1) (13 points) Consider the cereal dataset posted with the assignment. Suppose that you are getting this data in order to build a predictive model for nutritional rating.

a) Divide the data into test and training. Fit a linear model and report the MSE.

b) With the data in (a) perform either forward or backwards subset selection.

c) With the data in (a) perform exhaustive subset selection.

d) Draw some conclusions through comparisons between models (a-c). Reflect on the comparative predictive accuracy, and model interpretation. Which model would you say is the "best one" based on your results?