A standard error is the estimated standard deviation ˆσ(ˆθ) of an estimator ˆθ for a parameter θ.

Why is the estimated standard deviation of the residuals called “residual standard error” (e.g., in the output of R’s

`summary.lm`

function) and not “residual standard deviation”? What parameter estimate do we equip with a standard error here?Do we consider each residual as an estimator for “its” error term and estimate the “pooled” standard error of all these estimators?

**Answer**

I think that phrasing is specific to R’s `summary.lm()`

output. Notice that the underlying value is actually called “sigma” (`summary.lm()$sigma`

). I don’t think other software necessarily uses that name for the standard deviation of the residuals. In addition, the phrasing ‘residual standard deviation’ is common in textbooks, for instance. I don’t know how that came to be the phrasing used in R’s `summary.lm()`

output, but I always thought it was weird.

**Attribution***Source : Link , Question Author : Michael M , Answer Author : gung – Reinstate Monica*