In the frame of linear regression, how do I get the variance estimation using least squares as tool of building an estimator. I mean:

in the case I want to get the LS estimation of the beta's I know I have to minimize the sum of squares of the residuals. But what about the way to get to the variance which I know is:


Is this an LS estimator or just something we use cause it's natural.

I do this question cause in the case I build an Maximum Likelihood Estimator I know how to get the ML estimator of the variance. In the case of OLS it's like there with no proof provided.

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    $\begingroup$ Least squares is a method of estimating $\beta$. The model variance $\sigma^2$ is the variance of the response about the predicted means. The maximum likelihood estimator of $\sigma^2$ is $SSR/N$. The estimator $SSR/(N-K)$ is just the maximum likelihood estimator scaled to be unbiased. $\endgroup$ – user179309 Feb 11 '18 at 18:22
  • $\begingroup$ So there's no function to minimize to get the variance estimator in the case of LS, it's just a natural estimator. $\endgroup$ – Mario Migliaccio Feb 11 '18 at 18:25
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    $\begingroup$ That's correct. $\endgroup$ – user179309 Feb 11 '18 at 18:27

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