U5MR Linear Regression.Rmd

### Predicting Under 5 Mortality Rate (Linear Regression)

library(glmnet)
library(car)

# Read the data 
wbcc <- read.csv("wbcc_bc.csv")

# Keeping Variables for analysis
under5 <- wbcc[c(2,69:79)]
names(under5) <- c("Country", "GenderParity", "Education", "Mortality", "HealthWorker", "Underweight", "Poverty", "PopulationGrowth", "Population", "UrbanGrowth", "UrbanPopulation", "UrbanPercentage")

# Remove rows with missing values in under-five mortality rate
under5 <- subset(under5, (!is.na(under5$Mortality)))

# Subset without country
u5mr <- under5[c(-1)]

# Drop variables with high missing values 
u5mr$HealthWorker <- NULL

# Drop column with NA's
u5mr <- na.omit(u5mr)

#Fitting the linear model
lm.u5mr <- lm(formula = Mortality~., data=u5mr)
summary(lm.u5mr)

# Plot Residual and Studentized Residual
par(mfrow=c(1,2))
plot(lm.u5mr, which=1) # Fitting the residual plots
plot(lm.u5mr$fitted.values,studres(lm.u5mr)) #Fitting Studentized Residual Plot

# Removing outliers
r <- rstandard(lm.u5mr)  ## get standardised residuals
order(abs(r), decreasing = TRUE)[1:3]
u5mr2 <- u5mr[-c(93, 75, 58), ]

#Fitting the linear model
lm.u5mr2 <- lm(formula = Mortality~., data=u5mr2)
summary(lm.u5mr2)$r.squared

# Checking for Multicollinearity
vif(lm.u5mr2)

#Regularization method LASSO
X <- model.matrix(lm.u5mr2)[,-1]
Y <- u5mr2$Mortality

lasso.u5mr2 <- glmnet(X,Y, alpha=1)
plot(lasso.u5mr2, label=TRUE)

#Cross Validation for LASSO
cv_lasso.u5mr2 <- cv.glmnet(X,Y, alpha=1)
plot(cv_lasso.u5mr2)

#Lambda at tradeoff
cv_lasso.u5mr2$lambda.1se

#Fitting linear regression based on LASSO Variable Selections
lm.lasso2.u5mr2 <- lm(formula = Mortality~GenderParity+Education+Underweight+Poverty+PopulationGrowth, data=u5mr2)
summary(lm.lasso2.u5mr2)

# Variance Inflation Factor
vif(lm.lasso2.u5mr2)

# Residual plot
plot(lm.lasso2.u5mr2, which=1)