When we want to build a regression model $Y = f(X)+\epsilon$, why does the distribution of $\epsilon$ matter at all? Why don't we go ahead and find the best $f(X)$ that optimizes a performance measure (for example, minimizes the MSE)? What are the implications of assuming that $\epsilon$ has a normal, Poisson (when it is a count model), or any other distribution?
2026-04-07 22:57:53.1775602673
Why does the distribution of the error term in a regression model matter?
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