Car drivers like to adjust the seat position for their own comfort. Car designers find it helpful to know where different drivers will position the seat depending on their size and age. Researchers at the HuMoSim laboratory at the University of Michigan collected data on 38 drivers. The data reside in seatpos. txt. Age Age (in years) Weight Weight (in lbs) HtShoes Height in shoes (in cm) Ht Height bare foot (in cm) Seated Seated height (in cm) Arm Lower arm length (in cm) Thigh Thigh length (in cm) Leg Lower leg length (in cm) hipcenter Horizontal distance of the midpoint of the hips from a fixed location in the car (in mm) Suppose we fit a first order multiple regression model use hipcenter as the response and all the other 8 variables as predictors. And suppose the model meets all assumptions. (a) Perform forward variable selection via AIC and report the chosen model.
(b) Perform backward variable selection via AIC and report the chosen model.
(c) Perform forward variable selection via BIC and report the chosen model.
(d) Perform backward variable selection via BIC and report the chosen model.
(e) (Bonus,) State the difference in the models selected by AIC and BIC. Explain what causes this difference.
(f) Compare the models selected by the above four procedures with the following criterion
i. AIC
ii. BIC
iii. PRESS
iv. Adjusted R2
v. Individual t-test.
vi. If there are models that can be compared by General linear F-test, state the null and alternative hypothesis and run the General linear F-test.
(g) Based on the comparison in (f), choose your best model with reasonable support.
Using R studio and also need the R code