Given the Linear Regression model $y=X\beta+\epsilon$, where $\epsilon \sim D(0_n,\sigma^2 I_n)$ and $D$ is some distribution. How to find the OLS estimator of $\sigma^2$. I know that the sum of least-squares residuals has a distribution equal to $\sigma^2$ times $\chi^2_{n-1}$. So I can therefore determine the unbiased estimator of $\sigma^2$. But how to prove that sum of least-squares residuals follows such distribution. Also anyone with new way to find it are welcome. Login To add answer/comment