The residual standard error is an [[estimator]] of the [[variance]] $\sigma^2$ for a [[base/Linear Regression/linear regression|linear regression]]. $RSE = \sqrt{\hat \sigma^2} = \sqrt{\frac{RSS}{n - (p+1)}}$ where $p$ is the number of parameters in the model, or the number of [[degrees of freedom]]. The RSS has $n - (p + 1)$ degrees of freedom because $p+1$ parameters must first be estimated to compute it, which results in a loss of $p+1$ df. It can be shown that this [[estimator]] $\hat \sigma^2$ is an unbiased estimator for $\sigma ^2$.