Week 8 Team 13

# Data Management from dateutil import relativedelta as rd import pandas as pd import numpy as np !pip install statsmodels # Visualization import matplotlib.pyplot as plt import plotly as py import plotly.express as px import plotly.graph_objects as go import plotly.offline as pyo pyo.init_notebook_mode() import seaborn as sns # Regression import statsmodels.api as sm from statsmodels.formula.api import ols import statsmodels.graphics.api as smg

# Import modules for API calls import requests import io import pandas as pd import requests import json from datetime import datetime # Import module for plotting import seaborn as sns ## JHU Vaccination Rates (Taken From: https://github.com/owid/covid-19-data/tree/master/public/data) url = 'https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/owid-covid-data.csv' download = requests.get(url).content covid = pd.read_csv(io.StringIO(download.decode('utf-8')), parse_dates=['date']) covid.tail() covid.info()

covid = covid.replace("", np.nan).fillna(0)

Here we compare the Stringency Index from the Covid dataset with the case positivity and the case fatality rate.

covid['case_positivity'] = round(covid["total_cases"] / covid["total_tests"], 2) covid['case_fatality'] = round(covid["total_deaths"] / covid["total_cases"], 2) date = covid['date'] stringency= covid['stringency_index'] covid[covid["case_positivity"] == np.inf] = 0 covid[covid["case_fatality"] == np.inf] = 0 covid[covid["stringency_index"] == np.inf] = 0

fig,ax=plt.subplots() sns.lineplot(date, case_positivity, color='orange', label='Case Positivity') sns.lineplot(date, case_fatality,color='red', label='Case Fatality') plt.xlabel('Date') plt.ylabel('Case Positivity & Case Fatality') plt.xticks(rotation=90) ax2= plt.twinx() sns.lineplot(date, stringency,color='blue', alpha=0.5, label='Stringency Index') ax2.set_ylabel('Stringency Index') ax2.legend(frameon=False, loc='center left') plt.title('Government Policy & Covid') plt.show()

According to the graph above, every spike in the case positivity and fatality is being met by an increase in the stringency index. From the graph it appears as though there is a fall in the case positivity and fatality after the implementation of government measures. However we look further into the actual impact of these measures on the covid cases down below.

We regress the total cases on the stringency index to see if government interventions have caused any impact on Covid 19.

covid[~covid['total_cases'].isnull()]['total_cases'].astype('float') print(covid['total_cases']) covid['log_total_cases'] = np.log(covid['total_cases']+1) covid['log_total_cases'].describe()

sns.lineplot(date, covid['total_cases'], label='Total Cases') sns.lineplot(date, covid['stringency_index'], label='Stringency Index') plt.legend() plt.xticks(rotation=90) #COMPARING THE Total Cases AND Stringency sns.jointplot(x='stringency_index', y='total_cases', data=covid, kind='reg', color='b')

This regression shows that the stringency and the total cases is positively correlated, wh=ith there being a rise in stringency post a rise in total cases and vice versa.

#Plot pairplot with countries organized by WHO regions #g = sns.pairplot(covid[['stringency_index', 'new_cases_smoothed', 'new_vaccinations', 'total_boosters', 'continent']], hue='continent')

#plt.matshow(full_grouped.corr()) #plt.show() f, ax = plt.subplots(figsize=(10, 8)) corr = covid.corr() # Generate a mask for the upper triangle mask = np.triu(np.ones_like(corr, dtype=bool)) # Generate a custom diverging colormap cmap = sns.diverging_palette(230, 20, as_cmap=True) # Plot heatmap sns.heatmap(corr, mask=mask, cmap=cmap, square=True, ax=ax)

# OLS regression y = covid['log_total_cases'] X = covid['stringency_index'] X = sm.add_constant(X) ols_model=sm.OLS(y,X.astype(float), missing='drop') result=ols_model.fit() print(result.summary2())

#OLS Interpretation: Here we take the total cases to be the dependent variable which is log transformed. To identify the percentage increase or decrease we exponentiate the coefficient, subtract one from this number, and multiply by 100. The coefficient is (e^(0.0123)-1) * 100 =1.24%. Therefore, the increase in the stringency index has actually seen a rise in the total cases by 1.24% rather than a fall. Every rise in the total number of cases is being met by an increase in government measures. This does however lead to a fall in the covid cases in the next few periods as identified earlier.

We are seeing a positive coefficient for the stringency. We inferred that this is the result from the fact that policies tightening the government restriction usually come in place right after a spike in total case. Therefore, we see a positive correlation between the 2. Although we have used the log of the total cases as the dependent variable, it appears as though the stringency index is dependent on the number of cases.

from statsmodels.graphics.gofplots import ProbPlot model_norm_residuals = result.get_influence().resid_studentized_internal QQ = ProbPlot(model_norm_residuals) plot_lm_2 = QQ.qqplot(line='45', alpha=0.5, color='#4C72B0', lw=1) plot_lm_2.axes[0].set_title('Normal Q-Q') plot_lm_2.axes[0].set_xlabel('Theoretical Quantiles') plot_lm_2.axes[0].set_ylabel('Standardized Residuals'); # annotations abs_norm_resid = np.flip(np.argsort(np.abs(model_norm_residuals)), 0) abs_norm_resid_top_3 = abs_norm_resid[:3] for r, i in enumerate(abs_norm_resid_top_3): plot_lm_2.axes[0].annotate(i, xy=(np.flip(QQ.theoretical_quantiles, 0)[r], model_norm_residuals[i]));

from statsmodels.graphics.regressionplots import plot_leverage_resid2 fig, ax = plt.subplots(figsize=(8,6)) fig = plot_leverage_resid2(result, ax = ax)

import statsmodels.stats.api as sms from statsmodels.compat import lzip name = ['Breusch-Pagan Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value'] test = sms.het_breuschpagan(result.resid, result.model.exog) lzip(name, test)