How do horsepower and weight affect the mileage of family cars? Data from a sample of 16 2012 family cars were collected, organized, and stored in Auto2012. (Data extracted from "Top 2012 Cars," Consumer Reports, April 2012, pp. 40-73.) Develop a regression model to predict mileage (as measured by miles per gallon) based on the horsepower of the car's engine and the weight of the car (in pounds).
a. State the multiple regression equation.
b. Interpret the meaning of the slopes, b1 and b2, in this problem.
c. Explain why the regression coefficient, b0, has no practical meaning in the context of this problem.
d. Predict the miles per gallon for cars that have 190 horsepower and weigh 3,500 pounds.
e. Construct a 95% confidence interval estimate for the mean miles per gallon for cars that have 190 horsepower and weigh 3,500 pounds.
f. Construct a 95% prediction interval for the miles per gallon for an individual car that has 190 horsepower and weighs 3,500 pounds.