Use the Body Fat data set with Density as the response variable and Age, Height, Neck, Chest, Abdomen, Thigh, Ankle, Biceps, and Forearm as the explanatory variables to answer the following:

(a) Fit the full model and check the regression assumptions.

(b) Apply the BIC variable selection procedure and determine the three best fitting models.

(c) Based on the three best fitting models does it appear that age is an important variable for predicting body density? Explain.

(d) Based on the three best fitting models does it appear that biceps circumference is an important variable for predicting body density? Explain.

(e) If any two models with BIC values differing by less than 2 are not practically different, which model having the fewest variables is the best model?