",
       "      <td>100000</td>\n",
       "      <td>/boardgame/12333/twilight-struggle</td>\n",
       "      <td>2005.0</td>\n",
       "      <td>58790.0</td>\n",
       "      <td>8.283</td>\n",
       "      <td>3.59</td>\n",
       "      <td>13.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>[Ananda Gupta, Jason Matthews]</td>\n",
       "      <td>[GMT Games, (Self-Published), Asterion Press, ...</td>\n",
       "      <td>[Modern Warfare, Political, Wargame]</td>\n",
       "      <td>[Action/Event, Advantage Token, Area Majority ...</td>\n",
       "      <td>4.769303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington's War</th>\n",
       "      <td>9000</td>\n",
       "      <td>/boardgame/38996/washingtons-war</td>\n",
       "      <td>2010.0</td>\n",
       "      <td>4499.0</td>\n",
       "      <td>7.636</td>\n",
       "      <td>2.84</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>90.0</td>\n",
       "      <td>[Mark Herman]</td>\n",
       "      <td>[GMT Games, Spielworxx]</td>\n",
       "      <td>[Age of Reason, American Revolutionary War, Wa...</td>\n",
       "      <td>[Area Majority / Influence, Campaign / Battle ...</td>\n",
       "      <td>3.653116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wilderness War</th>\n",
       "      <td>11000</td>\n",
       "      <td>/boardgame/1822/wilderness-war</td>\n",
       "      <td>2001.0</td>\n",
       "      <td>3977.0</td>\n",
       "      <td>7.714</td>\n",
       "      <td>3.30</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>[Volko Ruhnke]</td>\n",
       "      <td>[GMT Games]</td>\n",
       "      <td>[Age of Reason, American Indian Wars, Wargame]</td>\n",
       "      <td>[Campaign / Battle Card Driven, Dice Rolling, ...</td>\n",
       "      <td>3.599556</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                        num_sold  \\\n",
       "name                                               \n",
       "Battle Line                                40000   \n",
       "Combat Commander: Europe                   13000   \n",
       "Commands & Colors: Ancients                20000   \n",
       "Commands & Colors: Napoleonics              9000   \n",
       "Dominant Species                           25000   \n",
       "Formula Motor Racing                        9000   \n",
       "Here I Stand                                8500   \n",
       "Ivanhoe                                     9000   \n",
       "Labyrinth: The War on Terror, 2001 – ?     11000   \n",
       "Paths of Glory                             16000   \n",
       "Thunder Alley                               9500   \n",
       "Twilight Struggle                         100000   \n",
       "Washington's War                            9000   \n",
       "Wilderness War                             11000   \n",
       "\n",
       "                                                                                 url  \\\n",
       "name                                                                                   \n",
       "Battle Line                                               /boardgame/760/battle-line   \n",
       "Combat Commander: Europe                    /boardgame/21050/combat-commander-europe   \n",
       "Commands & Colors: Ancients                /boardgame/14105/commands-colors-ancients   \n",
       "Commands & Colors: Napoleonics          /boardgame/62222/commands-colors-napoleonics   \n",
       "Dominant Species                                   /boardgame/62219/dominant-species   \n",
       "Formula Motor Racing                             /boardgame/635/formula-motor-racing   \n",
       "Here I Stand                                           /boardgame/17392/here-i-stand   \n",
       "Ivanhoe                                                       /boardgame/883/ivanhoe   \n",
       "Labyrinth: The War on Terror, 2001 – ?    /boardgame/62227/labyrinth-war-terror-2001   \n",
       "Paths of Glory                                             /boardgame/91/paths-glory   \n",
       "Thunder Alley                                        /boardgame/108906/thunder-alley   \n",
       "Twilight Struggle                                 /boardgame/12333/twilight-struggle   \n",
       "Washington's War                                    /boardgame/38996/washingtons-war   \n",
       "Wilderness War                                        /boardgame/1822/wilderness-war   \n",
       "\n",
       "                                          year  num_owned  rating  weight  \\\n",
       "name                                                                        \n",
       "Battle Line                             2000.0    19632.0   7.414    1.90   \n",
       "Combat Commander: Europe                2006.0     8296.0   7.946    3.25   \n",
       "Commands & Colors: Ancients             2006.0    10626.0   7.776    2.69   \n",
       "Commands & Colors: Napoleonics          2010.0     5073.0   8.009    2.74   \n",
       "Dominant Species                        2010.0    20123.0   7.841    4.04   \n",
       "Formula Motor Racing                    1995.0     2320.0   6.408    1.18   \n",
       "Here I Stand                            2006.0     5161.0   7.911    4.17   \n",
       "Ivanhoe                                 2000.0     2562.0   6.539    1.61   \n",
       "Labyrinth: The War on Terror, 2001 – ?  2010.0     8964.0   7.595    3.63   \n",
       "Paths of Glory                          1999.0     8850.0   8.057    3.84   \n",
       "Thunder Alley                           2014.0     4169.0   7.321    2.38   \n",
       "Twilight Struggle                       2005.0    58790.0   8.283    3.59   \n",
       "Washington's War                        2010.0     4499.0   7.636    2.84   \n",
       "Wilderness War                          2001.0     3977.0   7.714    3.30   \n",
       "\n",
       "                                        player_age  min_players  max_players  \\\n",
       "name                                                                           \n",
       "Battle Line                                   12.0          2.0          2.0   \n",
       "Combat Commander: Europe                      12.0          2.0          2.0   \n",
       "Commands & Colors: Ancients                   12.0          2.0          2.0   \n",
       "Commands & Colors: Napoleonics                14.0          2.0          2.0   \n",
       "Dominant Species                              14.0          2.0          6.0   \n",
       "Formula Motor Racing                           8.0          3.0          6.0   \n",
       "Here I Stand                                  12.0          2.0          6.0   \n",
       "Ivanhoe                                       10.0          2.0          5.0   \n",
       "Labyrinth: The War on Terror, 2001 – ?        12.0          1.0          2.0   \n",
       "Paths of Glory                                14.0          2.0          2.0   \n",
       "Thunder Alley                                 10.0          2.0          7.0   \n",
       "Twilight Struggle                             13.0          2.0          2.0   \n",
       "Washington's War                              12.0          2.0          2.0   \n",
       "Wilderness War                                12.0          2.0          2.0   \n",
       "\n",
       "                                        min_time  max_time  \\\n",
       "name                                                         \n",
       "Battle Line                                 30.0      30.0   \n",
       "Combat Commander: Europe                    60.0     180.0   \n",
       "Commands & Colors: Ancients                 60.0      60.0   \n",
       "Commands & Colors: Napoleonics              90.0      90.0   \n",
       "Dominant Species                           120.0     240.0   \n",
       "Formula Motor Racing                        20.0      20.0   \n",
       "Here I Stand                               180.0     360.0   \n",
       "Ivanhoe                                     45.0      45.0   \n",
       "Labyrinth: The War on Terror, 2001 – ?     180.0     180.0   \n",
       "Paths of Glory                             480.0     480.0   \n",
       "Thunder Alley                               90.0      90.0   \n",
       "Twilight Struggle                          120.0     180.0   \n",
       "Washington's War                            90.0      90.0   \n",
       "Wilderness War                             180.0     180.0   \n",
       "\n",
       "                                                             designers  \\\n",
       "name                                                                     \n",
       "Battle Line                                            [Reiner Knizia]   \n",
       "Combat Commander: Europe                                 [Chad Jensen]   \n",
       "Commands & Colors: Ancients                             [Richard Borg]   \n",
       "Commands & Colors: Napoleonics                          [Richard Borg]   \n",
       "Dominant Species                                         [Chad Jensen]   \n",
       "Formula Motor Racing                                   [Reiner Knizia]   \n",
       "Here I Stand                                                [Ed Beach]   \n",
       "Ivanhoe                                    [Reiner Knizia, Andy Lewis]   \n",
       "Labyrinth: The War on Terror, 2001 – ?                  [Volko Ruhnke]   \n",
       "Paths of Glory                                            [Ted Raicer]   \n",
       "Thunder Alley                              [Jeff Horger, Carla Horger]   \n",
       "Twilight Struggle                       [Ananda Gupta, Jason Matthews]   \n",
       "Washington's War                                         [Mark Herman]   \n",
       "Wilderness War                                          [Volko Ruhnke]   \n",
       "\n",
       "                                                                               publishers  \\\n",
       "name                                                                                        \n",
       "Battle Line                             [GMT Games, Chrononauts Games, Lavka Games, Ne...   \n",
       "Combat Commander: Europe                                               [GMT Games, Devir]   \n",
       "Commands & Colors: Ancients                         [GMT Games, Wargames Club Publishing]   \n",
       "Commands & Colors: Napoleonics                                                [GMT Games]   \n",
       "Dominant Species                        [GMT Games, Asmodee, Asterion Press, Filosofia...   \n",
       "Formula Motor Racing                    [Egmont Polska, Gibsons, GMT Games, Die Spiege...   \n",
       "Here I Stand                            [GMT Games, Banana Games, Devir, Udo Grebe Gam...   \n",
       "Ivanhoe                                                      [Asmodee, GMT Games, Maldón]   \n",
       "Labyrinth: The War on Terror, 2001 – ?  [GMT Games, Asterion Press, Bard Centrum Gier,...   \n",
       "Paths of Glory                          [GMT Games, Devir, DiceTree Games, Udo Grebe G...   \n",
       "Thunder Alley                                                                 [GMT Games]   \n",
       "Twilight Struggle                       [GMT Games, (Self-Published), Asterion Press, ...   \n",
       "Washington's War                                                  [GMT Games, Spielworxx]   \n",
       "Wilderness War                                                                [GMT Games]   \n",
       "\n",
       "                                                                               categories  \\\n",
       "name                                                                                        \n",
       "Battle Line                                               [Ancient, Card Game, Deduction]   \n",
       "Combat Commander: Europe                                          [Wargame, World War II]   \n",
       "Commands & Colors: Ancients                                            [Ancient, Wargame]   \n",
       "Commands & Colors: Napoleonics                                      [Napoleonic, Wargame]   \n",
       "Dominant Species                                    [Animals, Environmental, Prehistoric]   \n",
       "Formula Motor Racing                                          [Card Game, Racing, Sports]   \n",
       "Here I Stand                            [Negotiation, Pike and Shot, Political, Religi...   \n",
       "Ivanhoe                                                   [Card Game, Fighting, Medieval]   \n",
       "Labyrinth: The War on Terror, 2001 – ?      [Arabian, Modern Warfare, Political, Wargame]   \n",
       "Paths of Glory                                                     [Wargame, World War I]   \n",
       "Thunder Alley                                                            [Racing, Sports]   \n",
       "Twilight Struggle                                    [Modern Warfare, Political, Wargame]   \n",
       "Washington's War                        [Age of Reason, American Revolutionary War, Wa...   \n",
       "Wilderness War                             [Age of Reason, American Indian Wars, Wargame]   \n",
       "\n",
       "                                                                                mechanics  \\\n",
       "name                                                                                        \n",
       "Battle Line                             [Card Play Conflict Resolution, Hand Managemen...   \n",
       "Combat Commander: Europe                [Advantage Token, Campaign / Battle Card Drive...   \n",
       "Commands & Colors: Ancients             [Campaign / Battle Card Driven, Command Cards,...   \n",
       "Commands & Colors: Napoleonics          [Campaign / Battle Card Driven, Command Cards,...   \n",
       "Dominant Species                        [Action Queue, Area Majority / Influence, Card...   \n",
       "Formula Motor Racing                    [Dice Rolling, Hand Management, Relative Movem...   \n",
       "Here I Stand                            [Campaign / Battle Card Driven, Dice Rolling, ...   \n",
       "Ivanhoe                                 [Auction/Bidding, Hand Management, Set Collect...   \n",
       "Labyrinth: The War on Terror, 2001 – ?  [Action Points, Action/Event, Area Majority / ...   \n",
       "Paths of Glory                          [Campaign / Battle Card Driven, Dice Rolling, ...   \n",
       "Thunder Alley                                                     [Hand Management, Race]   \n",
       "Twilight Struggle                       [Action/Event, Advantage Token, Area Majority ...   \n",
       "Washington's War                        [Area Majority / Influence, Campaign / Battle ...   \n",
       "Wilderness War                          [Campaign / Battle Card Driven, Dice Rolling, ...   \n",
       "\n",
       "                                        log_owned  \n",
       "name                                               \n",
       "Battle Line                              4.292965  \n",
       "Combat Commander: Europe                 3.918869  \n",
       "Commands & Colors: Ancients              4.026370  \n",
       "Commands & Colors: Napoleonics           3.705265  \n",
       "Dominant Species                         4.303693  \n",
       "Formula Motor Racing                     3.365488  \n",
       "Here I Stand                             3.712734  \n",
       "Ivanhoe                                  3.408579  \n",
       "Labyrinth: The War on Terror, 2001 – ?   3.952502  \n",
       "Paths of Glory                           3.946943  \n",
       "Thunder Alley                            3.620032  \n",
       "Twilight Struggle                        4.769303  \n",
       "Washington's War                         3.653116  \n",
       "Wilderness War                           3.599556  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gt_df = num_sold_df.set_index(\"name\").join(game_df.set_index(\"name\"))\n",
    "gt_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "4d7c54fc",
   "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": [
    "\n",
    "ax = gt_df.plot(x='num_owned', y='num_sold', kind='scatter')\n",
    "ax.plot(x, np.exp(game_model.params.const + game_model.params.weight * x), color = \"red\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "1b645814",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rsolava/opt/anaconda3/lib/python3.8/site-packages/scipy/stats/stats.py:1603: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=14\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>num_sold</td>     <th>  R-squared:         </th> <td>   0.974</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.972</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   444.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Nov 2021</td> <th>  Prob (F-statistic):</th> <td>7.55e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:33:59</td>     <th>  Log-Likelihood:    </th> <td> -135.34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    14</td>      <th>  AIC:               </th> <td>   274.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    12</td>      <th>  BIC:               </th> <td>   276.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>     <td> 1589.9024</td> <td> 1428.204</td> <td>    1.113</td> <td> 0.287</td> <td>-1521.886</td> <td> 4701.691</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>num_owned</th> <td>    1.6422</td> <td>    0.078</td> <td>   21.078</td> <td> 0.000</td> <td>    1.472</td> <td>    1.812</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.015</td> <th>  Durbin-Watson:     </th> <td>   2.434</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.081</td> <th>  Jarque-Bera (JB):  </th> <td>   2.290</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.913</td> <th>  Prob(JB):          </th> <td>   0.318</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.771</td> <th>  Cond. No.          </th> <td>2.37e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.37e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               num_sold   R-squared:                       0.974\n",
       "Model:                            OLS   Adj. R-squared:                  0.972\n",
       "Method:                 Least Squares   F-statistic:                     444.3\n",
       "Date:                Tue, 09 Nov 2021   Prob (F-statistic):           7.55e-11\n",
       "Time:                        19:33:59   Log-Likelihood:                -135.34\n",
       "No. Observations:                  14   AIC:                             274.7\n",
       "Df Residuals:                      12   BIC:                             276.0\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       1589.9024   1428.204      1.113      0.287   -1521.886    4701.691\n",
       "num_owned      1.6422      0.078     21.078      0.000       1.472       1.812\n",
       "==============================================================================\n",
       "Omnibus:                        5.015   Durbin-Watson:                   2.434\n",
       "Prob(Omnibus):                  0.081   Jarque-Bera (JB):                2.290\n",
       "Skew:                          -0.913   Prob(JB):                        0.318\n",
       "Kurtosis:                       3.771   Cond. No.                     2.37e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.37e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = gt_df.num_sold\n",
    "X = gt_df.num_owned\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "model = sm.OLS(y,X)\n",
    "game_model = model.fit()\n",
    "\n",
    "game_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "b0453465",
   "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": [
    "x = np.arange(0, 60000)\n",
    "\n",
    "ax = gt_df.plot(x='num_owned', y='num_sold', kind='scatter')\n",
    "ax.plot(x, game_model.params.const + game_model.params.num_owned * x, color = \"red\")\n",
    "\n",
    "plt.title(\"Sales data for publisher GMT Games\")\n",
    "plt.ylabel(\"Number of copies sold\")\n",
    "plt.xlabel(\"Number owned by BGG users\")\n",
    "\n",
    "plt.savefig(\"owned_v_sales.png\",bbox_inches=\"tight\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "178f10cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.986762754618917"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gt_df.num_owned.corr(gt_df.num_sold)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d23771d",
   "metadata": {},
   "source": [
    "There is a strong linear relationship between games sold and games owned for this publisher. That's very promising for our analysis, although it may not hold as strongly for all games. It is a very small sample and not representative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3382c0a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.scatter(game_df.weight*game_df.weight,game_df.num_owned)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4f5d02bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08607119106869912"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.num_owned.corr(game_df.weight*game_df.weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "46466a06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09418162849367459"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.num_owned.corr(game_df.weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "60026ac0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='num_owned', ylabel='Count'>"
      ]
     },
     "execution_count": 27,
     "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": [
    "import seaborn as sns\n",
    "sns.histplot(game_df[\"num_owned\"], log_scale=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "56f2b69b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xTdctnnnaMEdjZlaNWnYfmZlZNZwUzMys0FZSkPS6dsrMzKze2m0pfL3NMjMzq7EBB5ol7QS8Fhgr6SOlVRsBo6oMzMzMht/KWgprAxuQkseGpZ/HgP2rDa01X6dgZlaNAVsKEXEtcK2kcyPi/mGKaaW6cZ2CmdlI0O51CutImg5MLG8TEW+qIigzM+uOdpPCD4AzgbOBp6sLx8zMuqndpLAsIr5ZaSQ11moKDE9/YWZ1025SuEzS+4EfAU/2F0bEo5VEVTOtpsDw9BdmVjftJoVD8+/jS2UBbNXZcMzMrJvaSgoRsWXVgZiZWfe1lRQkHdKsPCLO62w4ZmbWTe12H72qtLwusBtwC+CkYGa2Gmm3++jY8mNJo4HvVhKRmZl1zapOnf04sE0nAwGQtK+ksyT9RNIena7fzMwG1u6YwmWks40gTYS3HTCjzW3PAfYGHoqIl5TKpwBfy/WdHRGnRMSPgR9L2hj4EnBlm6/DzMw6oN0xhS+VlpcB90fEwja3PRc4ndL4g6RRwBnAm4GFwI2SLo2I2/NTPpXXm5nZMGqr+yhPjHcnaYbUjYGn2t1BRMwBGi9y2xGYHxELIuIp4CJgHyWfB66IiFua1SdpmqSbJN308MMPtxuGmZm1od07r70LuAF4J/Au4DeShjJ19jjggdLjhbnsWGB3YH9JRzfbMCKmR0RfRPSNHTt2CCGYmVmjdruPTgJeFREPAUgaC1wFXLyK+1WTsoiI0wDPDWFm1iXtnn20Rn9CyB4ZxLbNLATGlx5vDixqd2PfZMfMrBrtfrD/TNIsSYdJOgy4HJg5hP3eCGwjaUtJawMHAJe2u3FEXBYR00aPHj2EEMzMrNGASUHSJEmvi4jjgW8BLwNeDlwPTG9nB5IuzM/fVtJCSUdExDLgGGAWcAcwIyLmtRu0WwpmZtVY2ZjCqcAnASLih8APAST15XVTV7aDiFjxRgOpfCar2Nrw7TjNzKqxsu6jiRExt7EwIm4i3ZrTzMxWIytrKaw7wLrndDKQwZA0FZg6adKkboUwJAcfeTSLl6zY9eU7tZlZt60sKdwo6aiIOKtcKOkI4ObqwhpYXbqPWt2m886772HnD319hXLfqc3Mum1lSeFDwI8kHcSzSaAPWBt4e4VxrRZa3aZz7rz3dSEaM7OVGzApRMSDwGslvRHon8zu8oi4uvLIBlD37iMzs17V7v0UrgGuqTiWttWl+8jMrG6GclWymZmtZpwUzMysUMuk4CuazcyqUcuk4LmPzMyq0e7U2TYMWl3X4IvazGy4OCn0kFbXNfiiNjMbLrXsPvKYgplZNWrZUhhp1ym4W8nMhkstk8JI424lMxsutew+MjOzajgpmJlZwUnBzMwKtUwKPvvIzKwatUwKvqLZzKwatUwKZmZWDScFMzMr+DqFGvNFbWbWaU4KNeaL2sys09x9ZGZmBScFMzMr1LL7SNJUYOqkSZO6HUpP8liDma2qWiaFkTZL6mB5rMHMVpW7j8zMrOCkYGZmBScFMzMrOCmYmVmhlgPN1lkHH3k0i5esOONsq7OVBvt8M6sPJwVj8ZKlgzpbabDPN7P6cPeRmZkVnBTMzKzg7qMRpNWVznfefQ9j9+pCQGbWc3omKUjaCjgJGB0R+3c7ntVRqyud5857XxeiMbNeVGn3kaRzJD0k6baG8imS7pI0X9KJABGxICKOqDIeMzMbWNVjCucCU8oFkkYBZwB7ApOBAyVNrjgOMzNrQ6XdRxExR9LEhuIdgfkRsQBA0kXAPsDt7dQpaRowDWDChAmdC9ZW4DEIs5GnG2MK44AHSo8XAq+W9Dzgv4AdJH0iIj7XbOOImA5MB+jr64uqgx3JPAZhNvJ0IymoSVlExCPA0W1V4PspmJlVohvXKSwExpcebw4sGkwFEXFZREwbPXp0RwMzMxvpupEUbgS2kbSlpLWBA4BLuxCHmZk1qPqU1AuB64FtJS2UdERELAOOAWYBdwAzImLeIOudKmn60qUrTspmZmarruqzj1Y8dSWVzwRmDqFe347TzKwCPXNF82B4oHn15+m5zbqjlknBLYXVn6fnNusOz5JqZmYFJwUzMyvUMin47CMzs2rUMin44jUzs2rUMimYmVk1ann2kU9JtXb51FazwallUvApqdYun9pqNjjuPjIzs4KTgpmZFZwUzMysUMsxBQ80rz5aDQR365afreK57967mbj1C1co94C1rW5qmRQ80Lz6aDUQ3K1bfraM54vv84C1jQjuPjIzs4KTgpmZFZwUzMys4KRgZmaFWg40++yj+unUWUZ33D6P3fZd8S6vrc4O6tZZTKvCU3JYL6hlUvDZR/XTqbOM/hVrDOrsoG6dxbQqPCWH9QJ3H5mZWcFJwczMCk4KZmZWcFIwM7OCk4KZmRWcFMzMrFDLU1J9nUJvanUNAdTreoFOaHXNAXTuuoNOXdfQa/XY8ob7uNYyKfg6hd7U6hoCqNf1Ap3Q6poD6Nx1B526rqHX6rHlDfdxdfeRmZkVnBTMzKzgpGBmZgUnBTMzKzgpmJlZwUnBzMwKTgpmZlZwUjAzs4KTgpmZFXrmimZJ6wPfAJ4CZkfEBV0OycxsxKm0pSDpHEkPSbqtoXyKpLskzZd0Yi7eD7g4Io4C3lZlXGZm1lzV3UfnAlPKBZJGAWcAewKTgQMlTQY2Bx7IT3u64rjMzKyJSruPImKOpIkNxTsC8yNiAYCki4B9gIWkxHArAyQrSdOAaQATJkzofNBmFWs1m2zVM8m2mm1zpM1g2011mEm2G2MK43i2RQApGbwaOA04XdJbgctabRwR04HpAH19fVFhnGaVaDWbbNUzybaabXOkzWDbTXWYSbYbSUFNyiIi/gEc3lYFvp+CmVklunFK6kJgfOnx5sCiwVQQEZdFxLTRo0d3NDAzs5GuG0nhRmAbSVtKWhs4ALh0MBVImipp+tKlze9sZWZmq6bqU1IvBK4HtpW0UNIREbEMOAaYBdwBzIiIeYOp1y0FM7NqVH32UdMb9kbETGBmlfs2M7PBq+U0F+4+MjOrRi2TgruPzMyqUcukYGZm1VBEfa//kvQwcP8qbj4GWNLBcIZTXWN33MOrrnFDfWOvS9xbRMTYZitqnRSGQtJNEdHX7ThWRV1jd9zDq65xQ31jr2vcZe4+MjOzgpOCmZkVRnJSmN7tAIagrrE77uFV17ihvrHXNe7CiB1TMDOzFY3kloKZmTVwUjAzs8KITAot7hE9nPsfL+kaSXdImifpg7n8ZEl/knRr/tmrtM0ncrx3SXpLqfyVkn6f150mSbl8HUnfz+W/aXIHvKHEf1/e562Sbsplm0j6uaR78u+Neyl2SduWjuutkh6T9KFePObN7m0+XMdX0qF5H/dIOrRDsX9R0p2S5kr6kaTn5vKJkp4oHfszS9sMa+wt4h6W98ZQj3nHRcSI+gFGAfcCWwFrA78DJg9zDJsCr8jLGwJ3k+5XfTLwsSbPn5zjXAfYMsc/Kq+7AdiJdPOiK4A9c/n7gTPz8gHA9zsY/33AmIayLwAn5uUTgc/3Yuyl98CfgS168ZgDbwBeAdw2nMcX2ARYkH9vnJc37kDsewBr5uXPl2KfWH5eQz3DGnuLuCt/b3TimHf6ZyS2FIp7REfEU0D/PaKHTUQsjohb8vLfSFOIjxtgk32AiyLiyYj4AzAf2FHSpsBGEXF9pHfYecC+pW2+k5cvBnbr/9ZSkfL+vtMQR6/Fvhtwb0QMdDV81+KOiDnAo03iqfr4vgX4eUQ8GhF/AX4OTBlq7BFxZaQp8wF+TbqxVkvdiL3FMW+lp455p43EpNDsHtEDfSBXKjcjdwB+k4uOyc3sc0pdBK1iHpeXG8uX2yb/Qy4FntehsAO4UtLNkqblshdExOK8v8XA83s0dkjf1C4sPa7DMR+O4zsc/xvvIX2D7relpN9KulbSzqX4eiX2qt8bPfV5BCMzKTS9R/SwRwFI2gC4BPhQRDwGfBPYGtgeWAx8uf+pTTaPAcoH2qYTXhcRrwD2BD4g6Q0DPLenYle629/bgB/koroc81Y6GWel8Us6CVgGXJCLFgMTImIH4CPA9yRttJI4hjP24Xhv9MznUb+RmBSGfI/oTpC0FikhXBARPwSIiAcj4umIeAY4i9TVBa1jXsjyTfHyaym2kbQmMJr2m8cDiohF+fdDwI9ynA/m5nN/8/+hXoydlMhuiYgH82uoxTFneI5vZf8beQB1b+Cg3LVC7n55JC/fTOqbf2GvxD5M742e+DwqG4lJYcj3iB6q3Jf4beCOiPhKqXzT0tPeDvSfCXEpcEA+g2FLYBvghtyN8DdJr8l1HgL8pLRN/5kM+wNX9/8zDjH29SVt2L9MGkS8rWF/hzbE0ROxZwdS6jqqwzFvUndVx3cWsIekjXNXyR65bEgkTQFOAN4WEY+XysdKGpWXt8qxL+iV2IfpvVHJMR+Sbo5yd+sH2It0xs+9wEld2P/rSU3EucCt+Wcv4LvA73P5pcCmpW1OyvHeRT6jIZf3kd6s9wKn8+xV6uuSukjmk86I2KpDsW9FOvPid8C8/uNH6h/9BXBP/r1JD8a+HvAIMLpU1nPHnJS0FgP/In2TPGK4ji+pz39+/jm8Q7HPJ/Wb97/X+8/CeUd+D/0OuAWY2q3YW8Q9LO+NoR7zTv94mgszMyuMxO4jMzNrwUnBzMwKTgpmZlZwUjAzs4KTgpmZFZwUbJVICklfLj3+mKSTO1T3uZL270Rd3SRptqQVbuKuNMvsmFWsszxz552SvilpjbxuTUn/nWfb7J/Z86TSti+Q9D1JC/IUJddLevuqv0JbHTkp2Kp6EthvVT/cqtJ/MdRq7qsRsT1pts6XArvk8s8CmwEvzet3BtaC4oLJHwNzImKriHgl6cLNASen65R8Fa/VgJOCraplpPvRfrhxReM3fUl/z793zROfzZB0t6RTJB0k6QalOei3LlWzu6Rf5uftnbcfpTQ3/415krL3luq9RtL3SBcbNcZzYK7/Nkmfz2XvkvSVvPxBSQvy8taSrsvL90n6tKRb8vYvyuXrK02QdqPSZG775PLnSLoox/Z94DkDHL/j8+u+QdIkSRtK+oPS9CdI2ijvf60B6libdFHUXyStBxwFHBsR/4Q0A29EnJyf+ybgqYgo7lkQEfdHxNebHK9dJf209Ph0SYfl5VMk3Z5f45dy2VhJl+TjcaOk1+XykyVNl3QlcJ6kF+fXe2vefpsBXpt1ibO3DcUZwFxJXxjENi8HtiPN+7IAODsidlS60dCxwIfy8yaSvgFvDVwjaRJp2oClEfEqSesAv8ofOJDmpXlJpKmMC5I2I83h/0rgL6TZXfcF5gDH56ftDDwiaRzpavNflqpYEhGvkPR+4GPAkaSrWa+OiPco3TDmBklXAe8FHo+Il0l6Gekq3VYey6/7EODUiNhb0mzgraRv9AcAl0TEv5ps+2FJB5PuB3FFRNya9/fHSFOxN/PilcSzUpI2IU338KKIiPzaAb5Gar1cJ2kCaZqG7fK6VwKvj4gnJH0d+FpEXKA0xcxIaNXVjlsKtsoizex6HnDcIDa7MdL9JJ4kTQXQ/6H+e1Ii6DcjIp6JiHtIyeNFpHlhDpF0K2mq8eeR5p2BNPfMcgkhexUwOyIejjRl8QXAGyLiz8AGSvM4jQe+R7rRys4snxR+mH/fXIpvD+DEHMds0rf1CXn78wEiYi5peoRWLiz93ikvnw0cnpcPB/6nxbb93UfPB9aXdEDjEyQdnr+RPyBpfJP1Z0j6naQbB4ix0WPAP4GzJe0H9M9jtDtwej4elwIb5eMKcGlEPJGXrwc+KekEYItSufUQJwUbqlNJ88SsXypbRn5v5b7stUvrniwtP1N6/AzLt1wb51/pn2b42IjYPv9sGRH9SeUfLeIb6CY315M+fO8iJYKdSR/Qv2oS79Ol+AS8oxTHhIi4o0XcrUTjckT8CpgoaRfSnbxua7pl/0apFfEzUjKaD0zo/zCOiP/JiWMp6Rv5PNKdxfq3/QDpZkNjm1Rd/P2ydfM2y0gtsktIN4/5WV6/BrBT6XiMK7VYir9LRHyPNG35E8AsSW8a6PVZdzgp2JBExKPADFJi6HcfqdsA0h2nBuoXb+WdktbI4wxbkT64ZwHvK/W7v1BpptaB/AbYRdIYpUHoA4Fr87o5pC6hOcBvgTcCT0bE0pXUOQs4Nic8JO1Qqu+gXPYS4GUD1PHu0u/rS+XnkVoPrVoJhbz/15LuIvc4aebd0yWtm9eP4tmEfDWwrqT3lapYr0XV9wOTlWYBHU1KHv33/xgdETNJ3Xzb5+dfCRxTimt7mlCaCXVBRJxGalEMdHysS5wUrBO+DJTPQjqL9EF8A/BqWn+LH8hdpA/vK4Cj8+Dp2cDtwC1KN1j/FisZF4s0nfEngGvIs3FGRP90xr8kdR3NiYinSTN5XtdGbJ8hJbq5OY7P5PJvkrqk5gIfJ82G2co6kn4DfJDlB+svIN2r98KmWyUfzl01t5Fe/zdy+UmkmT5vk/Tb/Pq+AyyKNPPlvqS/yx/y3+Y7pCmtlxMRD5AS/dwcz2/zqg2Bn+bXd20p7uOAvjx4fDtwdIu4351ju5XUHXjeAK/RusSzpJr1EKWztvaJiH/vdiw2MvnsI7Mekc/O2ZN0bw2zrnBLwczMCh5TMDOzgpOCmZkVnBTMzKzgpGBmZgUnBTMzK/wvi57ntn8tI4QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(x=game_df[\"num_owned\"],bins=50, log_scale=(False,True))\n",
    "\n",
    "plt.xlabel(\"Number owned by BGG users\")\n",
    "\n",
    "plt.title(\"Distribution of number of games owned\")\n",
    "\n",
    "\n",
    "plt.savefig(\"owned_dist.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c237b07b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='num_owned'>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oFl0N9MyGHwWuAp6rZrmvAkuBfxtms/8EfKK6aD8RsSgiTqm29zvVuey5wPLxjl/yFIQm0meAv42Iq4Fv1rTNNuDzETEbeB74PYBSSmfjcru9M95/BU4tpbw21MZKKQ9FxPuAx6qvPwRcVUp5PCL+BngC2MPRpzKkMfFylJKUxFMQkpTEUxCaFCLiszRe1dDXxlLKlzLGI9XBUxCSlMRTEJKUxABLUhIDLElJDLAkJfl/eP473D14z8EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "sns.boxplot(x=np.log(game_df[\"num_owned\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33bc3c3f",
   "metadata": {},
   "source": [
    "Dealing with categorical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ed314838",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_publishers = set(game_df.publishers.dropna().sum())\n",
    "all_designers = set(game_df.designers.dropna().sum())\n",
    "all_categories = set(game_df.categories.dropna().sum())\n",
    "all_mechanics = set(game_df.mechanics.dropna().sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "36b0d3fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5148 different publishers.\n",
      "8669 different designers.\n",
      "83 different categories.\n",
      "182 different mechanics.\n"
     ]
    }
   ],
   "source": [
    "print(\"{} different publishers.\".format(len(all_publishers)))\n",
    "print(\"{} different designers.\".format(len(all_designers)))\n",
    "print(\"{} different categories.\".format(len(all_categories)))\n",
    "print(\"{} different mechanics.\".format(len(all_mechanics)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "3a530ae9",
   "metadata": {},
   "outputs": [],
   "source": [
    "cat_stats = {} #Key categories ,values are (count, mean owned, median owned)\n",
    "for cat in all_categories:\n",
    "    mask = game_df[\"categories\"].apply(lambda x: False if x is None else cat in x)\n",
    "    owned = game_df[mask].num_owned\n",
    "    cat_stats[cat] = (mask.sum(), stats.gmean(owned), owned.mean(), owned.median(), owned.std())\n",
    "\n",
    "cat_list = list(all_categories)\n",
    "cat_list.sort(key=lambda x:cat_stats[x][0], reverse=True)\n",
    "top10cats = cat_list[:10]\n",
    "top5cats = cat_list[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "1d660cd4",
   "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": [
    "top10cats.sort(key=lambda x:cat_stats[x][1])\n",
    "graph = sns.barplot(y= top10cats, x = [cat_stats[s][1] for s in top10cats])\n",
    "graph.axvline(stats.gmean(game_df.num_owned), color = \"red\")\n",
    "\n",
    "plt.ylabel(\"Genre\")\n",
    "plt.xlabel(\"Geometric mean of number owned\")\n",
    "\n",
    "plt.savefig(\"genre_owned.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "0fcc3f8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "mech_stats = {} #Key categories ,values are (count, mean owned, median owned)\n",
    "for mech in all_mechanics:\n",
    "    mask = game_df[\"mechanics\"].apply(lambda x: False if x is None else mech in x)\n",
    "    owned = game_df[mask].num_owned\n",
    "    mech_stats[mech] = (mask.sum(), stats.gmean(owned), owned.mean(), owned.median(), owned.std())\n",
    "    \n",
    "mech_list = list(all_mechanics)\n",
    "mech_list.sort(key=lambda x:mech_stats[x][0], reverse=True)\n",
    "top10mechs = mech_list[:10]\n",
    "top5mechs = mech_list[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "9ca58015",
   "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": [
    "top10mechs.sort(key=lambda x:mech_stats[x][1])\n",
    "graph = sns.barplot(y= top10mechs, x = [mech_stats[s][1] for s in top10mechs])\n",
    "graph.axvline(stats.gmean(game_df.num_owned), color = \"red\")\n",
    "\n",
    "plt.ylabel(\"Mechanics\")\n",
    "plt.xlabel(\"Geometric mean of number owned\")\n",
    "\n",
    "plt.savefig(\"mechs_owned.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "bb237cdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "pub_stats = {} #Key categories ,values are (count, mean owned, median owned)\n",
    "for pub in all_publishers:\n",
    "    mask = game_df[\"publishers\"].apply(lambda x: False if x is None else pub in x)\n",
    "    owned = game_df[mask].num_owned\n",
    "    pub_stats[pub] = (mask.sum(), stats.gmean(owned), owned.mean(), owned.median(), owned.std())\n",
    "\n",
    "pub_list = list(all_publishers)\n",
    "pub_list.sort(key=lambda x:pub_stats[x][0], reverse=True)\n",
    "top10pubs = pub_list[:10]\n",
    "top5pubs = pub_list[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "64d79ea0",
   "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": [
    "top10pubs.sort(key=lambda x:pub_stats[x][1])\n",
    "graph = sns.barplot(y= top10pubs, x = [pub_stats[s][1] for s in top10pubs])\n",
    "graph.axvline(stats.gmean(game_df.num_owned), color = \"red\")\n",
    "plt.ylabel(\"Publisher\")\n",
    "plt.xlabel(\"Geometric mean of number owned\")\n",
    "\n",
    "plt.savefig(\"pub_owned.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac890801",
   "metadata": {},
   "source": [
    "Let's add those top categories/mechanics as rows to the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "88e1f8c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "des_stats = {} #Key categories ,values are (count, mean owned, median owned)\n",
    "for des in all_designers:\n",
    "    mask = game_df[\"designers\"].apply(lambda x: False if x is None else des in x)\n",
    "    owned = game_df[mask].num_owned\n",
    "    des_stats[des] = (mask.sum(), stats.gmean(owned), owned.mean(), owned.median(), owned.std())\n",
    "\n",
    "des_list = list(all_designers)\n",
    "des_list.sort(key=lambda x:des_stats[x][0], reverse=True)\n",
    "top10dess = des_list[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "3e74d4b6",
   "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": [
    "top10dess.sort(key=lambda x:des_stats[x][1])\n",
    "graph = sns.barplot(y= top10dess, x = [des_stats[s][1] for s in top10dess])\n",
    "graph.axvline(stats.gmean(game_df.num_owned), color = \"red\")\n",
    "\n",
    "plt.ylabel(\"Designer\")\n",
    "plt.xlabel(\"Geometric mean of number owned\")\n",
    "\n",
    "plt.savefig(\"designer_owned.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e6c94b7",
   "metadata": {},
   "source": [
    "Add rows for the top 5 most common categories, mechanics, and publishers, as well as Uncredited in the designer feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "503889f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "for cat in top5cats:\n",
    "    game_df[cat] = game_df.categories.apply(lambda x: 0 if x is None or cat not in x else 1)\n",
    "\n",
    "for mech in top5mechs:\n",
    "    game_df[mech] = game_df.mechanics.apply(lambda x: 0 if x is None or mech not in x else 1)\n",
    "    \n",
    "for pub in top5pubs:\n",
    "    game_df[pub] = game_df.publishers.apply(lambda x: 0 if x is None or pub not in x else 1)\n",
    "\n",
    "game_df[\"(Uncredited)\"] = game_df.designers.apply(lambda x: 0 if x is None or \"(Uncredited)\" not in x else 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5af2c44e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18678, 32)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "game_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "5b882b95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>log_owned</td>    <th>  R-squared:         </th> <td>   0.283</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.282</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   234.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Nov 2021</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:28:04</td>     <th>  Log-Likelihood:    </th> <td> -9705.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 13074</td>      <th>  AIC:               </th> <td>1.946e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 13051</td>      <th>  BIC:               </th> <td>1.963e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    22</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "             <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>                  <td>   10.8735</td> <td>    1.064</td> <td>   10.223</td> <td> 0.000</td> <td>    8.789</td> <td>   12.958</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>year</th>                   <td>   -0.0049</td> <td>    0.001</td> <td>   -9.199</td> <td> 0.000</td> <td>   -0.006</td> <td>   -0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>rating</th>                 <td>    0.1913</td> <td>    0.007</td> <td>   29.359</td> <td> 0.000</td> <td>    0.179</td> <td>    0.204</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th>                 <td>    0.0965</td> <td>    0.008</td> <td>   12.362</td> <td> 0.000</td> <td>    0.081</td> <td>    0.112</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>player_age</th>             <td>    0.0147</td> <td>    0.002</td> <td>    7.707</td> <td> 0.000</td> <td>    0.011</td> <td>    0.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Card Game</th>              <td>    0.0064</td> <td>    0.011</td> <td>    0.563</td> <td> 0.574</td> <td>   -0.016</td> <td>    0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Wargame</th>                <td>   -0.2414</td> <td>    0.018</td> <td>  -13.515</td> <td> 0.000</td> <td>   -0.276</td> <td>   -0.206</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Fantasy</th>                <td>    0.0470</td> <td>    0.014</td> <td>    3.339</td> <td> 0.001</td> <td>    0.019</td> <td>    0.075</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Party Game</th>             <td>    0.0446</td> <td>    0.016</td> <td>    2.703</td> <td> 0.007</td> <td>    0.012</td> <td>    0.077</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Dice</th>                   <td>    0.0452</td> <td>    0.018</td> <td>    2.453</td> <td> 0.014</td> <td>    0.009</td> <td>    0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Dice Rolling</th>           <td>    0.0639</td> <td>    0.013</td> <td>    5.037</td> <td> 0.000</td> <td>    0.039</td> <td>    0.089</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Hand Management</th>        <td>    0.1720</td> <td>    0.012</td> <td>   14.039</td> <td> 0.000</td> <td>    0.148</td> <td>    0.196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Set Collection</th>         <td>    0.1607</td> <td>    0.013</td> <td>   11.993</td> <td> 0.000</td> <td>    0.134</td> <td>    0.187</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Variable Player Powers</th> <td>    0.1330</td> <td>    0.015</td> <td>    9.050</td> <td> 0.000</td> <td>    0.104</td> <td>    0.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Hexagon Grid</th>           <td>   -0.0289</td> <td>    0.020</td> <td>   -1.455</td> <td> 0.146</td> <td>   -0.068</td> <td>    0.010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Asmodee</th>                <td>    0.6439</td> <td>    0.028</td> <td>   23.388</td> <td> 0.000</td> <td>    0.590</td> <td>    0.698</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Hasbro</th>                 <td>    0.3918</td> <td>    0.028</td> <td>   13.893</td> <td> 0.000</td> <td>    0.337</td> <td>    0.447</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Self-Published)</th>       <td>   -0.3214</td> <td>    0.028</td> <td>  -11.297</td> <td> 0.000</td> <td>   -0.377</td> <td>   -0.266</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Web published)</th>        <td>   -0.2864</td> <td>    0.029</td> <td>  -10.000</td> <td> 0.000</td> <td>   -0.343</td> <td>   -0.230</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>999 Games</th>              <td>    0.7108</td> <td>    0.030</td> <td>   23.650</td> <td> 0.000</td> <td>    0.652</td> <td>    0.770</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Uncredited)</th>           <td>   -0.1530</td> <td>    0.020</td> <td>   -7.485</td> <td> 0.000</td> <td>   -0.193</td> <td>   -0.113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>avg_time</th>               <td>-7.688e-06</td> <td> 2.62e-05</td> <td>   -0.294</td> <td> 0.769</td> <td> -5.9e-05</td> <td> 4.36e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>avg_players</th>            <td>    0.0006</td> <td>    0.001</td> <td>    0.969</td> <td> 0.333</td> <td>   -0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>294.368</td> <th>  Durbin-Watson:     </th> <td>   1.973</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 358.879</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.306</td>  <th>  Prob(JB):          </th> <td>1.18e-78</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.533</td>  <th>  Cond. No.          </th> <td>4.80e+05</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 4.8e+05. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              log_owned   R-squared:                       0.283\n",
       "Model:                            OLS   Adj. R-squared:                  0.282\n",
       "Method:                 Least Squares   F-statistic:                     234.7\n",
       "Date:                Tue, 09 Nov 2021   Prob (F-statistic):               0.00\n",
       "Time:                        21:28:04   Log-Likelihood:                -9705.9\n",
       "No. Observations:               13074   AIC:                         1.946e+04\n",
       "Df Residuals:                   13051   BIC:                         1.963e+04\n",
       "Df Model:                          22                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==========================================================================================\n",
       "                             coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------\n",
       "const                     10.8735      1.064     10.223      0.000       8.789      12.958\n",
       "year                      -0.0049      0.001     -9.199      0.000      -0.006      -0.004\n",
       "rating                     0.1913      0.007     29.359      0.000       0.179       0.204\n",
       "weight                     0.0965      0.008     12.362      0.000       0.081       0.112\n",
       "player_age                 0.0147      0.002      7.707      0.000       0.011       0.018\n",
       "Card Game                  0.0064      0.011      0.563      0.574      -0.016       0.029\n",
       "Wargame                   -0.2414      0.018    -13.515      0.000      -0.276      -0.206\n",
       "Fantasy                    0.0470      0.014      3.339      0.001       0.019       0.075\n",
       "Party Game                 0.0446      0.016      2.703      0.007       0.012       0.077\n",
       "Dice                       0.0452      0.018      2.453      0.014       0.009       0.081\n",
       "Dice Rolling               0.0639      0.013      5.037      0.000       0.039       0.089\n",
       "Hand Management            0.1720      0.012     14.039      0.000       0.148       0.196\n",
       "Set Collection             0.1607      0.013     11.993      0.000       0.134       0.187\n",
       "Variable Player Powers     0.1330      0.015      9.050      0.000       0.104       0.162\n",
       "Hexagon Grid              -0.0289      0.020     -1.455      0.146      -0.068       0.010\n",
       "Asmodee                    0.6439      0.028     23.388      0.000       0.590       0.698\n",
       "Hasbro                     0.3918      0.028     13.893      0.000       0.337       0.447\n",
       "(Self-Published)          -0.3214      0.028    -11.297      0.000      -0.377      -0.266\n",
       "(Web published)           -0.2864      0.029    -10.000      0.000      -0.343      -0.230\n",
       "999 Games                  0.7108      0.030     23.650      0.000       0.652       0.770\n",
       "(Uncredited)              -0.1530      0.020     -7.485      0.000      -0.193      -0.113\n",
       "avg_time               -7.688e-06   2.62e-05     -0.294      0.769    -5.9e-05    4.36e-05\n",
       "avg_players                0.0006      0.001      0.969      0.333      -0.001       0.002\n",
       "==============================================================================\n",
       "Omnibus:                      294.368   Durbin-Watson:                   1.973\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              358.879\n",
       "Skew:                           0.306   Prob(JB):                     1.18e-78\n",
       "Kurtosis:                       3.533   Cond. No.                     4.80e+05\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 4.8e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X =game_df.drop(columns =[\"name\",\"url\",\"num_owned\",\"designers\",\"publishers\",\"categories\",\"mechanics\",\"log_owned\"])\n",
    "#X[\"weight_sq\"] = X.weight*X.weight\n",
    "#X = X.drop(columns=\"weight\")\n",
    "X[\"avg_time\"] = (X.min_time + X.max_time)/2\n",
    "X = X.drop(columns=[\"min_time\",\"max_time\"])\n",
    "X[\"avg_players\"] = (X.min_players + X.max_players)/2\n",
    "X = X.drop(columns=[\"min_players\",\"max_players\"])\n",
    "y = game_df.log_owned\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "X, X_test, y, y_test = train_test_split(X,y, test_size=0.3)\n",
    "\n",
    "model = sm.OLS(y,X)\n",
    "game_model = model.fit()\n",
    "\n",
    "game_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "eaff6dcf",
   "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": [
    "y_pred = game_model.predict(X_test)\n",
    "residuals = y_test - y_pred\n",
    "\n",
    "plt.scatter(y_pred, residuals)\n",
    "\n",
    "plt.xlabel(\"Fitted values\")\n",
    "plt.ylabel(\"Residual\")\n",
    "\n",
    "\n",
    "plt.savefig(\"heteroskadicity.png\",bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "587cf758",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c63be562",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "82be1747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='year', ylabel='num_owned'>"
      ]
     },
     "execution_count": 45,
     "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": [
    "vals = game_df.sort_values(by=\"year\").groupby(by=\"year\").num_owned.median()\n",
    "sns.lineplot(x = vals.index, y = vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "fd576dac",
   "metadata": {},
   "outputs": [],
   "source": [
    "#game_df[game_df.year==1630]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "79e312cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(max_depth=100, max_features=None)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = game_df.log_owned\n",
    "X = game_df.drop(columns =[\"name\",\"url\",\"num_owned\",\"designers\",\n",
    "                           \"publishers\",\"categories\",\"mechanics\",\"log_owned\"])\n",
    "\n",
    "X, X_test, y, y_test = train_test_split(X,y, test_size=0.3)\n",
    "\n",
    "reg_tree = RandomForestRegressor(max_depth=100,n_estimators = 100,max_features=None)\n",
    "reg_tree.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "41e165ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4588581819552201"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_tree.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "bb9fdaa3",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = reg_tree.predict(X_test)\n",
    "residuals = y_test - y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "4b9f16f7",
   "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": [
    "from statsmodels.graphics.gofplots import qqplot\n",
    "\n",
    "qp = qqplot(residuals, line = 'q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "150c703e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a29ef2b0>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_test, residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "7920661b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12291669, 0.3271045 , 0.07028551, 0.03147653, 0.06578217,\n",
       "       0.05760102, 0.06876673, 0.01641372, 0.01011061, 0.01444497,\n",
       "       0.00755012, 0.01005713, 0.01559797, 0.01848169, 0.01703609,\n",
       "       0.02012112, 0.00883316, 0.04612147, 0.00721124, 0.00823228,\n",
       "       0.00772112, 0.04071279, 0.00742138])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_tree.feature_importances_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "16907948",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.inspection import permutation_importance\n",
    "\n",
    "result = permutation_importance(reg_tree, X, y, n_repeats=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "a9a7fe53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'importances_mean': array([0.29384146, 0.92076188, 0.17256168, 0.05408161, 0.14973852,\n",
       "        0.14109201, 0.24018507, 0.02888382, 0.0498965 , 0.02660935,\n",
       "        0.01618004, 0.01525439, 0.03857762, 0.16883147, 0.06217166,\n",
       "        0.13005699, 0.01919834, 0.10534696, 0.01745561, 0.01256313,\n",
       "        0.01091112, 0.10475558, 0.02156174]),\n",
       " 'importances_std': array([0.0038007 , 0.0073547 , 0.00255616, 0.0008331 , 0.00162216,\n",
       "        0.00222762, 0.00385062, 0.00049023, 0.0016332 , 0.00089466,\n",
       "        0.00045416, 0.00030033, 0.00083289, 0.0023574 , 0.00161652,\n",
       "        0.00269667, 0.00121799, 0.00355438, 0.00071259, 0.00108956,\n",
       "        0.00052197, 0.00216156, 0.0006232 ]),\n",
       " 'importances': array([[0.28769582, 0.29042561, 0.29508048, 0.29807504, 0.29392092,\n",
       "         0.29312764, 0.29046383, 0.29142334, 0.29799147, 0.30021044],\n",
       "        [0.91822937, 0.92955599, 0.93416532, 0.92624608, 0.9172388 ,\n",
       "         0.91010474, 0.91056086, 0.92114543, 0.92306527, 0.91730693],\n",
       "        [0.1688157 , 0.16850125, 0.17170208, 0.1769682 , 0.17162737,\n",
       "         0.17327946, 0.17183677, 0.1754319 , 0.17467468, 0.17277936],\n",
       "        [0.05558868, 0.05472948, 0.05373567, 0.05470791, 0.05289522,\n",
       "         0.05418526, 0.05482236, 0.05337585, 0.05299422, 0.05378143],\n",
       "        [0.15198193, 0.15068056, 0.14961864, 0.15040343, 0.14727945,\n",
       "         0.15138924, 0.1506201 , 0.14654754, 0.1493377 , 0.14952661],\n",
       "        [0.13935239, 0.1416291 , 0.14025353, 0.14349228, 0.1416036 ,\n",
       "         0.13674421, 0.14251948, 0.13857025, 0.14433508, 0.14242024],\n",
       "        [0.23643907, 0.24607182, 0.23685823, 0.24090904, 0.23771446,\n",
       "         0.24369961, 0.23365441, 0.24101288, 0.24018724, 0.24530399],\n",
       "        [0.02906535, 0.02900961, 0.02814511, 0.02905912, 0.02907873,\n",
       "         0.02935249, 0.02889251, 0.02859843, 0.02966406, 0.02797274],\n",
       "        [0.05311591, 0.04860174, 0.05014722, 0.0501219 , 0.0506366 ,\n",
       "         0.04687084, 0.04897858, 0.04858242, 0.05101248, 0.05089729],\n",
       "        [0.02588661, 0.02680579, 0.02614161, 0.02693587, 0.0245649 ,\n",
       "         0.02812509, 0.02719198, 0.02714159, 0.02656462, 0.02673539],\n",
       "        [0.01671552, 0.0161474 , 0.01536755, 0.01642118, 0.01599538,\n",
       "         0.0160508 , 0.01544103, 0.01649642, 0.01671561, 0.0164495 ],\n",
       "        [0.01475256, 0.01547522, 0.01522569, 0.01519817, 0.01535925,\n",
       "         0.01496397, 0.01549035, 0.0148964 , 0.01580495, 0.01537729],\n",
       "        [0.038515  , 0.03633576, 0.03870692, 0.03966986, 0.03828585,\n",
       "         0.03848028, 0.0390395 , 0.03907233, 0.03875836, 0.03891238],\n",
       "        [0.16926876, 0.16597962, 0.17071786, 0.17092583, 0.17078958,\n",
       "         0.17117928, 0.17048267, 0.16680493, 0.16808522, 0.16408092],\n",
       "        [0.06046996, 0.06152138, 0.06309221, 0.06086101, 0.06164079,\n",
       "         0.06439482, 0.0612954 , 0.06072052, 0.06206481, 0.06565567],\n",
       "        [0.13009492, 0.13186528, 0.12540886, 0.13300756, 0.12852519,\n",
       "         0.1327863 , 0.13272966, 0.12824831, 0.1260809 , 0.13182295],\n",
       "        [0.01972915, 0.01920953, 0.01991111, 0.01808249, 0.02057031,\n",
       "         0.01961813, 0.01900718, 0.02086238, 0.0185319 , 0.01646123],\n",
       "        [0.10255837, 0.10577578, 0.10047476, 0.10357912, 0.10751351,\n",
       "         0.10608979, 0.11168881, 0.10958587, 0.10010195, 0.10610162],\n",
       "        [0.01661777, 0.01894085, 0.01687945, 0.01743008, 0.01664923,\n",
       "         0.01739985, 0.01754669, 0.01777843, 0.01695317, 0.01836062],\n",
       "        [0.01196826, 0.01508128, 0.01187901, 0.0111482 , 0.01214414,\n",
       "         0.01197333, 0.01323344, 0.01378149, 0.01223612, 0.01218599],\n",
       "        [0.01119824, 0.00954139, 0.01097945, 0.01118057, 0.01093597,\n",
       "         0.01084846, 0.01116011, 0.01146494, 0.01050406, 0.01129801],\n",
       "        [0.10728794, 0.10005317, 0.10633056, 0.10429228, 0.10540592,\n",
       "         0.10757882, 0.10475129, 0.10471441, 0.10210452, 0.10503694],\n",
       "        [0.02175078, 0.02187727, 0.02222194, 0.02175333, 0.02135543,\n",
       "         0.02072242, 0.02048029, 0.02143197, 0.02269648, 0.02132746]])}"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "20480efe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['year', 'weight', 'player_age', 'min_players', 'max_players',\n",
       "       'min_time', 'max_time', 'Card Game', 'Wargame', 'Fantasy', 'Party Game',\n",
       "       'Dice', 'Dice Rolling', 'Hand Management', 'Set Collection',\n",
       "       'Variable Player Powers', 'Hexagon Grid', 'Asmodee', 'Hasbro',\n",
       "       '(Self-Published)', '(Web published)', '999 Games', '(Uncredited)'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "2a02c5cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "\n",
    "lr.fit(X, np.log10(y))\n",
    "y_pred = lr.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "8043c93f",
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = np.log10(y_test) - y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "9a42e0cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JYBjDLLqxHYClnM6dTCZOjPmMZCcVWbet00kiLSeTq57+EbgD6AAcY2bDgB+6+6fzXJsUqSFDYOXKg/f34j3GUZ0Ih36sA+AtBvIEnyFOjFmMYTM9s25TwSBSOJmcerqFYH3r2QDuviw8/SRtSKreQ2c+4gLmJq5OOpXlAGzhcKoZx21hZLzFsTm1qXAQKQ6ZBMVed99uB5581j/hNiJ5QLodeziTxYkewwiepT17+YRDmMf5PMLniRNjGcOyHmeop3AQKT6ZBMVyM/scUG5mg4AbgYX5LUsKqaICdu4EcE5mVTifapzRzOZQdrAPYwlncAffIk6MhZzLJ3TKqS0Fg0jxyyQobgCmALuAxwhWpLstn0VJy6u/+a036/nnpHGGvuES5as5jkf5HDMYzyzGsJXDc2pHwSDS+mRy1VMtQVBMyX850lLqew1d+ZBRzOE7YTAMIRil3sQRVDMusXDP2+Q2LKV7GkRav0aDwsz+l4ixCF311PoMGQKvrdzD2TzHTeFMq2fzHO2oo5ZOzOUCfsOXiBPjJYbilGXdhnoMIqUnqkdxR4tVIXlx3XVw993OEFYQI86PiTOKOXTlI+ooYzFnMo2biRPjWUawm0NyaqdTJ6itbebiRaRoNBoU7j4nX42a2eHAb4GBwNvAZ9x9a4Nj+gEPAUcB+4Dp7n5nvmoqFbEYvFK9LjHG8APiHMX7ALzKCTzEvxAnxmxGs43uObdTVgZ1dc1VtYgUs6hTT0+4+2fM7GVSnIJy96FNaPdmoNrdp5nZzeH2TQ2O2Qt8092XmllXYImZzXD3FLd6tW0TRm+HObOJEeeXzOAkXgXgfY4M4yIYZ3gnuLm+SdR7EGl7ok49TQ4fL85DuxOA0eHzBwlu5jsgKNx9A7AhfL7DzFYBfYE2HxQ3fnUXL05flOg1PMXzlLOPj6lgDqP4b75KnBjLOYVsJ9RL5ZFHYOLEptctIq1T1KmnDeHT69z9gC9xM/sxB/cAstGr/vPdfYOZRc4dbWYDgdOB5yKOmQRMAujfv+m/OReVffvg5ZdZ8h9xNj4a53bm0pla9lLO85zFVKYQJ8YizmEPHZqlyWuvhbvuapaPEpFWzjzNZSpmttTdhzfY91K6U09mFicYX2hoCvCgu3dLOnaru6c8YW5mXYA5BLPXPhVZbKiystJramoyObR4rV0L8XjwU10NGzcCsJKTE6eT5jCKDzmsyU116wZbt6Y9TERKmJktcffKVK9FjVFcC1wHHGtmLyW91BVYkK5Rd49FfPb7ZtY77E30BjY2clx7ghX2qjINiVZr61aYNWt/OLz+OgAbOIo4f5cIh/X0bbYm1WsQkUxEjVE8CvwfcDvBYHO9He7+QRPbfZpgIaRp4eMfGx5gweRS9wGr3P1nTWyv+HzyCSxcuD8YliwJTjF16cKzHUfzOF8jToyVDKY5xhkAxo0LmhIRyUbaU08AZlYO9CIpWNx9bc6NmvUAniBY42ItcLm7f2BmfYB73f0iMxsJzANeJrg8FuB77v5Mus8vylNP+/bBiy8G39QzZsC8eUFYtGsH55wDsRh3LIvx3f85i73NtIBgu3bwwAMaiBaR9HI69ZT05usJphp/n/1f2A7kfHmsu28BxqXYvx64KHw+n+b6VbpQ3nrrwHGGLVuC/UOGwFe/Gtz0MGoU193UlbtvaZ4mBw+GFSua57NERCCzSQG/DpwYfrlLlC1bYObM/eHw5pvB/j594OKLg2AYNw569068Jbh7Ovcm1WsQkXzLJCjegXANSznQzp2wYMH+YFi6NJjsqGtXGDMGvvGNIBxOPPGgxaSrqmDy5P2djFxoMFpEWkImQfEmMNvM/kww1TgAJTnAnE5dHbzwwv5gmD8fdu2C9u1hxAi49dYgGM48M/hVP4WqquCs08cf515Gly5wzz3qRYhIy8gkKNaGPx3Cn7bDPTh9NGNGEAwzZ+6/4WDoUPja14JgOP/84Ns7QlMComNHuPdeBYOIFEYm61Hc2hKFFI1Nmw4cZ3j77WB/v35w6aVBMIwdC716ZfRxCggRae0yueqpJ/AdYAjQsX6/u4/NY10tp7Y2uFS1PhiWLQv2H3ZYEAjf/nYQDoMGHTTOkE5VFXzpS7BnT3YlmcHDDysgRKQ4ZHLqqYpgSvCLgWsIbpDblM+i8qquLri5rf5+hoULYfdu6NABzjsPpk4NgmH48EbHGTI1eXL2IdGhA9x/v0JCRIpHJt+EPdz9PjObHK5RMcfM8rZWRd488AA8/XQwTca2bcG+YcOCb/NYDEaODNYHbSZVVdlf0dSjB9x5p0JCRIpLJkFR/zvxBjP7B2A9cHT+SsqTP/whuDP6ssv2jzP07Jm35qZkuMK4rmASkWKXSVD8yMwOA74J/AI4FPhGXqvKh0cfDXoMWY4z5GptmglOFBAi0lpkctXTn8Kn24Ex+S0njzp3btHm+veHNWsO3l9WBg89pIAQkdYjk6uefkPqpVCvzktFrVQmd1pXVMD06QoJEWldMjn19Kek5x2BSwnGKSSUyWWwGqgWkdYqk1NPTyZvm9ljgFY1SDJlSvrLYLt0UUiISOtUlsN7BhGsIyGhdAPXmR4jIlKMMhmj2EEwRmHh43vATXmuq1VpbOC64TEiIq1R2h6Fu3d190OTHk9oeDqqrZs6NZhAtjEVFcExIiKtUWSPwsw6AROBweGuGuD37r4734W1JvVjD8lXPZWVBaufDhgQhITGJ0SktWq0R2FmpwKrgPOBt4E1wN8DC8ysm5n9qEUqbCUmToTNm4OZyd2DKaXcg8lnFRIi0ppF9Sh+DnzF3Wck7zSzGLAcyHllZjM7nGCiwYEEIfQZd9/ayLHlBD2Zd9394lzbFBGR3ESNUfRuGBIA7h4nmP/p0ia0ezNQ7e6DgOpwuzGTCXo2IiJSAFFBUWZmhzTcaWYdgT3uXtuEdicAD4bPHwQuSXWQmR0N/ANwbxPaEhGRJogKioeAJ81sYP2O8PkTwMNNbLeXu28ACB+PbOS4/yJYNGlfug80s0lmVmNmNZs2td7lMkREik2jQeHuPwL+Asw1s81mthmYA8xw99vSfbCZxc1seYqfCZkUZmYXAxvdfUkmx7v7dHevdPfKnnmcPhyCKTsGDgyubDriiOCnrCzYV1WV16ZFRFpc5OWx7v5L4Jdm1jXc3pHpB7t7rLHXzOx9M+vt7hvMrDewMcVh5wGfNrOLCOaYOtTMHnH3z2daQz5UVcGkScEKqnDgJIBr1gSvga50EpHSkdEUHu6+I5uQyMDTBEuqEj7+MUWb33X3o919IHAFMLPQIQHBvE61EaMztbWZL1okItIa5DLXU3OYBow3s9eB8eE2ZtbHzJ4pUE0Z0bxOItLWZDLNeLNz9y3AuBT71wMXpdg/G5id98IyoHmdRKStSdujMLMKM/u+mf063B4UDjS3SVOnBnM3NUbzOolIqcnk1NNvgF3AiHB7HdDmpu+ov9LpC1+ATp2ChYjMgsf65wMGaAU7ESk9mZx6Os7dP2tmVwK4+04zszzXVVRSXelUUQEPP6xQEJHSl0mPYnc4i6wDmNlxBD2MkpZ8r8RVVx18pZOubhKRtiKTHsW/Edx418/Mqgjub/hiPosqtIY9iLq61Mfp6iYRaQsyWTN7hpktBc4hWOVusrtvzntlBZTuXol6urpJRNqCRoPCzIY32LUhfOxvZv3dfWn+yiqsTHoKurpJRNqKqB7FTyNec2BsM9dSNBq7V6K8PFi1rn9/rVonIm1Ho0Hh7mNaspBiMnXqgWMUEPQgdOmriLRFmdxw19HM/tXMnjKzJ83s6+GaFCVr4sQgFAYM0P0RIiLm7tEHmD0B7AAeCXddCXR398vzXFvOKisrvaamptBliIi0Gma2xN0rU72WyX0UJ7r7l919VvgzCTiheUssrOR7JrSmhIjIgTIJihfM7Jz6DTM7G1iQv5JaVv09E2vWgPv+NSUUFiIigUxOPa0CTgTqLxrtD6wiWJ7U3X1oXivMQTanngYOTH2F04AB8PbbzVqWiEjRijr1lMmd2Rc2cz1FpbF7JnTXtYhIIO2pJ3dfA3wIHAb0qP9x9zXha61aY3dX665rEZFA2h6Fmd1GMLfTG4QTA1JCN9w1ds+E7roWEQlkcurpMwRTje/OdzGFUH9vxJQpwekm3XUtInKgTIJiOdAN2JjfUgpn4kQFg4hIYzIJitsJLpFdTtI6FO7+6VwbNbPDgd8CA4G3gc+4+9YUx3UD7gVOITjddbW7P5truyIikr1MguJB4MfAywSXxDaHm4Fqd59mZjeH2zelOO5O4C/ufpmZdQAiVqsWEZF8yCQoNrv7z5u53QnA6PD5g8BsGgSFmR0KXEC4SFI4RlKS4yQiIsUsk6BYYma3A09z4KmnpqxH0cvdN4Sfs8HMjkxxzLHAJuA3ZnYasIRg0aSPm9CuiIhkKZOgOD18PCdpX9rLY80sDhyV4qVMV5puBwwHbnD358zsToJTVN9vpL1JwCSA/roJQkSk2WSyFGpO61K4e6yx18zsfTPrHfYmepP6iqp1wDp3fy7c/j1BUDTW3nRgOgRTeORSs4iIHCyTHgVm9g/AECCxDoW7/7AJ7T4NXAVMCx//2PAAd3/PzN4xsxPd/VVgHLCyCW2KiEgOMlm46B7gs8ANgAGXAwOa2O40YLyZvQ6MD7cxsz5m9kzScTcAVWb2EjAM+PcmtisiIlnKpEdxrrsPNbOX3P1WM/sp8FRTGnX3LQQ9hIb71wMXJW0vA1LOZigiIi0jk/UodoaPtWbWB9gDHJO/kkREpJhk0qP4U3iH9E+ApQRXPP06n0WJiEjxyOSqp9vCp0+a2Z+Aju6+Pb9liYhIsWj01JOZnWlmRyVt/wvwBHBbOFeTiIi0AVFjFP9NOGWGmV1AcGXSQ8B2wvsVRESk9EWdeip39w/C558Fprv7kwSnoJblvTIRESkKUT2KcjOrD5JxwMyk1zK6UU9ERFq/qC/8x4A5ZraZ4BLZeQBmdjzB6ScREWkDGg0Kd59qZtVAb+Bv7l4/f1IZwR3TIiLSBkSeQnL3RSn2vZa/ckREpNhkcme2iIi0YQoKERGJpKAQEZFICgoREYmkoBARkUgKChERiaSgEBGRSAoKERGJpKAQEZFICgoREYlUkKAws8PNbIaZvR4+dm/kuG+Y2QozW25mj5lZx5auVUSkrStUj+JmoNrdBwHV4fYBzKwvcCNQ6e6nAOXAFS1apYiIFCwoJgAPhs8fBC5p5Lh2QKdwXYwKYH3+SxMRkWSFCope7r4BIHw8suEB7v4ucAewFtgAbHf3vzX2gWY2ycxqzKxm06ZNeSpbRKTtyVtQmFk8HFto+DMhw/d3J+h5HAP0ATqb2ecbO97dp7t7pbtX9uzZs3n+ECIikr8lTd091thrZva+mfV29w1m1hvYmOKwGPCWu28K3/MUcC7wSF4KFhGRlAp16ulp4Krw+VXAH1McsxY4x8wqzMwI1u1e1UL1iYhIqFBBMQ0Yb2avA+PDbcysj5k9A+DuzwG/B5YCL4e1Ti9MuSIibZftXwq7dFRWVnpNTU2hyxARaTXMbIm7V6Z6TXdmi4hIJAWFiIhEUlCIiEgkBYWIiERSUIiISCQFhYiIRFJQiIhIJAWFiIhEUlCIiEgkBYWIiERSUIiISCQFhYiIRFJQiIhIJAWFiIhEUlCIiEgkBYWIiERSUIiISCQFhYiIRFJQiIhIpIIEhZldbmYrzGyfmaVcozU87kIze9XMVpvZzS1Zo4iIBArVo1gO/BMwt7EDzKwc+BXwKWAwcKWZDW6Z8kREpF67QjTq7qsAzCzqsLOA1e7+Znjs48AEYGXeCxQRkYRiHqPoC7yTtL0u3JeSmU0ysxozq9m0aVPeixMRaSvy1qMwszhwVIqXprj7HzP5iBT7vLGD3X06MB2gsrKy0eNERCQ7eQsKd4818SPWAf2Sto8G1jfxM0VEJEvFfOppMTDIzI4xsw7AFcDTBa5JRKTNKdTlsZea2TpgBPBnM/truL+PmT0D4O57geuBvwKrgCfcfUUh6hURacsKddXTH4A/pNi/HrgoafsZ4JkWLE1ERBoo5lNPIiJSBBQUIiISqU0ERVUVDBwIZWXBY1VVoSsSEWk9CjJG0ZKqqmDSJKitDbbXrAm2ASZOLFxdIiKtRcn3KKZM2R8S9Wprg/0iIpJeyQfF2rXZ7RcRkQOVfFD075/dfhEROVDJB8XUqVBRceC+iopgv4iIpFfyQTFxIkyfDgMGgFnwOH26BrJFRDJV8lc9QRAKCgYRkdyUfI9CRESaRkEhIiKRFBQiIhJJQSEiIpEUFCIiEsncS295aTPbBKwpYAlHAJsL2H4uVHPLUM0tQzVnb4C790z1QkkGRaGZWY27Vxa6jmyo5pahmluGam5eOvUkIiKRFBQiIhJJQZEf0wtdQA5Uc8tQzS1DNTcjjVGIiEgk9ShERCSSgkJERCIpKPLAzG4zs5fMbJmZ/c3M+hS6pkyY2U/M7JWw9j+YWbdC15SOmV1uZivMbJ+ZFeWlhQBmdqGZvWpmq83s5kLXkwkzu9/MNprZ8kLXkikz62dms8xsVfj/xeRC15SOmXU0s+fN7MWw5lsLXVNDGqPIAzM71N0/DJ/fCAx292sKXFZaZvZ3wEx332tmPwZw95sKXFYkMzsZ2Af8N/Atd68pcEkHMbNy4DVgPLAOWAxc6e4rC1pYGmZ2AfAR8JC7n1LoejJhZr2B3u6+1My6AkuAS4r579rMDOjs7h+ZWXtgPjDZ3RcVuLQE9SjyoD4kQp2BVpHG7v43d98bbi4Cji5kPZlw91Xu/mqh60jjLGC1u7/p7ruBx4EJBa4pLXefC3xQ6Dqy4e4b3H1p+HwHsAroW9iqonngo3CzffhTVN8ZCoo8MbOpZvYOMBH4QaHrycHVwP8VuogS0Rd4J2l7HUX+5VUKzGwgcDrwXIFLScvMys1sGbARmOHuRVWzgiJHZhY3s+UpfiYAuPsUd+8HVAHXF7ba/dLVHR4zBdhLUHvBZVJzkbMU+4rqN8ZSY2ZdgCeBrzfo4Rcld69z92EEvfizzKyoTvW1iaVQ88HdYxke+ijwZ+Df8lhOxtLVbWZXARcD47xIBrCy+LsuVuuAfknbRwPrC1RLyQvP8z8JVLn7U4WuJxvuvs3MZgMXAkVzEYF6FHlgZoOSNj8NvFKoWrJhZhcCNwGfdvfaQtdTQhYDg8zsGDPrAFwBPF3gmkpSODB8H7DK3X9W6HoyYWY9668wNLNOQIwi+87QVU95YGZPAicSXI2zBrjG3d8tbFXpmdlq4BBgS7hrUbFfrWVmlwK/AHoC24Bl7v73BS0qBTO7CPgvoBy4392nFrai9MzsMWA0wfTX7wP/5u73FbSoNMxsJDAPeJng3x/A99z9mcJVFc3MhgIPEvy/UQY84e4/LGxVB1JQiIhIJJ16EhGRSAoKERGJpKAQEZFICgoREYmkoBARkUgKCilaZtYjnIF3mZm9Z2bvhs+3mVmLTvJmZpeY2eCk7R+aWdY3AprZwMZmYzWzIWY208xeM7M3zOxWM2v2f6NRfxYzm13Ms/BKYSgopGi5+xZ3HxZObXAP8J/h82Hsv0a+2ZhZ1EwFlwCJL1d3/4G7x5ux7U4EN+FNc/cTgFMJJhPMxzTZl5DHP4uUHgWFtFblZvbrcP7+v4VftJjZcWb2FzNbYmbzzOykcP8AM6sO19qoNrP+4f4HzOxnZjYL+HGq95vZuQR32P8k7NEcF77vsvAzzjSzheF6As+bWdew5zDPzJaGP+em+fN8Dljg7n8DCO+Mvx74dtjGLWb2rfqDw7muBobP/yesd4WZTUo65qNwcsoXzWyRmfVK92dJZmZ/Z2bPhvX/Lpw/CTObZmYrw7/LO7L/TyetjYJCWqtBwK/cfQjBHdn/HO6fDtzg7mcA3wLuCvf/kmBdhaEEkx3+POmzTgBi7v7NVO9394UEv+1/O+zhvFH/xnBKjt8SrB9wGsH0CzsJZgEd7+7Dgc82aC+VIQRrJySE7XSy9AtIXR3WWwncaGY9wv2dCe6uPw2YC3wl6s+SzMyOAP5f+PcyHKgB/tXMDgcuBYaEf5c/SlOblABNCiit1Vvuvix8vgQYGP7Gey7wu2DKHyCYkgRgBPBP4fOHgf9I+qzfuXtdmvc35kRgg7svhv1rkZhZZ+CXZjYMqCMIoyhG6hllU80829CN4VQmEEw+OIhgGpbdwJ/C/UsIFk7K1DkEp6cWhH8XHYBngQ+BT4B7zezPSZ8vJUxBIa3VrqTndUAngh7ytnAcI53kL+WPw8ds3l+vsS/4bxDMj3Ra+LmfpPmcFcAFB3yw2bHA5nBG0b0ceAagY3jMaIJezAh3r7Vg5tGO4TF7kmYAriO7f+9GsC7ClQe9YHYWMI5gcsPrgbFZfK60Qjr1JCUj/G3+LTO7HIKZRM3stPDlhQRfbBAsJjU/y/fvALqmaPYVoI+ZnRm+p2s4KH4YQU9jH/AFggnfolQBI5OuPupEcLqqfnr6t4Hh4WvDgWPC/YcBW8OQOImgJ5BOY3+WZIuA88zs+LDNCjM7Iex1HRZOsvd1ggsLpMQpKKTUTAS+bGYvEvyWXr+40Y3Al8zsJYIv7sauJmrs/Y8D3zazF8zsuPqDw6VNPwv8InzPDILf6O8CrjKzRQSnnT4mgrvvJBhknmJmrwGbCQa36xePehI43IJV0K4lWIMb4C9Au/DPdRvBF3w6Kf8sDerZBHwReCz87EXASQQB86dw3xyCnpOUOM0eK1KEzOwS4GfAGHdfU+BypI1TUIiISCSdehIRkUgKChERiaSgEBGRSAoKERGJpKAQEZFICgoREYn0/wEecD1eM8bKOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot\n",
    "\n",
    "qp = qqplot(residuals, line = 'q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "bda2a296",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x131f510a0>"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_pred, residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca394ed5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "aea4d105",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "scaler = preprocessing.StandardScaler().fit(X)\n",
    "X_scaled = scaler.transform(X)\n",
    "\n",
    "lr = HuberRegressor()\n",
    "\n",
    "lr.fit(X_scaled, np.log10(y))\n",
    "y_pred = lr.predict(scaler.transform(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "1f22e2a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = np.log10(y_test) - y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "24e2207e",
   "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": [
    "qp = qqplot(residuals, line = 'q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "790ee7b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x13214af40>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_pred, residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05d7b10b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2164ad17",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}