It is 1993. A well know US manufacturer has developed a new make of sporty car - Vehicle X. The sales director wants to get some idea of how Vehicle X should be priced. Using the Cars93 data set, our aim is to find the regression which best explains price in terms of the other numeric and integer variables (obviously not using the other price variables). To find out the class of the variables try > for (j in 1:27) cat (names (Cars93) [j], ": ", class (Cars93 [[j]]), " ") 1. Using the variable selection method of your choice propose an initial model for Price. 2. Construct diagnostic plots and comment on the quality of the model that you have proposed. 3. Attempt model improvement; you might like to consider excluding certain points, transfor- mations or the inclusion of higher order terms. Be careful not to make your model too complicated. 4. The sales director does not trust any model with more than three explanatory variables in it. Reformulate your model (if necessary) in light of this information. 5. Vehicle X has CityMPG 25, Highway MPG 35, 2.4 litre engine, 130 horsepower, 5500 rpm, 1500 revs per mile, 11.3 litre fuel tank, passenger capacity 2, length 175 inches, wheelbase 98 inches, width 64 inches, turn circle 40 feet, no rear seats or luggage room, and weight 2700 pounds. Using the model you feel most appropriate, suggest a price range for Vehicle X. Do you have any reservations about this prediction? 6. Write a function that takes a linear model object as input and draws a selection of diagnostic plots (different from those generated by the generic plot(...) command). 7. Write a function that takes a data frame and a numeric variable from this data frame(the response) as arguments and does step wise selection using all of the other numeric variables as candidate explanatory variables (the aim of this function is to avoid having to type out a big list of variables when we want to do stepwise selection). 8. Simulate a harmonic regression model for monthly data (s = 12) in with two frequencies (m= 2). For each simulated replication fit a model that has three frequencies (m = 3). What are the properties of a3 and 3? -