library(tidyverse)
library(ISLR2)
fit.crim <- lm(medv ~ crim, data=Boston)
summary(fit.crim)

fit.lstat <- lm(medv ~ lstat, data=Boston)
summary(fit.lstat)

fit.lstat.crim <- lm(medv ~ crim + lstat, data=Boston)
summary(fit.lstat.crim)

cor(Boston$crim, Boston$lstat)

fit.full <- lm(medv ~ ., data=Boston)
summary(fit.full)
confint(fit.full)

AIC(fit.lstat)
AIC(fit.crim)
AIC(fit.lstat.crim)
AIC(fit.full)

auto.fit <- step(fit.full, direction="both")
summary(auto.fit)

fit.empty <- lm(medv ~ 1, data=Boston)
full.formula <- formula(fit.full)
auto.fit2 <- step(fit.empty, scope=full.formula, direction="both")