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"Although it is nice to have an unbiased estimator of the variance, we do not really need it to understand the relation between our independent variable and our dependent variable. Why?"

I think I kind of get it, but he wants a specific answer, and he picks on me...

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    $\begingroup$ You could describe what you thought about the topic this far and the implicit ideas that made you "kind of get it". We can help you make it more explicit. Presumably you are talking about a linear model? $\endgroup$ – Momo Nov 17 '12 at 16:31
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Depends on what your end goal is. It the end goal is inference on regression coefficients (t-tests) then the unbiased variance estimator is just a stepping stone, and unimportant in itself.

But for some uses of the estimated model, the error variance is important information, and for such uses an unbiased variance estimator could be useful.

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