Regression Analysis United States Motors Inc. (USMI) manufactures automobiles and light tr...

Regression Analysis United States Motors Inc. (USMI) manufactures automobiles and light trucks and distributes them for sale to consumers through franchised retail outlets. As part of the franchise agreement, dealerships must provide monthly financial statements following the USMI accounting procedures manual. USMI has developed the following financial profile of an average dealership that sells 1,500 new vehicles annually.

USMI is considering a major expansion of its dealership network. The vice president of marketing has asked Jack Snyder, corporate controller, to develop some measure of the risk associated with the addition of these franchises. Jack estimates that 90% of the mixed costs shown are variable for purposes of this analysis. (Recall that mixed costs are a combination of variable and fixed costs.) He also suggests performing regression analyses on the various components of the mixed costs to more definitively determine their variability.

Required

1. Calculate the composite dealership profit if 2,000 units are sold.

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2. Assume that regression analyses were performed on the separate components of the mixed costs and that a coefficient of determination value of .60 was determined as applicable to aggregate mixed costs over the relevant range.

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a. Define the term relevant range.

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b. Explain the significance of an R-squared value of .60 to USMI’s analysis.

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c. Describe the limitations that may exist in applying the composite-based relationships to specific new dealerships that have been proposed.

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d. Define the standard error of the estimate.

3. The regression equation that Jack Snyder developed to project annual sales of a dealership has an R-squared of 60% and a standard error of the estimate of $4,500,000. If the projected annual sales for a dealership total $28,500,000, determine the approximate 95% confidence range for Jack’s prediction of sales.

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4. What is the strategic role of regression analysis for USMI?

(CMA Adapted)