Question: Small cars offer higher fuel efficiency, are easy to maneuver and park, and have generally performed well in road tests. The following data show the overall fuel efficiency rating (miles per gallon), predicted reliability (highest = 5), safety rating (highest = 5), and the price ($) for 20 small cars.

Make & Model MPG Reliability Safety Price

Chevy Aveo LT 25 2 2 16,205

Chevy Cobalt LT 24 3 3 17,450

Ford Focus SES 26 4 3 18,490

Ford Focus SES MT 29 4 3 17,440

Honda Civic EX 28 5 4 19,610

Honda Civic EX MT 31 5 4 18,810

Honda Fit Sport MT 33 5 4 16,730

Hyundai Accent GLS 28 4 2 14,230

Hyundai Elantra GLS 27 5 3 17,555

Hyundai Elantra SE 27 5 4 17,980

Kia Spectra EX 25 4 2 16,185

Kia Spectra EX MT 28 4 2 15,185

Nissan Versa 1.8 SL 28 3 3 16,675

Nissan Versa 1.85 27 1 3 16,130

Scion XD 29 5 3 16,620

Scion XD MT 34 5 3 15,820

Suzuki SX4 LE 26 5 3 17,378

Toyota Corolla MT 32 4 4 16,419

Toyota Corolla LE 32 4 4 18,404

Toyota Yaris Hatchback 30 5 3 16,095

a. Determine the estimated regression equation that can be used to predict the price of a small car given its overall fuel efficiency rating, predicted reliability, and safety rating.

b. Use the F test to determine the overall significance of the relationship. What is the conclusion at the .05 level of significance?

c. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?

d. Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation? Compare the value of R² for this estimated regression equation with the value of R² for the estimated regression equation from part (a). Discuss the differences.