Consider the multiple regression model Y = XA + Zy + e, where X is n x k + 1 and Z is n x { matrices. Let be the estimator of 6 = We showed that var(60) =0' (X'X) + LML' LM -ML' M where, L = (X'X) 'X'Z, M = (Z'RZ) ,R=I-X(X'X) X'. Suppose we want to predict Yo using the model Y = X8 + Zy +e and Y = X8 + e. Show mathematically that the variance of the predicted value using the short regression is smaller than the variance of the predicted value using the long regression