Overfitting and adjusted r square

adjrsq.r

# How does adjusted r-square do with overfitting?

rm(list=ls())
set.seed(101)

library(ggplot2)
library(tidyr)

y <- rnorm(1000)
x <- matrix(rnorm(1000 * 1000), 1000, 1000)

res <- expand.grid(var=1:300, r.squared=NA, adj.r.squared=NA, pred.r.squared=NA)

for(i in 1:nrow(res))
{
	message(i)
	ou <- summary(lm(y ~ x[,1:res$var[i]]))
	res$r.squared[i] <- ou$r.squared
	res$adj.r.squared[i] <- ou$adj.r.squared
	pred <- x[,1:res$var[i]] %*% as.matrix(coefficients(ou)[-1,1])
	res$pred.r.squared[i] <- cor(y, pred)^2
}

res <- gather(res, "key", "value", r.squared, adj.r.squared, pred.r.squared)
ggplot(res, aes(x=var, y=value)) +
geom_point(aes(colour=key)) +
geom_line(aes(colour=key)) +
labs(x="Number of variables", y="Rsq or Adjusted Rsq") +
scale_colour_brewer(type="qual")