Roger Gallagher owns a used car lot that deals solely in used Corvettes. He wants to develop a regression model to help predict the price he can expect to receive for the cars he owns. He collected the data found in the file Dat9-8.xls on your data disk describing the mileage, model year, presence of a T-top, and selling price of a number of cars he has sold in recent months. Let Y represent the selling price, X1 the mileage, X2 the model year, and X3 the presence (or absence) of a T-top.

a. If Roger wants to use a simple linear regression function to estimate the selling price of a car, which X variable do you recommend that he use?

b. Determine the parameter estimates for the regression function represented by:

Ŷ i = b0 + b1X1i + b2X2i

What is the estimated regression function? Does X2 help to explain the selling price of the cars if X1 is also in the model? What might be the reason for this?

c. Set up a binary variable (X3i) to indicate whether or not each car in the sample has a T-top. Determine the parameter estimates for the regression function represented by:

Ŷi = b0 + b1X1i + b3X3i

Does X3 help to explain the selling price of the cars if X1 is also in the model? Explain.

d. According to the previous model, on average, how much does a T-top add to the value of a car?

e. Determine the parameter estimates for the regression function represented by:

Ŷi= b0 + b1X1i + b2X2i + b3X3i

What is the estimated regression function?

f. Of all the regression functions considered here, which do you recommend that Roger use?