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daniel-covelli/covid.ipynb

Created March 23, 2020 21:19
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covid.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "COVID",
"provenance": [],
"collapsed_sections": [],
"mount_file_id": "1MHmAgjYyKt-4JR5PcZdB-tYKM8wmnRDG",
"authorship_tag": "ABX9TyPDt0l8OgN74/mxpW7W79Gg",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/daniel-covelli/0ca59c2c499ecbcb8cf37f57295286c8/covid.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "XEb-LtIhc6K-",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "tb0xHLW-DjwO",
"colab_type": "text"
},
"source": [
"**DISCLAIMER**: I am not a public health official. The findings in this notebook do not represent actual realities of COVID-19, its effect on the elderly, and its implications on matters of public health. This exercise is meant to be a way of teaching others how to conduct data analysis on important data. *PLEASE TAKE ALL FINDINGS WITH A GRAIN OF SALT.*"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IcTnlxSqza1O",
"colab_type": "text"
},
"source": [
"# Predicting COVID-19 Mortalities "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ORYAqroQovHa",
"colab_type": "text"
},
"source": [
"Lets look at the [Novel Corona Virus 2019 Dataset](https://www.kaggle.com/sudalairajkumar/novel-corona-virus-2019-dataset) available on Kaggle"
]
},
{
"cell_type": "code",
"metadata": {
"id": "6w85Fh_keBEH",
"colab_type": "code",
"outputId": "eb271d73-02ad-418a-f268-c7755bff3b44",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 561
}
},
"source": [
"data = pd.read_csv(\"/COVID19_open_line_list.csv\", index_col=0)\n",
"data.head()"
],
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
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"\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>age</th>\n",
" <th>sex</th>\n",
" <th>city</th>\n",
" <th>province</th>\n",
" <th>country</th>\n",
" <th>wuhan(0)_not_wuhan(1)</th>\n",
" <th>latitude</th>\n",
" <th>longitude</th>\n",
" <th>geo_resolution</th>\n",
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" <th>reported_market_exposure</th>\n",
" <th>additional_information</th>\n",
" <th>chronic_disease_binary</th>\n",
" <th>chronic_disease</th>\n",
" <th>source</th>\n",
" <th>sequence_available</th>\n",
" <th>outcome</th>\n",
" <th>date_death_or_discharge</th>\n",
" <th>notes_for_discussion</th>\n",
" <th>location</th>\n",
" <th>admin3</th>\n",
" <th>admin2</th>\n",
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" <th>ID</th>\n",
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" <th>1.0</th>\n",
" <td>30</td>\n",
" <td>male</td>\n",
" <td>Chaohu City, Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>1.0</td>\n",
" <td>31.646960</td>\n",
" <td>117.716600</td>\n",
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" <td>18.01.2020</td>\n",
" <td>20.01.2020</td>\n",
" <td>22.01.2020</td>\n",
" <td>NaN</td>\n",
" <td>yes</td>\n",
" <td>17.01.2020</td>\n",
" <td>Wuhan</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>http://ah.people.com.cn/GB/n2/2020/0127/c35826...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>Chaohu City</td>\n",
" <td>Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>340181</td>\n",
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" <tr>\n",
" <th>2.0</th>\n",
" <td>47</td>\n",
" <td>male</td>\n",
" <td>Baohe District, Hefei City</td>\n",
" <td>Anhui</td>\n",
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" <td>1.0</td>\n",
" <td>31.778630</td>\n",
" <td>117.331900</td>\n",
" <td>admin3</td>\n",
" <td>10.01.2020</td>\n",
" <td>21.01.2020</td>\n",
" <td>23.01.2020</td>\n",
" <td>NaN</td>\n",
" <td>no</td>\n",
" <td>10.01.2020</td>\n",
" <td>Luzhou Hunan, via Wuhan</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>http://ah.people.com.cn/GB/n2/2020/0127/c35826...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>Baohe District</td>\n",
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" <tr>\n",
" <th>3.0</th>\n",
" <td>49</td>\n",
" <td>male</td>\n",
" <td>High-Tech Zone, Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>1.0</td>\n",
" <td>31.828313</td>\n",
" <td>117.224844</td>\n",
" <td>point</td>\n",
" <td>15.01.2020</td>\n",
" <td>20.01.2020</td>\n",
" <td>23.01.2020</td>\n",
" <td>NaN</td>\n",
" <td>no</td>\n",
" <td>10.01.2020</td>\n",
" <td>Yinzhou Hunan, via Wuhan</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>http://ah.people.com.cn/GB/n2/2020/0127/c35826...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>High-Tech Zone</td>\n",
" <td>Shushan District</td>\n",
" <td>Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>340104</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
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" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.0</th>\n",
" <td>47</td>\n",
" <td>female</td>\n",
" <td>High-Tech Zone, Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>1.0</td>\n",
" <td>31.828313</td>\n",
" <td>117.224844</td>\n",
" <td>point</td>\n",
" <td>17.01.2020</td>\n",
" <td>20.01.2020</td>\n",
" <td>23.01.2020</td>\n",
" <td>NaN</td>\n",
" <td>no</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>contacted with confirmed case</td>\n",
" <td>NaN</td>\n",
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" </tr>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>50</td>\n",
" <td>female</td>\n",
" <td>Feidong County, Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>1.0</td>\n",
" <td>32.001230</td>\n",
" <td>117.568100</td>\n",
" <td>admin3</td>\n",
" <td>10.01.2020</td>\n",
" <td>21.01.2020</td>\n",
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" <td>NaN</td>\n",
" <td>no</td>\n",
" <td>07.01.2020</td>\n",
" <td>Wuhan</td>\n",
" <td>NaN</td>\n",
" <td>06.01.2020 went to Wuhan, 07.01.2020 returned ...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>http://ah.people.com.cn/GB/n2/2020/0127/c35826...</td>\n",
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" <td>NaN</td>\n",
" <td>NaN</td>\n",
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" <td>NaN</td>\n",
" <td>Feidong County</td>\n",
" <td>Hefei City</td>\n",
" <td>Anhui</td>\n",
" <td>China</td>\n",
" <td>340122</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
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" <td>NaN</td>\n",
" <td>NaN</td>\n",
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" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age sex ... Unnamed: 43 Unnamed: 44\n",
"ID ... \n",
"1.0 30 male ... NaN NaN\n",
"2.0 47 male ... NaN NaN\n",
"3.0 49 male ... NaN NaN\n",
"4.0 47 female ... NaN NaN\n",
"5.0 50 female ... NaN NaN\n",
"\n",
"[5 rows x 44 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "98dxbNjdAhM5",
"colab_type": "text"
},
"source": [
"We are interested in running a linear regression on factors that effect whether an individual succumbs to COVID-19; including age and sex. Lets created a subset of our data that captures this information. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "MGYxNYuZmrWD",
"colab_type": "code",
"outputId": "4670ecd7-119b-41f8-f631-1285cf33a4fa",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"data = data[['age', 'sex', 'outcome']]\n",
"data.head()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <th>2.0</th>\n",
" <td>47</td>\n",
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" <td>NaN</td>\n",
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" <th>3.0</th>\n",
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" <th>4.0</th>\n",
" <td>47</td>\n",
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],
"text/plain": [
" age sex outcome\n",
"ID \n",
"1.0 30 male NaN\n",
"2.0 47 male NaN\n",
"3.0 49 male NaN\n",
"4.0 47 female NaN\n",
"5.0 50 female NaN"
]
},
"metadata": {
"tags": []
},
"execution_count": 234
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "uVJH-Y8wwfF0",
"colab_type": "text"
},
"source": [
"# Cleaning and Visualizing the Data"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LNtpFz3EGk1e",
"colab_type": "text"
},
"source": [
"First we want to get rid of any wierd values in our age and sex columns (like nulls, etc)."
]
},
{
"cell_type": "code",
"metadata": {
"id": "7gepANBCGkKo",
"colab_type": "code",
"outputId": "10075bce-4eeb-4c88-d4f1-5bef1873e62a",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"# clean out all obsevations where age was not reported\n",
"clean = data[data['age'].notnull()]\n",
"\n",
"# clean out all observations where sex was not reported\n",
"clean = data[data['sex'].notnull()]\n",
"\n",
"# further clean out all other abnormalities in age data using regex\n",
"clean = clean[~clean['age'].astype(str).str.match('0{1}')]\n",
"clean = clean[clean['age'].astype(str).str.match('\\d{1,2}')]\n",
"clean = clean[~clean['age'].astype(str).str.match(\"\\d{1,2}\\-\")]\n",
"\n",
"clean.sample(5)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
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" <th></th>\n",
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" <th>2447.0</th>\n",
" <td>56</td>\n",
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" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1593.0</th>\n",
" <td>49</td>\n",
" <td>female</td>\n",
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" <tr>\n",
" <th>12036.0</th>\n",
" <td>51</td>\n",
" <td>male</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6137.0</th>\n",
" <td>48</td>\n",
" <td>female</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24.0</th>\n",
" <td>45</td>\n",
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],
"text/plain": [
" age sex outcome\n",
"ID \n",
"2447.0 56 female NaN\n",
"1593.0 49 female NaN\n",
"12036.0 51 male NaN\n",
"6137.0 48 female NaN\n",
"24.0 45 male NaN"
]
},
"metadata": {
"tags": []
},
"execution_count": 235
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pNfw1o2CDpiY",
"colab_type": "text"
},
"source": [
"First, lets get two tables that include those patients who had critical cases and those patients who were discharged. We will first want to clean out all individuals whos age was reported as null."
]
},
{
"cell_type": "code",
"metadata": {
"id": "mDlzqY_wnIzv",
"colab_type": "code",
"colab": {}
},
"source": [
"# create two tables with those who died and those who were discharged\n",
"critical = clean[clean['outcome'].str.contains(\"death|died\", na=False)]\n",
"recovered = clean[clean['outcome'].str.contains(\"discharge|discharged\", na=False)]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "8KDsHtCm0FlZ",
"colab_type": "code",
"outputId": "22e485a6-afba-430b-8bf2-29db2bde1f5c",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"critical.head()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"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>age</th>\n",
" <th>sex</th>\n",
" <th>outcome</th>\n",
" </tr>\n",
" <tr>\n",
" <th>ID</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>192.0</th>\n",
" <td>39</td>\n",
" <td>male</td>\n",
" <td>died</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1443.0</th>\n",
" <td>82</td>\n",
" <td>female</td>\n",
" <td>death</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4870.0</th>\n",
" <td>44</td>\n",
" <td>male</td>\n",
" <td>died</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5121.0</th>\n",
" <td>73</td>\n",
" <td>female</td>\n",
" <td>death</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11525.0</th>\n",
" <td>77</td>\n",
" <td>female</td>\n",
" <td>death</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age sex outcome\n",
"ID \n",
"192.0 39 male died\n",
"1443.0 82 female death\n",
"4870.0 44 male died\n",
"5121.0 73 female death\n",
"11525.0 77 female death"
]
},
"metadata": {
"tags": []
},
"execution_count": 237
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "14Es_oeR0BCi",
"colab_type": "code",
"outputId": "3388e526-4eee-41cb-8eb5-20b0c8a57fa2",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"recovered.head()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"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>age</th>\n",
" <th>sex</th>\n",
" <th>outcome</th>\n",
" </tr>\n",
" <tr>\n",
" <th>ID</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>56.0</th>\n",
" <td>44</td>\n",
" <td>female</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" <tr>\n",
" <th>164.0</th>\n",
" <td>29</td>\n",
" <td>male</td>\n",
" <td>discharge</td>\n",
" </tr>\n",
" <tr>\n",
" <th>320.0</th>\n",
" <td>39</td>\n",
" <td>female</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" <tr>\n",
" <th>344.0</th>\n",
" <td>46</td>\n",
" <td>male</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" <tr>\n",
" <th>620.0</th>\n",
" <td>27</td>\n",
" <td>male</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age sex outcome\n",
"ID \n",
"56.0 44 female discharged\n",
"164.0 29 male discharge\n",
"320.0 39 female discharged\n",
"344.0 46 male discharged\n",
"620.0 27 male discharged"
]
},
"metadata": {
"tags": []
},
"execution_count": 238
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ogOPTsVvAZHj",
"colab_type": "text"
},
"source": [
"Now, lets vizualize the relationship between age and whether someone was discharged or not. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "_3U_8fc1zU0k",
"colab_type": "code",
"outputId": "f145c494-09f8-468c-a86e-c18121267991",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 408
}
},
"source": [
"# use distplot in seaborn to plot the distribution of those recovered and those critically ill across age\n",
"plt.figure(figsize=(16, 6))\n",
"sns.distplot(recovered[\"age\"], color=\"skyblue\", rug=True, hist=False, label=\"Recovered\")\n",
"sns.distplot(critical[\"age\"], color=\"red\", rug=True, hist=False, label=\"Critical\");\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
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9yMciIhK3iqvCVIUtfXLVJhzPjDGc0jWTnBQPrxYFqdZ+1+R09dXw4YdOe/Cw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"text/plain": [
"<Figure size 1152x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1aJsXEMo0Pp6",
"colab_type": "text"
},
"source": [
"As we can see, age seems to be positively correlated with ciritcal cases of COVID-19. Lets dig a little deeper. \n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "JzznEPfJ_SX5",
"colab_type": "code",
"outputId": "4821b884-4ed0-4a01-e3c1-6c048bb80a86",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"# first lets merge our critical and recovered dataframes\n",
"sexage = pd.concat([recovered, critical], sort=False)\n",
"\n",
"# next we want to get rid of any unnecessary columns and convert ages to integer values\n",
"sexage['age'] = sexage['age'].astype(int)\n",
"\n",
"sexage.sample(5)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"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>age</th>\n",
" <th>sex</th>\n",
" <th>outcome</th>\n",
" </tr>\n",
" <tr>\n",
" <th>ID</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>6348.0</th>\n",
" <td>49</td>\n",
" <td>female</td>\n",
" <td>discharge</td>\n",
" </tr>\n",
" <tr>\n",
" <th>671.0</th>\n",
" <td>28</td>\n",
" <td>male</td>\n",
" <td>discharge</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1062.0</th>\n",
" <td>42</td>\n",
" <td>male</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1064.0</th>\n",
" <td>7</td>\n",
" <td>male</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" <tr>\n",
" <th>344.0</th>\n",
" <td>46</td>\n",
" <td>male</td>\n",
" <td>discharged</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age sex outcome\n",
"ID \n",
"6348.0 49 female discharge\n",
"671.0 28 male discharge\n",
"1062.0 42 male discharged\n",
"1064.0 7 male discharged\n",
"344.0 46 male discharged"
]
},
"metadata": {
"tags": []
},
"execution_count": 240
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "G6BAwqNpCS3Y",
"colab_type": "text"
},
"source": [
"Lets calculate the percentage of those who are 60 and older and those who are 80 and older who develop critical cases of COVID-19.\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "uKCU9isx_2hg",
"colab_type": "code",
"outputId": "2d801c1d-64f9-4a37-d27a-63e6f59113af",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 71
}
},
"source": [
"# create table with individuals who are 60 and older and those who \n",
"bin60 = sexage[sexage['age'] >= 60]\n",
"bin80 = sexage[sexage['age'] >= 80]\n",
"\n",
"# get the number of individuals who had critical cases \n",
"bin60critical = bin60[bin60['outcome'].str.contains(\"death|died\")]\n",
"bin80critical = bin80[bin80['outcome'].str.contains(\"death|died\")]\n",
"\n",
"# get percentage of those who had critical cases in the two groups\n",
"crit60 = bin60critical.shape[0] / bin60.shape[0]\n",
"crit80 = bin80critical.shape[0] / bin80.shape[0]\n",
"\n",
"print('The likelyhood that someone who is 60 or older will have a critical case of COVID-19 is:', crit60)\n",
"print('The likelyhood that someone who is 80 or older will have a critical case of COVID-19 is:', crit80)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"The likelyhood that someone who is 60 or older will have a critical case of COVID-19 is: 0.46153846153846156\n",
"The likelyhood that someone who is 80 or older will have a critical case of COVID-19 is: 0.5\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5KvTdwvLE92b",
"colab_type": "text"
},
"source": [
"**DISCLAIMER**: These numbers are not conclusive and do not represent the realities of COVID-19."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "o9dygwGA_Axj",
"colab_type": "text"
},
"source": [
"It looks like there is a higher likelyhood that those who are older will contract critical cases of COVID-19. However, if we want to accurately predict outcomes using age, we need to do a little more. In order to predict how gender and age effects mortality rate, lets first turn our age and gender catagories into dummy variables."
]
},
{
"cell_type": "code",
"metadata": {
"id": "ZKUkBp_OF-B3",
"colab_type": "code",
"outputId": "c4dbf39a-c2e1-4f7a-d02b-1702b8f268b5",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 235
}
},
"source": [
"# now lets construct dummys for sex\n",
"sexage['sex_male'] = sexage.sex.map({'female':0,'male':1})\n",
" \n",
"# now lets construct a dummy for outcome\n",
"sexage['outcome_death'] = sexage.outcome.map({'discharged':0, 'discharge':0,'death': 1,'died':1})\n",
"\n",
"# select the new dummy variables\n",
"sexage = sexage[['age', 'sex_male', 'outcome_death']]\n",
"\n",
"# here is our resulting dataframe, with males as 1 and critical outcomes as 1\n",
"sexage.sample(5)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"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>age</th>\n",
" <th>sex_male</th>\n",
" <th>outcome_death</th>\n",
" </tr>\n",
" <tr>\n",
" <th>ID</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>12043.0</th>\n",
" <td>33</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>56.0</th>\n",
" <td>44</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1063.0</th>\n",
" <td>38</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6131.0</th>\n",
" <td>63</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11275.0</th>\n",
" <td>30</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age sex_male outcome_death\n",
"ID \n",
"12043.0 33 0 0\n",
"56.0 44 0 0\n",
"1063.0 38 0 0\n",
"6131.0 63 1 0\n",
"11275.0 30 1 0"
]
},
"metadata": {
"tags": []
},
"execution_count": 242
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "EcBMvg7pLIlH",
"colab_type": "text"
},
"source": [
"*where critical cases are encoded as 1 and non-critical cases enconded as 0 in the 'outcome_death' column*"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Hyd5e5YuXDVF",
"colab_type": "text"
},
"source": [
"Because we want to use both sex, age, and an **intercept** to predict the likelyhood of critical illness, we will construct a matrix with 3 column vectors, the first vector being the all ones vector.\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "zO2B7oTxU5zl",
"colab_type": "code",
"colab": {}
},
"source": [
"# first lets put create a function that will add a one to our input matrix \n",
"def add_ones(data):\n",
" return np.hstack([np.ones((data.shape[0],1)), data])"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "SVHwWclhXzpS",
"colab_type": "code",
"outputId": "78b47fac-ffcf-438a-8ca6-5aa9adee7489",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"# now lets run our input matrix through this function\n",
"X = add_ones(sexage[['age', 'sex_male']])\n",
"\n",
"# lets get the first individual in our dataset\n",
"X[0]"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([ 1., 44., 0.])"
]
},
"metadata": {
"tags": []
},
"execution_count": 245
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jFreMf_g07oN",
"colab_type": "text"
},
"source": [
"As we can see, our first value is 1. This will later allow us to compute an intercept value. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9rLO_FmIwvkq",
"colab_type": "text"
},
"source": [
"# Defining a Linear Model"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4BEbyj8qrUM7",
"colab_type": "text"
},
"source": [
"Now that we have added a ones column to our matrix, we can go on to construct our linear model for predicting critical COVID-19 cases using an intercept, age and sex. Here we want to multiply our matrix with our theta coefficients. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "Wogw_PmgUdEO",
"colab_type": "code",
"colab": {}
},
"source": [
"# use matrix multiplication to assign a theta value for each column element in our matrix\n",
"def linear_model(theta, xt): \n",
" return xt @ theta "
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "0EhiEuUOsCc2",
"colab_type": "text"
},
"source": [
"Now lets create an array of random guesses for our theta coefficients and find out what our model will predict."
]
},
{
"cell_type": "code",
"metadata": {
"id": "e9lT09RlY9Rg",
"colab_type": "code",
"outputId": "0ea290af-e25c-45a7-be88-901a5500a24d",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# will construct an array of three row elements of random value as our theta coefficients\n",
"np.random.seed(42)\n",
"theta_guess = np.random.randn(X.shape[1], 1)\n",
"theta_guess"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 0.49671415],\n",
" [-0.1382643 ],\n",
" [ 0.64768854]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 246
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1LZFZ0LYsvUR",
"colab_type": "text"
},
"source": [
"Now, lets use this random guess of coefficients on our third row from our matrix."
]
},
{
"cell_type": "code",
"metadata": {
"id": "5JgU2thfUJYs",
"colab_type": "code",
"outputId": "45b0156d-d7bb-4560-fc00-9b2fafb73d55",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"# use our random thetas to predict the outcome of the third individual in our sexage data set\n",
"linear_model(theta_guess, X[2,:])"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-4.89559359])"
]
},
"metadata": {
"tags": []
},
"execution_count": 247
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Bb8l-S53s8Hi",
"colab_type": "text"
},
"source": [
"The prediction is -4.89 meaning that with these random coefficients, the individual who represents the third row of our matrix is likely to survive. Lets compare this to the actual outcome for the individual at the third row. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "LPMyr8TyU2LV",
"colab_type": "code",
"outputId": "20861bc0-3f2b-4475-83af-1956c8265362",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 85
}
},
"source": [
"# get the third individual from our sexage dataset\n",
"sexage.iloc[2]"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"age 39\n",
"sex_male 0\n",
"outcome_death 0\n",
"Name: 320.0, dtype: int64"
]
},
"metadata": {
"tags": []
},
"execution_count": 248
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gwKrQsNFuYRj",
"colab_type": "text"
},
"source": [
"A below 0 outcome in this context means that for our random theta coefficients, our model predicts that the third individual will survive. Despite its randomness, this prediction was right. However it may not be right with other individuals in our dataset, therefore we need to choose better thetas. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "f33pPJc5v7BT",
"colab_type": "text"
},
"source": [
"# Calculating Theta Values"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Uj0G6u4LwLHr",
"colab_type": "text"
},
"source": [
"First lets get a column vector of our observed Y values that we will use in our loss function to find our optimal theta values. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "e5CvyWsXW25z",
"colab_type": "code",
"outputId": "10658e96-8e84-4dd2-b322-5a74e19aabb8",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 102
}
},
"source": [
"# create an array (as a column vector) composed of all the outcome values in our sexage dataset\n",
"sexage['outcome_death'] = sexage['outcome_death'].astype(int)\n",
"\n",
"Y = sexage[['outcome_death']].to_numpy()\n",
"\n",
"# here are the first five elements of that column vector Y\n",
"Y[:5]"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[0],\n",
" [0],\n",
" [0],\n",
" [0],\n",
" [0]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 252
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "V0VAZROKxR1Y",
"colab_type": "text"
},
"source": [
"Now we need to pick a loss function. Here we will use squared loss or the distance our predicted Y value is from the observed Y value for each individual in our data set."
]
},
{
"cell_type": "code",
"metadata": {
"id": "57ziexu9fw7y",
"colab_type": "code",
"colab": {}
},
"source": [
"# define an average squred loss function\n",
"def squared_loss(theta):\n",
" return np.mean((Y - X @ theta)**2) # 'X @ theta' here is our Y_hat prediction "
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "q-U6bbxeglzm",
"colab_type": "code",
"outputId": "8a8bab99-58fb-4d04-b572-8f1b68ebf68e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"squared_loss(theta_guess)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"32.82412334239557"
]
},
"metadata": {
"tags": []
},
"execution_count": 147
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kUiVnIUAyVWr",
"colab_type": "text"
},
"source": [
"Using our theta guesses, we get a loss of ~32. Our objective in calculating better thetas is to reduce the output of the loss function by optimizing our theta values. \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "sDDdPGkAyM9a",
"colab_type": "text"
},
"source": [
"# Minimizing the Loss with the Normal Equation"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "EUWPZrg8zFZe",
"colab_type": "text"
},
"source": [
"Using the normal equation in linear algebra, we can get our optimal theta values by using dot production, matrix multiplication, transposition and invertion."
]
},
{
"cell_type": "code",
"metadata": {
"id": "ePW7xfyRhd8t",
"colab_type": "code",
"colab": {}
},
"source": [
"# in order to compute the normal equation we will need the ability to invert a matrix\n",
"from numpy.linalg import inv"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "S9BkFL0sJPzt",
"colab_type": "code",
"colab": {}
},
"source": [
"# define the normal equation\n",
"def norm_equ(X, Y):\n",
" return inv(X.T @ X) @ X.T @ Y"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "Upg5RS5-hYd6",
"colab_type": "code",
"outputId": "e8218f00-2621-46c6-f87f-6e9300572ce6",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# minimize loss using the normal equation\n",
"theta_hat = norm_equ(X, Y)\n",
"theta_hat"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[-0.19245584],\n",
" [ 0.00786593],\n",
" [-0.03575496]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 255
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tTP8HlVQ2v2N",
"colab_type": "text"
},
"source": [
"Now that we have better thetas, lets verify this is the case by throwing these thetas into our loss fuction as defined above. If our thetas are indeed better, the output of the loss funciton should be less than the output of the loss function when we used random thetas."
]
},
{
"cell_type": "code",
"metadata": {
"id": "w2092lvfiZ3W",
"colab_type": "code",
"outputId": "c6e1f334-f089-4a95-f7ea-0e76237ad6dd",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"# compute the loss using our optimal thetas\n",
"squared_loss(theta_hat)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0.08093504311091328"
]
},
"metadata": {
"tags": []
},
"execution_count": 167
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "G0gnlvEo3KQZ",
"colab_type": "text"
},
"source": [
"Using the normal equation we have minimized the loss of our model with more optimal thetas. Lets predict the output of our model for the third individual in our data; except this time, using our optimal theta values. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "UzhasJpx3vrD",
"colab_type": "code",
"outputId": "25874f62-28e4-4d2e-eb92-35cb8b78142b",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"# predict the outcome of the third individual in the data set\n",
"linear_model(theta_hat, X[2,:])"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([0.11431536])"
]
},
"metadata": {
"tags": []
},
"execution_count": 256
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5alUk0wT399R",
"colab_type": "text"
},
"source": [
"This is much closer to the actual outcome (0) then it was when we used random thetas. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "O74b0SA74T-v",
"colab_type": "text"
},
"source": [
"# Diagnosing the Model"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "eZhBNqtB4-L9",
"colab_type": "text"
},
"source": [
"Now lets see how good our predicitions are. First we can see how our residuals are distributed across the age variable."
]
},
{
"cell_type": "code",
"metadata": {
"id": "ozi2zkflnEDK",
"colab_type": "code",
"outputId": "b83dec7f-0081-40d2-96cb-148af7439c49",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 404
}
},
"source": [
"# lets plot our resulting residuals against our dimension 'Age'\n",
"plt.figure(figsize=(10, 6))\n",
"sns.scatterplot(x = X[:,1], y = (Y - Y_hat).flat)\n",
"plt.title('Residuals vs Age')\n",
"plt.xlabel('Age')\n",
"plt.ylabel('Residuals');"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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PZeYE8H7gwgbX/Q7wVuDJThYnSZJUpjJD2ibg4RnHY8W5IyLi+4BTMvMjnSxMkiSpbJWd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\npAr6v4UL3WBOWL6nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j4jpLaD848vZ",
"colab_type": "text"
},
"source": [
"As we can see, there are two groups, those who fell critically ill to COVID-19 represented in the data cloud above, and those who survived below. Our model, consistently underestimates the likelyhood of an individual having a critical case of COVID. This is likely due to the fact that we don't have enough data. For instance, there are only 9 individuals in the data set who were labeled as having critical cases of COVID-19. This is a serious problem for health officials if this is the only data set available for predicting how age effects the likelyhood of having a critical case of COVID-19. Now lets compare how the observed Y values correspond to our predicted Y values.\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "l6vhvhKjjw1v",
"colab_type": "code",
"outputId": "ace65fd7-2765-4e95-a483-91b65f7da4eb",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 404
}
},
"source": [
"# lets plot our resulting Y_hat predictions relative to our observed Y values\n",
"plt.figure(figsize=(10, 6))\n",
"sns.regplot(Y[1:,0], Y_hat[1:,0], ci=None, line_kws = {'color': 'r', 'alpha': 1})\n",
"plt.title('Example Plot')\n",
"plt.xlabel('Y')\n",
"plt.ylabel('Y_hat');\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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USJhyOdd4lkmuAADE2tjYzN2158s0dBYtenHsWnGXLYTuWjVCD3K1kHPXWCarhKTmpsZI\nzAAAYBbcpZMnp3fWKu2urV17eVetuLtmVpcfoRZiGeQk5e82Z1LH4gVhVwIAACo1NiYdOjS9u3bw\nYGXdteKQNvnYsCES3bVqxDLImaTmZEJZd7lzaRUAgIbiLp04Mb2zNtldK/Vvt9nM3bVrr410d60a\nsQxyktSUNK1YvEAXxmt3Ez4AAFDCxYvTu2uTj9HR0vsuXjy9s9bTk++uLVxYn/ojIJZBriWVVHfH\nYqXHM+psawm7HAAA4muyuxY0M/Spp8p31667bvrl0J4eaeXKedddq0Ysg9zYRFaHTo2qraVJ73/D\nDWGXAwBA9KXTM3fXzp8vvW9b2/RbeEyOXaO7NiuxDHIuaTyb09gEl1UBAKiYu3T8+PTF3Se7a6WY\nSV1dwWPXVqygu1YjsQxyJimVSOjiRE4f+MIPWNkBAIBi6XR+FmhQd+3ChdL7LlkSPDN0/Xq6ayGI\nZ5Ar3BDYc64nn0uHXQ4AAPXnLg0NBd937emnS++bSEzvrk0+v+YaumsNJJZBDgCAeePChZm7a+ky\nzYylS4PXDF2/XmphsmAUxDLIuVw5d+Vc2tARzxsAAgDmkVwuP3YtaGbosWOl900kpHXrgi+H0l2L\nvHgGOZfGMzktWdik37mtJ+xyAACozPnzwd21gwfLd9eWLbs8pE0Gt/XrpQWschRXsQxyJmlBKqFU\nknVWAQANJpfLd9GCZoYODZXeN5GQuruDx651dNBdm4diGeRaUklt6GxTejyjXXsHmbUKAKi/8+eD\nJxocPJhf8aCUye7a1Nt4XH893TVcJpZBbtLCVFJDI8xaBQDUSHF3rXiB9wMH8mPaSkkm82PXpnbW\nNm2iuzZP7BkY1q69g0p1dN1U7TFiHeQuTmS1ur017DIAAFE3Onr5pdAr6a61tweHteuvl5qb61M/\nGs6egWHt6NuvVNIkz2WqPU4sgxxLdAEArlgul7+/WlB37ZlnSu+bTOaDWdAyVMuX013DNLv2DiqV\nNLU2zy6KxTLISZIsv1QXAACXef756Z21gYH8OqJjY6X3veqq4LFr3d1013BFjo2ktWxhatbHiWWQ\nY7IDAMxz2ezM3bUTJ0rv29SUD2ZT77nW05PvrgFzYE17q4ZHx+jIlcJkBwCIueLu2tSZoZculd73\n6qtn7q6lZt8pAUrZvrlbO/r2Kz1e9fA4STEPckx2AIAYyGalp54K7q6dPFl636am/Ni1qd21ybFr\nQEi29HRqp/Jj5WSJqvNYbINcejyjiaxr++busEsBAFTi3Lng9UIPHSrfXVu+PPgmuevW0V1Dw9rS\n06ktPZ2y7Ue/W+0xYhnksjlXZ1uLtm/uZnwcADSSbFY6enR6YBsYkE6dKr1vU1N+uamgmaFXX12X\n8oFGE8sgt2lFmx7adkvYZQDA/HX2bPASVIcOSePjpfft6Ji5u9YUy3+2gKrxGwEAqE4mE9xdO3Cg\nfHctlXqxuzZ1/NpVV9WlfCAOCHIAgNJGRoK7a4cPl++udXYGhzW6a8Cc4LcIAJDvrj35ZPDYtdOn\nS++bSkkbNgSPXWtvr0/9wDwVyyA3cHJUW3fvY7IDAEw1MjI9qE121yYmSu97zTXBYa2ri+4aEJJY\n/uY1JUzDo2Pa0bdfOyXCHID5JZORBgeDL4eW6641N8/cXVu2rD71A6hYLIOcJLU2N7FEF4B4O3Mm\nuLt25Ej57tqKFcFj17q68gvAA4iEioKcma1z9yfLvdcoxiayGjx9XssXN7NEF4Bom5h4sbs2dWbo\ns8+W3nfBgsu7a8XBbenS+tQPoKYq7ch9RtIrp7z3iKQfntty5k4m6zp+dkzrOxaFXQoAlPfcc8FL\nUB05kr9UWsrKlcH3XVu7lu4aEHMlg5yZ9Ui6UdJSM/t3RR8tkdQyFwWY2W2S/kxSUtJH3f0DUz5/\nj6R3SMpIOi3pV9z9qdIHLTxcMrO5KBMAZm+yuza1szYwkA9ypUx216Yu8L5xI901YB4r15HbJOmn\nJS2T9DNF749Keudsv9zMkpLul/Q6SUOSHjezPnf/ftFm35TU6+5pM/tVSR+U9JaSB/b8hIcVSxbo\n/KUy/ycLAHPt2WeDu2uDg5V116Z21jZtorsGIFDJIOfun5P0OTN7tbt/rQbff7Okw+4+KElm9rCk\nOyS9EOTc/Z+Ktt8n6W3lDtqSSqq7Y7HS4xl1ts1J4xAALjc+nr/sWdxZmwxtZ86U3relJd9JmxrW\nNm6UliypT/0AYqHSMXLfNLNfU/4y6wvJyN1/ZZbfv0rSsaLXQ5JeVWL7t0v6QtAHZrZN0jZJalrS\noUOnRtXW0qT3v+GGWZYIYN5yL91dy2ZL779qVfBtPNaulRKJ+vwMAGKt0iD3CUkDkn5S0k5JvyDp\nB7UqKoiZvU1Sr6TXBH3u7rsl7ZaklpUbXCZ5HesDEGHj4/kb4gbdd21kpPS+LS3Bs0I3bpTa2upT\nP4B5q9Igt97d32Rmd7j7g2b2SUn/Mgfff1zSmqLXqwvvXcbMbpX0PkmvcfdLlRw4aaamhHEfOQB5\n7vmb4QZ11558srLu2tR7rvX0SGvW0F0DEJpKg9zknSXPmtlLJZ2UNBfp6HFJG8xsnfIB7k5Jby3e\nwMxeIWmXpNvcfbjSA2eyrucujCuTfX4OygQQGZcuvTh2berNcs+eLb3vwoX5TlrQzNDFi+tTPwBc\ngUqD3G4za5f0fkl9khZL2jHbL3f3jJndI+kx5W8/8oC77zeznZL63b1P0ocK3/fpwq1Ennb320sd\n18yUSJhyOdd4lgusQOy4S8PDM3fXcrnS+69eHdxdW72a7hqASKkoyLn7RwtP/1lS91wW4O6PSnp0\nyns7ip7fesXHlCvnLrnU3MRfykBkXbqUH7sWdN+1c+dK79vaOnN3bRE3CgcQD5Uu0bVA0hsldRXv\n4+47a1PW7LhLE9mcli1MaUMng42BhuYunToVfCn06NHy3bU1a6ZPNOjpyY9po7sGIOYqvbT6OUnn\nJD0hqaLJBmEyScmE6dxYRq/uvirscgBI0tjY5TNDi0NbJd21oCWoNmyguwZgXqs0yK1299tqWskc\nckkTWdei5oS+NnhG7wq7IGC+cJdOngxe4L2S7tratcGBbdUqieX2AGCaSoPcv5rZTe7+3ZpWM8cu\njOf0veNlZqkBuHJjY9KhQ8HdtefLzBRftGj6ZdBNm/LdtdbW+tQPADFRMsiZ2XeVb3A1SfplMxtU\n/tKqSXJ3f1ntS6yOWb45kJ4o0wEAEMxdOnEieOzaU0/lPy/luuuCVzWguwYAc6ZcR+6nKzmImbW7\ne5nbn9fX5L8xXu4fG2C+u3hx5u7a6GjpfRcvDg5rdNcAoC5KBjl3f6rC43xF0itnX87ca2lKhl0C\nED536ZlngpegKtddMwvurvX0SCtX0l0DgBBVOkaunIb9m/yqRamwSwDq5+JF6eDB4O7a+fOl921r\nm95Zm+yuLVxYn/oBAFdkroJcw12/TJh09aKUjG4B4sZdOn48eGbo00+X7651dQUv8k53DQAiZ66C\nXENZmErqxmuXKj2eUWdbS9jlANVJp/Nj16YuQXXwYGXdtaAlqNavp7sGADFSbtbqo5L+g7sfLXOc\nhvrf+LGJrA4Nj2rxgia9/w03hF0OMLOZumsDA/nuWimT3bWpt/HYtElasYLuGgDMA+U6ch+T9H/N\n7EFJH3T3iRm2e+3cljUHvMHSJea3dDrfSQvqrl24UHrfJUum3yB306Z8d62FjjMAzGflZq1+2sy+\nIOn9kvrN7BOSckWff7jw55maVnmFWlJJbbimTenxjHbtHdSWns6wS8J8kMtJQ0OXj1mbDG3HjpXe\nN5GQ1q0LvpXHNdfQXQMABKpkjNy4pAuSFkhqU1GQa3QLU0kNjaTDLgNxc+HCzN21dJn/3pYuDb6N\nx/r10oIF9akfABAb5cbI3Sbpw5L6JL3S3SOVii5OZLW6nZuSogpTu2vFoW1oqPS+k921oLFrnZ10\n1wAAc6ZcR+59kt7k7vvrUcxcSo9nNJF1bd/cHXYpaGTnz1/eXZsMawcP5u/JVsqyZcEzQ6+/nu4a\nAKAuyo2R+7F6FTKXLk5kdXr0kt7xo+sYH4d8d+3YseCZocePl943mZy5u9bRQXcNABCq2N5HrqNt\ngR75xnG9bPUywtx8MToaPHbt0KHy3bX29uDuWnc33TUAQMOKZZC7OJHVk89e0NKFTcxajZtcLn9/\ntaCxa888U3rfZDIfzIJu5bF8Od01AEDkxDLISVLOpZF0Rt87fjbsUlCN0dHg9UIr6a5ddVXwzNDu\nbqm5uT71AwBQB7ENcmb5m+anJyJzt5T5J5sN7q4dOFBZd+3662furgEAMA/ENsipsG64l1pAHPXx\n/PPBC7wfPChdulR636uvnj7JYLK7lkrVp34AABpUbIOcmZSQtGhBbH/ExpLNSk89FdxdO3Gi9L5N\nTdO7a5OB7eqr61M/AAARFMuUY5KSCVPOpXf86Lqwy4mXc+eCb+Nx+HD57try5cFLUNFdAwCgKrEM\ncq78LUje8aPr9K5bN4ZdTvRks9LRo8EzQ0+dKr1vKpXvrk0Na5s20V0DAKDInoFh7do7qFRH103V\nHiOWQe6mVUvV/wc/GXYZje/s2emLux84UFl3raMjeGbounX5S6UAAGBGewaGtaNvv1JJkzyXqfY4\nsfwXd+DkqLbu3qftm7u5h1w2Kz35ZPDYtUq6a+vXT++sbdqUv8UHAACoyq69g0olTa3Ns4tisQxy\nTQnT8OiYdvTt105pfoS5kZHgmaGHD0vj46X37egIvo0H3TUAAGri2EhayxbOfnx4LP+VnlzZYUlL\nzFZ2yGTyY9emLkE1MCCdPl163+bmfHdt6qzQTZvyy1MBAIC6WdPequHRMTpyM8m5dPZiRt87PhJ2\nKVcuqLs2OTN0YqL0vtdcEzwztKuL7hoAAA1i++Zu7ejbr/R41cPjJMU4yE06f6lBV3bIZPJj16Z2\n1w4cqKy7tmHD9MC2cSPdNQAAImBLT6d2Kj9WTpaoOo+FHuTM7DZJfyYpKemj7v6BKZ9vlvSnkl4m\n6U53f+RKjh/6ug7PPXf5mLXJ0HbkSOXdtZ6e6d21ZLIu5QMAgNrY0tOpLT2dsu1Hv1vtMUINcmaW\nlHS/pNdJGpL0uJn1ufv3izZ7WtLdkn6z/hVWaGJi5u7as8+W3re4u1Z8G4+NG6Vly+pTPwAAiKSw\nO3I3Szrs7oOSZGYPS7pD0gtBzt2PFj4L/xppcXetOLQdOZK/VFrKypXBEw2uu47uGgAAqErYQW6V\npGNFr4ckvWouv6BtQeLKdpiYkAYHp080OHAgH+RKWbAg30mbGtg2bpSWLq3+hwAAAAgQdpCbM2a2\nTdI2SUou6VDCpCUtTXrJyhkC1LPPBs8MHRysrLtWfBl0MrStXUt3DQAA1E3YQe64pDVFr1cX3rti\n7r5b0m5JWra2x9ctXyS/NK7fWJWRPvvZ6aHtzJnSByzurk0du7ZkSTUlAgAAzKmwg9zjkjaY2Trl\nA9ydkt4624N2Dh/TX/3xL+i6c6eUzGVLb3zttcFLUNFdAwAADS7UIOfuGTO7R9Jjyt9+5AF3329m\nOyX1u3ufmf2IpL+T1C7pZ8zsP7v7jaWOu+RSWt2X0i++0dIyc3etra1mPx8AAEAtmXvod1qbc+sW\nLfO7/81bdKR9lZ7sWKt/+e+/JCWucNIDAABAHZjZE+7eW82+YV9arYlnlnTo472364WMSogDAAAN\nZs/AsHbtHVSqo+umao8RyyBXLJmwsEsAAAC4zJ6BYe3o269U0iTPVb3gamxbVZPduNtftiLcQgAA\nAKbYtXdQqaSptXl2PbXYBrlkwvRzL1+pj9z5yrBLAQAAuMyxkbQWpmZ/d4xYXlq9adVS9f/JT4Vd\nBgAAQKA17a0aHh2jIxdk4OSotu7epz0Dw2GXAgAAMM32zd2ayLrS41UPj5MU0yDXlDANj45pR99+\nwhwAAGg4W3o6tfP2G9XZ1iJZouq2XCyDnCS1NjcplTTt2jsYdikAAADTbOnp1EPbbtHE6aPfrfYY\nsQxyYxNZDZ4+r0w2p6GRdPkdAAAAIiiWQU4mZXKu42fHtHhBLOdzAAAAxDTIeeEhKY5LkAEAAEgx\nDXIuaSKXU3trky6MZ8MuBwAAoCZiGeTMpFQyoZF0hkurAAAgtmKZctylS5lc4TmXVgEAQDzFsiNX\n7PhZZq0CAIB4im2QM8v/mbEguvIAAAzMSURBVJ6gIwcAAOIptkHOmbUKAABiLrZBblJLUzLsEgAA\nAGoi9kHuqkWpsEsAAACoidgHuefHMmGXAAAAUBOxD3LnLxHkAABAPMU+yOWY6wAAAGIq9kHOwi4A\nAACgRmIf5FIJohwAAIin2Ae5ZJIgBwAA4in2QW48yyA5AAAQT7EPcqzsAAAA4ir2QY6VHQAAQFzF\nPsixsgMAAIirWAe55oRkxmQHAAAQT7EOcuM5Kc3KDgAAIKZiHeQk6Ux6IuwSAAAAaiL0IGdmt5nZ\nATM7bGb3Bny+wMw+Vfj862bWdSXHZ84qAACIq1CDnJklJd0v6fWSbpC01cxumLLZ2yWNuPt6SR+R\ndF99qwQAAGhMYXfkbpZ02N0H3X1c0sOS7piyzR2SHiw8f0TSa40ZDAAAAKEHuVWSjhW9Hiq8F7iN\nu2cknZN09dQDmdk2M+s3s/5s+lyNygUAAGgcYQe5OePuu9291917k61LX3g/Qe8OAADEVNhB7rik\nNUWvVxfeC9zGzJokLZX0XKVf0L6QGwIDAIB4CjvIPS5pg5mtM7NmSXdK6puyTZ+kuwrPf17SP/oV\nLKDKaDoAABBXTWF+ubtnzOweSY9JSkp6wN33m9lOSf3u3ifpryV9wswOSzqjfNgrK2H5EDee5QYk\nAAAgnkINcpLk7o9KenTKezuKno9JetOVH1fKkeEAAECMhR7kasUs/OvGAAAAtRTLIGeSUomEcnI1\nJxkkBwAA4imWQU6SmpKmtpaU1i1fHHYpAAAANRHLINeSSmrF0hZNZF3bN3eHXQ4AAEBNxDLIZXOu\nzrYWbd/crS09nWGXAwAAUBOxnA/AZFUAADAfxDLINSVMw6Nj2tG3X3sGhsMuBwAAoCZiGeQkqbW5\nSamkadfewbBLAQAAqInYBjlJWphKamgkHXYZAAAANRHrIHdxIqvV7a1hlwEAAFATsQ1y6fEMtx8B\nAACxxu1HAAAAIiqWQW7TijY9tO2WsMsAAACoqdheWgUAAIg7ghwAAEBEEeQAAAAiiiAHAAAQUQQ5\nAACAiIplkBs4Oaqtu/exzioAAIi1WAa5poRpeHRMO/r2E+YAAEBsxTLISVJrc5NSSdOuvYNhlwIA\nAFATsQ1ykrQwldTQSDrsMgAAAGoi1kHu4kRWq9tbwy4DAACgJmIb5NLjGU1kXds3d4ddCgAAQE3E\ncq3VbM7V2dai7Zu7taWnM+xyAAAAaiKWQW7TijY9tO2WsMsAAACoqdheWgUAAIg7ghwAAEBEEeQA\nAAAiiiAHAAAQUQQ5AACAiAotyJnZVWb2JTM7VPizfYbtvmhmZ83sH+pdIwAAQCMLsyN3r6SvuPsG\nSV8pvA7yIUm/WLeqAAAAIiLMIHeHpAcLzx+U9LNBG7n7VySN1qsoAACAqAgzyF3j7icKz09KuibE\nWgAAACKnpis7mNmXJa0I+Oh9xS/c3c3MZ/ld2yRtk6S1a9fO5lAAAACRUNMg5+63zvSZmZ0ys5Xu\nfsLMVkoanuV37Za0W5J6e3tnFQoBAACiIMxLq32S7io8v0vS50KsBQAAIHLCDHIfkPQ6Mzsk6dbC\na5lZr5l9dHIjM/sXSZ+W9FozGzKznwylWgAAgAZT00urpbj7c5JeG/B+v6R3FL3+sXrWBQAAEBWs\n7AAAABBRBDkAAICIIsgBAABEFEEOAAAgoghyAAAAEUWQAwAAiCiCHAAAQEQR5AAAACKKIAcAABBR\nBDkAAICIIsgBAABEFEEOAAAgoghyAAAAEUWQAwAAiCiCHAAAQEQR5AAAACIqlkFu4OSotu7epz0D\nw2GXAgAAUDOxDHJNCdPw6Jh29O0nzAEAgNiKZZCTpNbmJqWSpl17B8MuBQAAoCZiG+QkaWEqqaGR\ndNhlAAAA1ESsg9zFiaxWt7eGXQYAAEBNxDLIjU1kdejUqJ6/OKHtm7vDLgcAAKAmYhnkJEkmedg1\nAAAA1FBsg1zSTE0JJjsAAID4agq7gFrJZF3PXRhXJvt82KUAAADURCw7cmamRMIkSeNZLrACAIB4\nimVHLueusUxWCUnNTbHMqgAAAPHsyEl6YaZDx+IF4dYBAABQI7EMciapOZmQmcmdS6sAACCeYnlp\nVZKakqYVixfowng27FIAAABqIpZBriWVVHfHYqXHM+psawm7HAAAgJqI5aVVSUqPZzSRdVZ2AAAA\nsRVakDOzq8zsS2Z2qPBne8A2Lzezr5nZfjP7jpm9pZJjZ3OuzrYW7bz9Rm3p6Zz74gEAABqAhTUZ\nwMw+KOmMu3/AzO6V1O7uvzNlm42S3N0Pmdm1kp6Q9BJ3P1vq2L29vd7f31+z2gEAAOaKmT3h7r3V\n7BvmpdU7JD1YeP6gpJ+duoG7H3T3Q4Xnz0galtRRtwoBAAAaWJhB7hp3P1F4flLSNaU2NrObJTVL\nOjLD59vMrN/M+k+fPj23lQIAADSgms5aNbMvS1oR8NH7il+4u5vZjNd4zWylpE9Iusvdc0HbuPtu\nSbul/KXVqosGAACIiJoGOXe/dabPzOyUma109xOFoDY8w3ZLJH1e0vvcfV+NSgUAAIicMC+t9km6\nq/D8Lkmfm7qBmTVL+jtJf+Puj9SxNgAAgIYXZpD7gKTXmdkhSbcWXsvMes3so4Vt3ixps6S7zexb\nhcfLwykXAACgsYR2+5Fa4vYjAAAgKqJ6+xEAAADMAkEOAAAgoghyAAAAERXLMXJmNirpQNh1oGrL\nJT0bdhGoGucvujh30cb5i65N7t5WzY41vY9ciA5UO2gQ4TOzfs5fdHH+ootzF22cv+gys6pnaHJp\nFQAAIKIIcgAAABEV1yC3O+wCMCucv2jj/EUX5y7aOH/RVfW5i+VkBwAAgPkgrh05AACA2It0kDOz\n28zsgJkdNrN7Az5fYGafKnz+dTPrqn+VmEkF5+89ZvZ9M/uOmX3FzK4Lo05MV+7cFW33RjNzM2Mm\nXQOp5PyZ2ZsLv3/7zeyT9a4RM6vg7861ZvZPZvbNwt+fPxVGnZjOzB4ws2Ez+94Mn5uZ/Xnh3H7H\nzF5Z7piRDXJmlpR0v6TXS7pB0lYzu2HKZm+XNOLu6yV9RNJ99a0SM6nw/H1TUq+7v0zSI5I+WN8q\nEaTCcycza5P0bklfr2+FKKWS82dmGyT9rqR/6+43SvqPdS8UgSr8/fs9SX/r7q+QdKekv6hvlSjh\n45JuK/H56yVtKDy2SfrLcgeMbJCTdLOkw+4+6O7jkh6WdMeUbe6Q9GDh+SOSXmtmVscaMbOy58/d\n/8nd04WX+yStrnONCFbJ754k/aHy//M0Vs/iUFYl5++dku539xFJcvfhOteImVVy/lzSksLzpZKe\nqWN9KMHd90o6U2KTOyT9jeftk7TMzFaWOmaUg9wqSceKXg8V3gvcxt0zks5Jurou1aGcSs5fsbdL\n+kJNK0Klyp67wuWANe7++XoWhopU8ru3UdJGM/t/ZrbPzEp1EFBflZy/P5D0NjMbkvSopF+vT2mY\nA1f6b2NsV3ZAjJjZ2yT1SnpN2LWgPDNLSPqwpLtDLgXVa1L+0s4W5Tvhe83sJnc/G2pVqNRWSR93\n9/9mZq+W9Akze6m758IuDHMvyh2545LWFL1eXXgvcBsza1K+xfxcXapDOZWcP5nZrZLeJ+l2d79U\np9pQWrlz1ybppZL2mNlRSbdI6mPCQ8Oo5HdvSFKfu0+4+5OSDiof7BC+Ss7f2yX9rSS5+9cktSi/\nDisaX0X/NhaLcpB7XNIGM1tnZs3KD+jsm7JNn6S7Cs9/XtI/OjfOaxRlz5+ZvULSLuVDHGN0GkfJ\nc+fu59x9ubt3uXuX8uMbb3f3qtcSxJyq5O/OzyrfjZOZLVf+UutgPYvEjCo5f09Leq0kmdlLlA9y\np+taJarVJ+mXCrNXb5F0zt1PlNohspdW3T1jZvdIekxSUtID7r7fzHZK6nf3Pkl/rXxL+bDygwvv\nDK9iFKvw/H1I0mJJny7MUXna3W8PrWhIqvjcoUFVeP4ek/QTZvZ9SVlJv+XuXM1oABWev/dK+isz\n+w3lJz7cTROjMZjZQ8r/T9LywhjG35eUkiR3/5/Kj2n8KUmHJaUl/XLZY3JuAQAAoinKl1YBAADm\nNYIcAABARBHkAAAAIoogBwAAEFEEOQAAgIgiyAFACYX7OX3VzF5f9N6bzOyLYdYFABK3HwGAsszs\npZI+LekVyt9/85uSbnP3I6EWBmDeI8gBQAXM7IOSLkhaJGnU3f8w5JIAgCAHAJUws0WSviFpXFIv\na/8CaASRXaILAOrJ3S+Y2acknSfEAWgUTHYAgMrlCg8AaAgEOQAAgIgiyAEAAEQUkx0AAAAiio4c\nAABARBHkAAAAIoogBwAAEFEEOQAAgIgiyAEAAEQUQQ4AACCiCHIAAAARRZADAACIqP8PnlBwmQFX\n3rIAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Rfj_h_20gkU9",
"colab_type": "text"
},
"source": [
"This plot reveals that our critical cases were consistently underestimated in our model. For instance, for all the values where Y = 1, their corresponding Y_hat values are all within a range of between 0.0 and 0.5. If our model was optimal, our desired Y_hat values would be much closer to 1 for critical case of COVID-19 then it is currently. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MgIQPc4l9mJ-",
"colab_type": "text"
},
"source": [
"# Takeaway"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tJcTffjz9qh-",
"colab_type": "text"
},
"source": [
"The big takeaway from this exercise is that current data publicly available on Kaggle is not enough. If the objective is to see how different variables effect the likelyhood that someone contracts a critical case of COVID-19, this dataset is insufficient. For public health officials, information scarcity (repressented accutely by this dataset) could me the difference between life and death for many. It is important that researchers, public health, and government officials have access to properly and consistently labeled data so that they can take informed measures to reduce the negative impacts of this pandemic. "
]
},
{
"cell_type": "code",
"metadata": {
"id": "Mk0VrZBFM8LV",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
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