Consider the gasoline mileage data in Table B.3.

a. Fit a multiple liner regression model relating gasoline mileage y(miles per gallon) to engine displacement x₁ and the number of carburetor barrels x₆.

b. Construct the analysis-of-variance table and test for significance of regression.

c. Calculate R² and  for this model. Compare this to the R² and the  for the simple linear regression model relating mileage to engine displacement in Problem 2.4.

d. Find a 95% CI for β₁.

e. Compute the t statistics for testing H₀: β₁ = 0 and H₀: β₆ =0. What conclusions can you draw?

f. Find a 95% CI on the mean gasoline mileage when x₁ = 275 in.³ and x₆ = 2 barrels.

g. Find a 95% prediction interval for a new observation on gasoline mileage when x₁ = 275 in.³ and x₆ = 2 barrels.

Problem 2.4

PANKRATZ · Forecasting with of least-squares estimat aid="5N5AR">Table B.3 presents data on the gasoline mileage performance of 32 different automobiles.

a. Fit a simple linear regression model relating gasoline mileage y (miles per gallon) to engine displacement x_l (cubic inches).

b. Construct the analysis-of-variance table and test for significance of regression.

c. What percent of the total variability in gasoline mileage is accounted for by the linear relationship with engine displacement?

d. Find a 95% CI on the mean gasoline mileage if the engine displacement is 275 in. ³

e. Suppose that we wish to predict the gasoline mileage obtained from a car with a 275-in. ³ engine. Give a point estimate of mileage. Find a 95% prediction interval on the mileage.

 

f. Compare the two intervals obtained in parts d and e. Explain the difference between them. Which one is wider, and why?