I have a problem that asks me the following:
" Consider the linear probability model, in which we specify the regression equation to be linear in X,
E(Y |X = x) = Pr(Y = 1|X = x) = x'β
We can accordingly express the regression equation by Y = X'β + e with E(e |X = x) = 0 for all x. Show that the conditional variance of e given X = x depends on x, i.e., e is heteroskedastic. "
Intuitively, I visualise why this is the case - but cannot figure out how to demonstrate this formally. Could someone help? Thanks in advance!