# Robust Residual standard error (in R)

I have a question regarding to the concept of robust standard errors. What I found about that topic is, that one can estimate the robust standard error for regression coefficients to eliminate problems with heteroscedasticity (when one wants to interpret a model). I want to know if there is a way not only to determine robust standard errors of coefficients but also of the standard error of the overall regression (residual standard error). When its possible, how can I calculate such a value in general?

Because I'm using R its also interesting for me if there is a R-function for this problem (I only know the sandwich-package for the normal robust SE of the coefficients).

Thanks.

• Is it still the policy of Cross Validated to refer problems relating to statistical packages to StackOverflow? – Cesare Camestre Aug 26 '13 at 15:29
• It depends, @CesareCamestre. If the question is about how to use R, such that an explanation of the ideas w/o reference to R, or demonstrated w/ different software, eg Stata, would not answer the question, then it belongs on SO. But if the issue is w/ understanding the ideas, then it can stay here, even if they as about R as well. (Which of the above applies to this Q is not clear to me yet.) – gung Aug 26 '13 at 15:33
• Welcome to the site, @Meiner. It is not clear to me if you are wondering about the nature of sandwich estimates, or if you are only wondering about another way to implement them in R. If the latter, this question would be off-topic for CV (see above), but on-topic on Stack Overflow. If your question is about the underlying ideas, please edit to clarify; if it's about implementation in R, flag your Q & we'll migrate it for you (please don't cross-post, though). – gung Aug 26 '13 at 15:37
• Do you mean forming confidence bands for predicted values or creating something like a global test for all regression parameters against a null intercept-only model? – AdamO Feb 13 '18 at 21:26

If you are interested in the conditional mean $$\mathop{\mathbb{E}} \bigl[ y_j|X_j \bigr] = X_j' \beta$$, where $$X_j$$ may be in or out of sample, then of course you can get the standard error for that as the square root of $$X_j' \, \hat v[\hat \beta] \, X_j$$ where $$\hat v[\hat \beta]$$ is the heteroskedasticity-corrected/sandwich variance estimator. But that conditional mean is rarely of huge interest; I believe you are interested in characterizing what the whole distribution of $$y_j = X_j + \varepsilon_j$$ may have looked like. Without knowing more about the distribution of $$\varepsilon_j$$ you, of course, won't be able to say much about what the variance of $$y_j$$ will be.