I googled and searched on stats.stackexchange but I cannot find the formula to calculate a 95% confidence interval for an $R^2$ value for a linear regression. Can anyone provide it?
Even better, let’s say I had ran the linear regression below in R. How would I calculate a 95% confidence interval for the $R^2$ value using R code.
lm_mtcars <- lm(mpg ~ wt, mtcars)
You can always bootstrap it:
> library(boot) > foo <- boot(mtcars,function(data,indices) summary(lm(mpg~wt,data[indices,]))$r.squared,R=10000) > foo$t0  0.7528328 > quantile(foo$t,c(0.025,0.975)) 2.5% 97.5% 0.6303133 0.8584067
Carpenter & Bithell (2000, Statistics in Medicine) provide a readable introduction to bootstrapping confidence intervals, though not specifically focused on $R^2$.