In logistic regression analysis, we mentioned that

Errors can’t be normally distributed. With proper analysis (or sound arguments) show why this is the case?

logit(P(Y=1|X))=xβ

Where P(Y=1|X)=f(x;β)=exβ1+exβ=11+e−xβ

So the loss function looks like:

∑i(yi−f(xi;β))2=∑i(yi−11+e−xβ)2

where yi’s take values 0/1.