How do you calculate the standard error of $R^2$ I would like to confirm something.
I know that $R^2$ (in a linear regression) can be found by taking the square of Pearson's $r$.
The standard error of Pearson's $r$ is calculated using the following formula.
$$SE = \sqrt{((1-r^2)/(n-2))}$$
Is the standard error of the $R^2$ therefore, simply the square of the standard error of $r$? If it is not, what is the formula for the standard error of $R^2$?
 A: One easy and robust estimator of the standard error of $R^2$ is bootstrapping. Obtain bootstrap samples of your data set (say there are $n$ observations) by sampling $n$ observations from your data with replacement $B$ times (e.g., $B = 1,000$). For each bootstrap sample $b = 1, 2, \ldots, B$, compute $R^2_b$ (the $R^2$ estimate for the $b$th bootstrap sample). As a result, you will have $B$ estimates of $R^2$ which already incorporate the sampling variability which you are trying to estimate. The bootstrap estimate of $SE(R^2)$ is simply the standard deviation of $R^2_1, R^2_2, \ldots, R^2_B$,
$$\hat{SE}(R^2) = \frac{1}{B-1} \sqrt{\sum_{b=1}^B \left[R^2_b - \left(B^{-1} \sum_{b=1}^B R^2_b\right)\right]^2}.$$
For more information, see, e.g., Wikipedia page on bootstrapping and the excellent introductory text An Introduction to the Bootstrap by Efron & Tibshirani.
A: I noticed that the MBESS package in R has the Variance.R2 function:

[It is a] function to determine the variance of the squared multiple correlation coefficient given the population squared multiple correlation coefficient, sample size, and the number of predictors.

That said, its not quite what you are after, because it assumes a given population r-squared value. If anything, sample adjusted r-squared would be a better estimate of population r-squared.
