Chapter 15, Problem 51SE

The Tire Rack, an online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, The Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences (The Tire Rack website, August 1, 2016). The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 high-performance all-season tires. The variable Tread Wear rates quickness of wear based on the driver’s expectations, the variable Dry Traction rates the grip of a tire on a dry road, the variable Steering rates the tire’s steering responsiveness, and the variable Buy Again rates the driver’s desire to purchase the same tire again.

1. a. Develop an estimated simple linear regression equation that can be used to predict the Buy Again rating given the Tread Wear rating. At the .01 level of significance, test for a significant relationship. Does this estimated regression equation provide a good fit to the data? Explain.
2. b. Develop an estimated multiple regression equation that can be used to predict the Buy Again rating given the Tread Wear rating and the Dry Traction rating. Is the addition of the Dry Traction independent variable significant at α = .01? Explain.
3. c. Develop an estimated multiple regression equation that can be used to predict the Buy Again rating given the Tread Wear rating, the Dry Traction rating, and the Steering rating. Is the addition of the Steering independent variable significant at α = .01? Explain.