Chapter 14.9, Problem 14.52ACB

Forecasting monthly car and truck sales. Forecasts of automotive vehicle sales in the United States provide the basis for financial and strategic planning at large automotive corporations. The following forecasting model was developed for Y_t, total monthly passenger car and light truck sales (in thousands):

E(Y_t) = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + β₅x₅

where x₁ = average monthly retail price of regular gasoline, x₂ = annual percentage change in GDP per quarter, x₃ = monthly consumer confidence index, x₄ = total number of vehicles scrapped (millions) per month, and x₅ = vehicle seasonality. The model was fit to monthly data collected over a 12-year period (i.e., n = 144 months), with the following results: R² = .856, Durbin-Watson d = 1.01.

a. Is there sufficient evidence to indicate that the overall model contributes information for the prediction of monthly passenger car and light truck sales? Test using a = .05.

b. Is there sufficient evidence to indicate that the regression errors are positively correlated? Test using α = .05.

c. Comment on the validity of the inference concerning model adequacy in light of the result of part b.