The sales manager of a large automotive parts distributor, Hartman Auto Supplies, wants to develop a model to forecast as early as May the total annual sales of a region. If regional sales can be forecast, then the total sales for the company can be forecast. The number of retail outlets in the region stocking the company's parts and the number of automobiles registered for each region as of May 1 are the two independent variables investigated. The data appear in Table P-12.

a. Analyze the correlation matrix.
b. How much error is involved in the prediction for region 1?
c. Forecast the annual sales for region 12, given 2,500 retail outlets and 20.2 million automobiles registered.
d. Discuss the accuracy of the forecast made in part c.
e. Show how the standard error of the estimate was computed.
f. Give an interpretation of the partial regression coefficients. Are these regression coefficients sensible?
g. How can this regression equation be improved?

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TABLE P-12 Number of Annual Sales (S millions) Retail Outlets Number of Automobiles Region X, Registered (S millions) 24.6 22.1 52.3 26.0 20.2 16.0 30.0 2.011 2.850 650 12.5 9.0 11.5 1,694 35.0 2.214 125 33.1 25.2 8.9 10 1,233 1,699 9.5