2. A response variable is related to two predictors through the multiple regression model with an interaction term Y = 3.6 + 2.7X1 + 0.9X2 + 1.5X1X2 + ε.

(a) If E(X1) = 10, E(X2) = 18, and Cov(X1,X2) = 80, find the (marginal) expected value of Y. (Hint.

Cov(X1,X2) = E(X1X2) − E(X1)E(X2).)

(b) Express the model in terms of the centered variables as Y = β0 + β1(X1 − μX1 ) + β2(X2 − μX2 ) + β3(X1 − μX1 )(X2 − μX2 ) + ε. Justify that β3 = 1.5. Next, show that β0 = E(Y) − β3Cov(X1,X2), and use part

(a) to find its value.