[lordnacho]

This might be what you're looking for:

https://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem

[mikorym]

Yes, I think so. Intuitively, how I would like to think of this is that we are getting to this from the Euclidean distance metric. But skimming the proof seems like we use variance (which is defined using squares) as a presupposition.

[flopska]

Ah, the good old BLUE (Best linear unbiased estimator). Had this in statistics and really really liked the proof.