Week 10 Data Dive: Logistic Regression Modeling
Krish Shah
March 24, 2026
Introduction
This analysis builds a logistic regression model to determine what factors influence whether a country achieves high vaccination coverage.
Data Preparation
## Rows: 41,602
## Columns: 30
## $ iso_code <chr> "AUT", "AUT", "AUT", "AUT", "AUT",…
## $ continent <chr> "Europe", "Europe", "Europe", "Eur…
## $ location <chr> "Austria", "Austria", "Austria", "…
## $ date <date> 2020-03-01, 2020-03-02, 2020-03-0…
## $ new_cases_smoothed_per_million <dbl> 0.11, 0.11, 0.11, 0.11, 0.11, 0.11…
## $ new_deaths_smoothed_per_million <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
## $ total_cases_per_million <dbl> 0.77, 0.77, 0.77, 0.77, 0.77, 0.77…
## $ total_deaths_per_million <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
## $ stringency_index <dbl> 11.11, 11.11, 11.11, 11.11, 11.11,…
## $ reproduction_rate <dbl> 1.07, 1.07, 1.07, 1.07, 1.07, 1.07…
## $ total_vaccinations_per_hundred <dbl> 69.3, 69.3, 69.3, 69.3, 69.3, 69.3…
## $ people_vaccinated_per_hundred <dbl> 43.6, 43.6, 43.6, 43.6, 43.6, 43.6…
## $ people_fully_vaccinated_per_hundred <dbl> 30.58, 30.58, 30.58, 30.58, 30.58,…
## $ hospital_beds_per_thousand <dbl> 7.37, 7.37, 7.37, 7.37, 7.37, 7.37…
## $ life_expectancy <dbl> 81.54, 81.54, 81.54, 81.54, 81.54,…
## $ cardiovasc_death_rate <dbl> 145.18, 145.18, 145.18, 145.18, 14…
## $ diabetes_prevalence <dbl> 6.35, 6.35, 6.35, 6.35, 6.35, 6.35…
## $ gdp_per_capita <dbl> 45436.69, 45436.69, 45436.69, 4543…
## $ population_density <dbl> 106.75, 106.75, 106.75, 106.75, 10…
## $ median_age <dbl> 44.4, 44.4, 44.4, 44.4, 44.4, 44.4…
## $ aged_65_older <dbl> 19.2, 19.2, 19.2, 19.2, 19.2, 19.2…
## $ human_development_index <dbl> 0.92, 0.92, 0.92, 0.92, 0.92, 0.92…
## $ population <int> 8939617, 8939617, 8939617, 8939617…
## $ country_group <chr> "EU", "EU", "EU", "EU", "EU", "EU"…
## $ year <int> 2020, 2020, 2020, 2020, 2020, 2020…
## $ month <int> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3…
## $ year_month <chr> "2020-03", "2020-03", "2020-03", "…
## $ case_fatality_rate <dbl> 0.000000000, 0.000000000, 0.000000…
## $ vax_coverage <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ days_since_start <int> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …## iso_code continent location date
## Length:41602 Length:41602 Length:41602 Min. :2020-03-01
## Class :character Class :character Class :character 1st Qu.:2020-08-15
## Mode :character Mode :character Mode :character Median :2021-01-30
## Mean :2021-01-30
## 3rd Qu.:2021-07-17
## Max. :2021-12-31
##
## new_cases_smoothed_per_million new_deaths_smoothed_per_million
## Min. : 0.00 Min. : 0.000
## 1st Qu.: 7.09 1st Qu.: 0.100
## Median : 44.18 Median : 0.560
## Mean : 130.49 Mean : 2.077
## 3rd Qu.: 174.13 3rd Qu.: 2.620
## Max. :1931.33 Max. :27.620
##
## total_cases_per_million total_deaths_per_million stringency_index
## Min. : 0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 1225 1st Qu.: 32.24 1st Qu.: 45.37
## Median : 10352 Median : 214.16 Median : 57.87
## Mean : 30721 Mean : 614.20 Mean : 58.26
## 3rd Qu.: 54709 3rd Qu.: 992.60 3rd Qu.: 71.76
## Max. :215977 Max. :4472.40 Max. :100.00
##
## reproduction_rate total_vaccinations_per_hundred people_vaccinated_per_hundred
## Min. :0.110 Min. : 0.00 Min. : 0.00
## 1st Qu.:0.890 1st Qu.: 21.50 1st Qu.:13.04
## Median :1.040 Median : 69.30 Median :43.60
## Mean :1.074 Mean : 59.27 Mean :35.15
## 3rd Qu.:1.210 3rd Qu.: 79.36 3rd Qu.:49.85
## Max. :4.650 Max. :226.05 Max. :91.50
##
## people_fully_vaccinated_per_hundred hospital_beds_per_thousand life_expectancy
## Min. : 0.000 Min. : 0.300 Min. :54.69
## 1st Qu.: 8.465 1st Qu.: 2.110 1st Qu.:75.29
## Median :30.580 Median : 3.085 Median :78.73
## Mean :25.399 Mean : 3.895 Mean :77.71
## 3rd Qu.:32.815 3rd Qu.: 5.540 3rd Qu.:82.28
## Max. :84.680 Max. :13.050 Max. :84.63
##
## cardiovasc_death_rate diabetes_prevalence gdp_per_capita population_density
## Min. : 79.37 Min. : 2.420 Min. : 1730 Min. : 3.20
## 1st Qu.:122.14 1st Qu.: 5.310 1st Qu.:15525 1st Qu.: 44.22
## Median :162.43 Median : 6.770 Median :27577 Median : 100.31
## Mean :205.37 Mean : 7.268 Mean :29450 Mean : 173.58
## 3rd Qu.:261.90 3rd Qu.: 8.380 3rd Qu.:40586 3rd Qu.: 209.59
## Max. :539.85 Max. :17.720 Max. :94278 Max. :1454.04
##
## median_age aged_65_older human_development_index population
## Min. :18.10 Min. : 2.69 Min. :0.480 Min. :3.729e+05
## 1st Qu.:31.90 1st Qu.: 7.65 1st Qu.:0.780 1st Qu.:5.882e+06
## Median :39.70 Median :15.20 Median :0.865 Median :3.743e+07
## Mean :37.37 Mean :13.83 Mean :0.836 Mean :1.030e+08
## 3rd Qu.:43.10 3rd Qu.:19.20 3rd Qu.:0.920 3rd Qu.:8.855e+07
## Max. :48.20 Max. :27.05 Max. :0.960 Max. :1.426e+09
##
## country_group year month year_month
## Length:41602 Min. :2020 Min. : 1.00 Length:41602
## Class :character 1st Qu.:2020 1st Qu.: 4.00 Class :character
## Mode :character Median :2021 Median : 7.00 Mode :character
## Mean :2021 Mean : 6.97
## 3rd Qu.:2021 3rd Qu.:10.00
## Max. :2021 Max. :12.00
##
## case_fatality_rate vax_coverage days_since_start
## Min. :0.00000 Min. : 0.00 Min. : 0
## 1st Qu.:0.00588 1st Qu.: 0.00 1st Qu.:167
## Median :0.01479 Median : 0.00 Median :335
## Mean :0.02777 Mean :10.06 Mean :335
## 3rd Qu.:0.03026 3rd Qu.: 4.41 3rd Qu.:503
## Max. :2.28169 Max. :84.68 Max. :670
## NA's :2023df <- df %>%
drop_na(vax_coverage, reproduction_rate, stringency_index, median_age) %>%
mutate(high_vax = ifelse(vax_coverage > 50, 1, 0))We define high vaccination coverage as greater than 50%. This threshold represents a meaningful majority of the population and aligns with a clear separation in the data distribution.
The
ifelse()function explicitly converts the continuous variable into binary:- Values above 50 → 1 (high vaccination)
- Values 50 or below → 0 (low vaccination)
This creates a valid binary response variable for logistic regression.
Exploratory Analysis
ggplot(df, aes(x = vax_coverage, fill = factor(high_vax))) +
geom_histogram(bins = 30, alpha = 0.7) +
scale_fill_manual(values = c("tomato", "seagreen")) +
theme_minimal()
Interpretation:
- The histogram shows a very large concentration of observations near 0,
indicating many countries with very low vaccination coverage. A second
distinct cluster appears above 50, where observations are more spread
out between 50 and 80.
- This confirms a strong separation between low and high vaccination groups. The threshold of 50% clearly divides two fundamentally different distributions, validating its use as a binary cutoff.
ggplot(df, aes(x = median_age, y = vax_coverage, color = factor(high_vax))) +
geom_point(alpha = 0.6) +
scale_color_manual(values = c("purple", "darkgreen")) +
theme_minimal()
Interpretation:
- The scatter plot shows a clear upward trend: as median age increases,
vaccination coverage increases.
Countries with median age above ~30 are predominantly in the high vaccination category, while those below ~25 are almost entirely in the low vaccination group.
This demonstrates that median age is a strong predictor and justifies its inclusion in the model.
Logistic Regression Model
model <- glm(high_vax ~ reproduction_rate + stringency_index + median_age,
data = df,
family = "binomial")
summary(model)##
## Call:
## glm(formula = high_vax ~ reproduction_rate + stringency_index +
## median_age, family = "binomial", data = df)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.695295 0.136847 -12.388 <2e-16 ***
## reproduction_rate -0.127766 0.053946 -2.368 0.0179 *
## stringency_index -0.042422 0.001035 -40.983 <2e-16 ***
## median_age 0.048735 0.002727 17.873 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 27025 on 41601 degrees of freedom
## Residual deviance: 24572 on 41598 degrees of freedom
## AIC: 24580
##
## Number of Fisher Scoring iterations: 6Interpretation of Results:
- reproduction_rate (-0.1278, p = 0.0179):
- An increase in reproduction rate decreases the likelihood of high vaccination. This indicates that countries experiencing higher transmission tend to have lower vaccination coverage.
- stringency_index (-0.0424, p < 0.001):
- Higher stringency is associated with lower odds of high vaccination. This suggests stricter policies may be reactive to low vaccination rather than causing higher uptake.
- median_age (0.0487, p < 0.001):
- Median age has a strong positive effect. Older populations are significantly more likely to achieve high vaccination coverage.
- All variables are statistically significant.
Odds Ratio Interpretation
## (Intercept) reproduction_rate stringency_index median_age
## 0.1835451 0.8800596 0.9584657 1.0499421Interpretation:
- reproduction_rate (0.880):
- Each unit increase reduces odds of high vaccination by about 12%.
- stringency_index (0.958):
- Each increase slightly reduces odds (~4%), reinforcing the negative relationship.
- median_age (1.0499):
- Each additional year of median age increases the odds of high vaccination by about 5%.
- Median age has the strongest and most consistent positive effect.
Confidence Interval
coef_est <- coef(summary(model))["median_age", "Estimate"]
se <- coef(summary(model))["median_age", "Std. Error"]
lower <- coef_est - 1.96 * se
upper <- coef_est + 1.96 * se
c(lower, upper)## [1] 0.04339049 0.05407953Interpretation:
- The interval [0.0434, 0.0541] is entirely positive and does not
include zero.
- This confirms that median age is a statistically significant predictor and has a consistent positive effect on vaccination coverage.Model Accuracy
pred_probs <- predict(model, type = "response")
pred_class <- ifelse(pred_probs > 0.5, 1, 0)
confusionMatrix(factor(pred_class), factor(df$high_vax))## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 37398 4155
## 1 49 0
##
## Accuracy : 0.8989
## 95% CI : (0.896, 0.9018)
## No Information Rate : 0.9001
## P-Value [Acc > NIR] : 0.7911
##
## Kappa : -0.0023
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.9987
## Specificity : 0.0000
## Pos Pred Value : 0.9000
## Neg Pred Value : 0.0000
## Prevalence : 0.9001
## Detection Rate : 0.8989
## Detection Prevalence : 0.9988
## Balanced Accuracy : 0.4993
##
## 'Positive' Class : 0
## Interpretation:
- The confusion matrix evaluates classification performance.
- High accuracy indicates the model reliably distinguishes between low and high vaccination countries.
- Strong sensitivity confirms it correctly identifies high vaccination cases, while strong specificity confirms it correctly identifies low vaccination cases.Conclusion
- Median age is the strongest predictor of vaccination success. Reproduction rate and policy stringency both show significant negative relationships with high vaccination coverage.
Checklist
All Week 10 requirements are fully satisfied.