Let’s look at the gapminder data. This is data from the World Bank on a ton of different outcomes, but we are going to look at a specific subset focused on, among other things, infant mortality. We will load it via the “dslabs” package, though there are a few different sources (including a gapminder package)
install.packages(“dslabs”)
library(dslabs)## Warning: package 'dslabs' was built under R version 4.4.3data(gapminder)
head(gapminder)## country year infant_mortality life_expectancy fertility
## 1 Albania 1960 115.40 62.87 6.19
## 2 Algeria 1960 148.20 47.50 7.65
## 3 Angola 1960 208.00 35.98 7.32
## 4 Antigua and Barbuda 1960 NA 62.97 4.43
## 5 Argentina 1960 59.87 65.39 3.11
## 6 Armenia 1960 NA 66.86 4.55
## population gdp continent region
## 1 1636054 NA Europe Southern Europe
## 2 11124892 13828152297 Africa Northern Africa
## 3 5270844 NA Africa Middle Africa
## 4 54681 NA Americas Caribbean
## 5 20619075 108322326649 Americas South America
## 6 1867396 NA Asia Western Asiacolnames(gapminder)## [1] "country" "year" "infant_mortality" "life_expectancy"
## [5] "fertility" "population" "gdp" "continent"
## [9] "region"dim(gapminder)## [1] 10545 9First Step: What do we care about? What is our outcome of interest?
I will do this one for us: infant mortality. This will be the outcome you are going to try to predict.
The rest of the assignment is straightforward; simply follow the steps below:
What could explain levels of infant mortality? Pick at least three of the variables in the dataset that you will use as predictors/covariates, and explain each decision.
#What variables are we using and why?
#Fertility: Countries with higher fertility rates often have higher infant mortality, partly due to resource constraints and limited maternal/child health capacity.
#Life_expectancy: Higher life expectancy is a strong signal of better health systems, nutrition, sanitation, and medical access, which are all linked to lower infant mortality.
#GDP: GDP per capita captures national economic development. Wealthier countries typically invest more in healthcare and public health, reducing infant mortality.
predictors <- c("fertility", "life_expectancy", "gdp")
predictors## [1] "fertility" "life_expectancy" "gdp"Set up our datasets for our analysis. Divide your dataset in half so that you have both a training and a testing dataset. Do so using random rows as discussed in class (which is important here!). Ensure that the datasets are mutually exclusive (rows are in one of the datasets, but not the other)
#Creating Training and Testing Sets
set.seed(7)
n <- nrow(gapminder)
#Randomly sample half the rows for training
train_index <- sample(1:n, size = n/2, replace = FALSE)
#Create training and testing datasets
train_set <- gapminder[train_index, ]
test_set <- gapminder[-train_index, ]
#Check
dim(train_set)## [1] 5272 9dim(test_set)## [1] 5273 9Regress and Predict. Run the actual regression, and then use the results to predict infant mortality in your testing set. Attach the predictions for the testing set directly to the testing set to make the next step easier.
#Regression model using my predictors
model <- lm(infant_mortality ~ fertility + life_expectancy + gdp, data = train_set)
summary(model)##
## Call:
## lm(formula = infant_mortality ~ fertility + life_expectancy +
## gdp, data = train_set)
##
## Residuals:
## Min 1Q Median 3Q Max
## -93.638 -9.077 0.226 9.110 94.071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.344e+02 4.036e+00 58.082 < 2e-16 ***
## fertility 6.091e+00 2.539e-01 23.991 < 2e-16 ***
## life_expectancy -3.155e+00 4.854e-02 -65.010 < 2e-16 ***
## gdp 1.506e-12 4.087e-13 3.685 0.000232 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.99 on 3558 degrees of freedom
## (1710 observations deleted due to missingness)
## Multiple R-squared: 0.8679, Adjusted R-squared: 0.8678
## F-statistic: 7793 on 3 and 3558 DF, p-value: < 2.2e-16#Predict infant mortality for the testing set
test_set$predicted_im <- predict(model, newdata = test_set)
#Check the first few
head(test_set[, c("infant_mortality", "predicted_im")])## infant_mortality predicted_im
## 1 115.4 NA
## 4 NA NA
## 7 NA NA
## 14 69.5 65.77299
## 16 29.5 30.75759
## 19 175.0 NA#Removing rows in the test set that are missing predictors
test_clean <- test_set %>%
filter(!is.na(fertility),
!is.na(life_expectancy),
!is.na(gdp),
!is.na(infant_mortality))
#Make predictions only on rows we can actually predict
test_clean$predicted_im <- predict(model, newdata = test_clean)
#Compare actual vs predicted
head(test_clean[, c("infant_mortality", "predicted_im")])## infant_mortality predicted_im
## 1 69.5 65.77299
## 2 29.5 30.75759
## 3 115.5 115.87990
## 4 190.0 162.47489
## 5 89.3 92.80090
## 6 209.6 122.36408Assess Prediction. Calculate the MAE and RMSE (mean absolute error and root mean square error) for your predictions. Compare them to the MAE and RMSE of simply guessing the mean infant mortality or median infant mortality as the rate for a given country in a given year.
#Absolute error for each observation
test_clean$abs_error <- abs(test_clean$infant_mortality - test_clean$predicted_im)
#Squared error for each observation
test_clean$sq_error <- (test_clean$infant_mortality - test_clean$predicted_im)^2
# MAE
MAE_model <- mean(test_clean$abs_error, na.rm = TRUE)
# RMSE
RMSE_model <- sqrt(mean(test_clean$sq_error, na.rm = TRUE))
MAE_model## [1] 12.15373RMSE_model## [1] 16.81808#Baseline: Mean guess
mean_guess <- mean(train_set$infant_mortality, na.rm = TRUE)
#Errors from simply guessing the mean
test_clean$mean_abs_error <- abs(test_clean$infant_mortality - mean_guess)
test_clean$mean_sq_error <- (test_clean$infant_mortality - mean_guess)^2
MAE_mean <- mean(test_clean$mean_abs_error)
RMSE_mean <- sqrt(mean(test_clean$mean_sq_error))
#Baseline: Median guess
median_guess <- median(train_set$infant_mortality, na.rm = TRUE)
test_clean$med_abs_error <- abs(test_clean$infant_mortality - median_guess)
test_clean$med_sq_error <- (test_clean$infant_mortality - median_guess)^2
MAE_median <- mean(test_clean$med_abs_error)
RMSE_median <- sqrt(mean(test_clean$med_sq_error))
#Print everything
MAE_model## [1] 12.15373RMSE_model## [1] 16.81808MAE_mean## [1] 38.50456RMSE_mean## [1] 46.45832MAE_median## [1] 37.22098RMSE_median## [1] 48.34491#My regression model seem to have performed better than either a mean-guess or median-guess baseline. The model produced a MAE of 12.15 and a RMSE of 16.82, showing that the typical prediction error was around 12 infant deaths per 1,000 live births. In contrast, simply guessing the mean infant mortality rate resulted in a MAE of 38.50 and RMSE of 46.46, while the median guess resulted in a MAE of 37.22 and RMSE of 48.34. Both approaches performed worse than the regression model. These results suggest that the predictors I selected (fertility, life expectancy, and GDP) provide meaningful explanatory power.