X 3. (20pts) Suppose that there are 4 predictors in a dataset. You can find the AIC, BIC, PRESS adjusted Rof all possible regression models. Variables AIC BIC PRESS adjusted R None -114.7 -111.0 193xxx -128.8 -123.1 149xxx 0.2637 X2 - 119.2 -113.6 175xxx 0.1055 X3 -120.0 -114.3 175xxx 0.1191 -129.1 -122.4 149xxx 0.2536 X1, X2 -126.8 -119.3 161xxx 0.2489 -128.1 -120.6 153xxx 0.2683 X1, X4 -127.6 -120.0 157xxx 0.2597 X2, X3 -118.7 -111.1 179xxx 0.1123 X2, X4 -126.1 -118.5 158xxx 0.2375 X , X, -131.1 -123.5 145xxx 0.3108 X1, X2, X3 -127.5 -118.0 158xxx 0.2726 X1, X2, X4 -125.6 -116.1 169xxx 0.2432 X1, X3, X4 -131.8 -122.3 145xxx 0.3337 X2, X3, X -131.0 -121.5 143xxx 0.3222 X1, X2, X3, X4 -131.4 -120.6 147xxx 0.3471 X1, X3 (a) (6pts) Perform forward selection via AIC. Give details 5/10 (b) (6pts) Perform backward elimination via BIC. Give details (c) (4pts) Suppose that both models selected in (a) and (b) meet all assumptions. Which model would you choose? Verify your answer. (c) (4pts) Suppose that both models selected in (a) and (b) meet all assumptions. Which model would you choose? Verify your answer. 5/10 (d) (4pts) Can we compare the selected models in (a) and (b) by the general linear F-test? If yes, state the relevant extra sum of squares. X 3. (20pts) Suppose that there are 4 predictors in a dataset. You can find the AIC, BIC, PRESS adjusted Rof all possible regression models. Variables AIC BIC PRESS adjusted R None -114.7 -111.0 193xxx -128.8 -123.1 149xxx 0.2637 X2 - 119.2 -113.6 175xxx 0.1055 X3 -120.0 -114.3 175xxx 0.1191 -129.1 -122.4 149xxx 0.2536 X1, X2 -126.8 -119.3 161xxx 0.2489 -128.1 -120.6 153xxx 0.2683 X1, X4 -127.6 -120.0 157xxx 0.2597 X2, X3 -118.7 -111.1 179xxx 0.1123 X2, X4 -126.1 -118.5 158xxx 0.2375 X , X, -131.1 -123.5 145xxx 0.3108 X1, X2, X3 -127.5 -118.0 158xxx 0.2726 X1, X2, X4 -125.6 -116.1 169xxx 0.2432 X1, X3, X4 -131.8 -122.3 145xxx 0.3337 X2, X3, X -131.0 -121.5 143xxx 0.3222 X1, X2, X3, X4 -131.4 -120.6 147xxx 0.3471 X1, X3 (a) (6pts) Perform forward selection via AIC. Give details 5/10 (b) (6pts) Perform backward elimination via BIC. Give details (c) (4pts) Suppose that both models selected in (a) and (b) meet all assumptions. Which model would you choose? Verify your answer. (c) (4pts) Suppose that both models selected in (a) and (b) meet all assumptions. Which model would you choose? Verify your answer. 5/10 (d) (4pts) Can we compare the selected models in (a) and (b) by the general linear F-test? If yes, state the relevant extra sum of squares
