In order to have its cars meet the corporate average fuel economy (CAFE) standard, a manufacturer needs to improve the mileage of two of its cars. One design, a small sports car, weighs 2,500 pounds. The other model, a four-door family sedan, weighs 4,000 pounds. If it can improve the mileage of either design by two more miles per gallon, its cars will meet the federal standards. Use the data for cars from the 1989 model year to answer these questions. Cars have changed since then, but many of the factors that influence mileage remain. The weight of the cars is measured in thousands of pounds, and the city mileage is expressed in miles per gallon.
Motivation
(a) Which of these two models should the manufacturer modify? In particular, if the manufacturer needs to reduce the weight of a car to improve its mileage, how can an equation that relates weight to mileage help?
Method
(b) Based on the analysis in this chapter for modern cars, what sort of relationship do you expect to fnd between weight and mileage (city driving) for cars from the 1989 model year—linear or curved?
(c) In order to choose the equation to describe the relationship between weight and mileage, will you be able to use summary measures like r2, or will you have to rely on other methods to pick the equation?
Mechanics
(d) Create a scatterplot for mileage on weight. De-scribe the association between these variables.
(e) Fit an equation using least squares that captures the pattern seen in these data. Why have you chosen this equation?
(f) Do the residuals from your fitted equation show random variation? Do any outliers stand out?
(g) Compare the ft of this equation to that used in this chapter to describe the relationship between weight and mileage for more recent cars. Include in your comparison the slope and intercept of the fitted equation as well as the two summary measures, r2 and se.
Message
(h) Summarize the equation developed in your modeling for the manufacturer’s management, using words instead of algebra.
(i) Provide a recommendation for management on the best approach to use to attain the needed improvement in fuel efficiency.