Start-up R and load the mtcars dataset (using the data command). This dataset is on Blackboard Strictly speaking a principal components analysis on this dataset is not quite kosher, since some of the variables are discrete. None the less, the PCA does yield some interpretable results. Answer the following questions. Also, submit your code. 1) Should a principal components analysis of this data be based on the covariance or the correlation matrix? Explain. 2) Which variables seem to have the strongest relation to the mileage? 3) Are Mercedes different from other cars? If so, what characteristic would you say they share? 4) What characteristics separate sports cars from the others? 5) Suppose your car gets good mileage. What else is likely to be true about it? 6) Suppose my car gets 20 mpg, has 6 cylinders, a displacement of 425, 200 horsepower, a rear axle ratio of 3.75, weighs 2000 pounds, can go a quarter mile in 16.5 seconds, has v/s (vertical steering?), automatic transmission, 4 gears and 1 carburetor. What are its scores on the first and second principal components? What sort of car, if any, is it most similar to? 7) Fit a regression to predict mpg. Evaluate the fit. What can be done to improve it? 8) Try your suggestion. Did it help? Whats the best predictor of mileage?