1. A response variable is related to two predictors through the multiple linear regression model Y = 3.6 + 2.7X1 + 0.9X2 + . (a)

1. A response variable is related to two predictors through the multiple linear regression model Y = 3.6 + 2.7X1 + 0.9X2 + ε.

(a) Give μY|X1,X2 (12, 25) = E(Y|X1 = 12,X2 = 25).

(b) If E(X1) = 10 and E(X2) = 18, find the (marginal)

expected value of Y.

(c) What is the expected change in Y when X1 increases by one unit while X2 remains fixed?

(d) The model can be expressed equivalently in terms of the centered variables as Y = β0 +β1(X1 −μX1 )+ β2(X2 − μX2 ) + ε. Using the information about the expected values of X1 and X2 given in part (b), give the values of β0, β1, and β2.