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How do we decide that distance measure to be minimized for normal distribution in linear regression is:

$||y−Xβ||^2$

from log-likelihood function:

$l(θ) = −\frac{1}{2}nlog(σ^{2})− \frac{1}{2σ^{2}}||y−Xβ||^2$

Is this the reason we use euclidean distance as to compute distances as well?

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  • $\begingroup$ It's unclear what you're trying to ask, because $l$ explicitly depends on the Euclidean distance: there's no decision to be made. Would you perhaps be trying to asking something like the question at stats.stackexchange.com/questions/32103? $\endgroup$
    – whuber
    Apr 14, 2020 at 0:42

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