Question: Consider the linear probability model. (a) When yi = 1, i = 1 ( + xi). When yi = 0, i = ( +

Consider the linear probability model.

(a) When yi = 1, εi = 1 − (α + βxi). When yi = 0, εi = −(α + βxi). If p =

P(yi = 1 | xi) and 1 − p = P(yi = 0 | xi), prove that E(εi) = p − (α + βxi).

Interpret this result.

(b) Based on the information in part

a, prove that

V(,) = P(y,=1|x)P(y, =0|x;).

V(,) = P(y,=1|x)P(y, =0|x;).

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