# SLR: why residual 'standard error' actually refers to RSS/(n-2) and not standard error?

From what I've learnt, standard error is a concept related to sampling distribution. So why is the term 'residual standard error' used to refer to $\sqrt{\frac{RSS}{n-2}}$ and not $\sqrt{E(r_i - E(r_i))^2}$ in SLR context?

(I mentioned Simple Linear Regression only because I have not learnt other regression techniques yet)

$$\hat{\mathbb{V}}(\varepsilon) = \text{MSE} = \frac{\text{RSS}}{\text{df}_\text{Res}} = \frac{\text{RSS}}{n-2}.$$
So the quantity you are referring to is $\hat{\mathbb{S}}(\varepsilon) = \sqrt{\text{RSS}/(n-2)}$. The other quantity you refer to is the standard deviation of the $i$th residual, which is not a fixed quantity over $i=1,...,n$ since it depends on the leverage values of the data points.
• Each of the random variables $R_1,...,R_n$ have a different variance, which is affected by the leverage of each data point. That means that there is no single generic variance for the residual. – Reinstate Monica Aug 9 '18 at 9:58