structural:expansion, structural:summarization, information:highlighting
Assuming normality

The variance of this estimator is equal to 2 σ /(n − p), which does not attain the Cramér–Rao bound of 2 σ / n. However it was shown that there are no unbiased estimators of σ with variance smaller than that of the estimator s. If we are willing to allow biased estimators, and consider the class of estimators that are proportional to the sum of squared residuals (SSR) of the model, then the best (in the sense of the mean squared error) estimator in this class will be σ = SSR / (n − p + 2), which even beats the Cramér–Rao bound in case when there is only one regressor (p = 1).