3. Use the data frame BigMac2003 in alr4, which contains the response BigMac, or the price of a Big Mac in various world cities in 2003, expressed in minutes of labor. It also contains quantitative predictors Bread, Rice, Bus, and Apt, which are prices of other goods, as well as economic indicators FoodIndex, TeachGI, TeachNI, TaxRate, and TeachHours.

a. Use principal components analysis on the nine predictors. Report your scree plot and a biplot.

b. How many principal components are necessary to use in order to account for at least 90% of the variance in the predictors?

c. Fit the MLR model with the response BigMac and the first four principal components as regressors. Then fit the model that contains all nine original predictors. Compare the coefficients of determination for the two models. Are you satisfied that the model with fewer regressors fits sufficiently well compared to the full model?