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 $R^2$?

  • I would expect it to be closer to something more like $(r +SE)^2-r^2 = 2\,r\, SE + SE^2$ and perhaps more complicated than that – Henry Sep 15 '15 at 21:14
  • No it is not. If you want an approximation of the standard error, consider using the Delta Method. – JohnK Sep 15 '15 at 22:30

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