How to adjust the standard error for a standardized beta after squaring the beta I have a standardized beta from a regression, which is equivalent to a correlation. I also have it's standard error (SE). I want to plot the R2 (explained variance) with an error bar, and to get the R2, I simply square the standardized beta. For the error bar, I want to use the SE for the R2, how do I transform the SE of the standardized beta so I can use it for the R2? Do I also simply square the SE, or is it more complicated than that?

From the delta method we have that
$$
\sqrt{N}[\hat{\beta}^2 - \beta^2] \stackrel{D}{\to} \operatorname{Normal}(0, 4 \beta^2 \sigma^2)
$$
where $\sigma / \sqrt{N}$ is the standard error of $\hat{\beta}$. Therefore, a consistent estimator of the standard error of $\hat{\beta}^2$ is
$$
2 |\hat{\beta}| \times \sigma / \sqrt{N}.
$$
So, basically, multiply the standard error of $\hat{\beta}$ by $2 |\hat{\beta}|$ to get the standard error of $\hat{\beta}^2$.
If you want a solution that doesn't rely so heavily on Taylor series approximations and a super large sample size, then you should look up how to perform a bootstrap in whatever software you are using. There are tons of tutorials out there --- I'm just showing you the delta method because it's a quick and elegant solution for this particular problem. Many people find the bootstrap confidence intervals more credible.
