For a binary model with Y as the dependent variable and X1, X2, and X3 as independent variable, my understanding is that the predicted value is the value of Y at specified values of of X1,X2,X3. Ex. if LPM is Y = β1∗X1+β2∗X2+β3∗X3+ϵ. The predicted value (Y) for X1 = X2 = X3 = 1 is β1+β2+β3.
For expected value, is it the average of the predicted value at specified values for all the observations in the sample? I am kind of confused about the difference between the two. Can someone explain the difference?
The expected value is $E(Y)=\sum_{k=1}^{3}\beta_k E(X_k)$, ignoring $\epsilon$, which isn't explained.