Consider fitting a multiple linear regression model Y = 0 1X1 2X2 3X3 4X4 , to the Hald data set (Montgomery and Peck, 1982). The correlation matrix of the predictors is rxx = X1 X2 X3 X4 X1 1.000 0.229 0.824 0.245 X2 0.229 1.000 0.139 0.973 X3 0.824 0.139 1.000 0.030 X4 0.245 0.973 0.030 1.000 with inverse r 1 xx = X1 X2 X3 X4 X1 38.496 94.120 41.884 99.786 X2 94.120 254.423 105.091 267.539 X3 41.884 105.091 46.868 111.145 X4 99.786 267.539 111.145 282.513 and rxy = 0.7307175 0.8162526 0.5346707 0.8213050 . (a) Which pairs of predictor variables are highly correlated? (2) (b) Determine the variance inflation factors (V IFj ) for each Xj , j = 1, 2, 3, 4, and give an interpretation for each