1.Based on our known "mtcars" dataset, we'll now build a model for predicting variable qsec, the time in seconds that it takes a car to drive 1/4 mile from a full stop.

(a) Select the optimal subset of independent variables for the prediction of the qsec using your favorite variable selection method. Show all methods used and justify your conclusion.

(b) Is there any indication of nonlinear relations? Explain how you reach this conclusion.

(c) Test significance of interaction between the weight (wt) and transmission (am, 0 = automatic, 1 = manual). (Hint: Use the "best" model according to part (a)).