Regression Analysis United States Motors Inc. (USMI) manufactures automobiles and lighttrucks and distributes them for sale to consumers through franchised retail outlets. As part of thefranchise agreement, dealerships must provide monthly financial statements following the USMIaccounting procedures manual. USMI has developed the following financial profile of an averagedealership that sells 1,500 new vehicles annually:AVERAGE DEALERSHIP FINANCIAL PROFILEComposite Income StatementSales $30,000,000Cost of goods sold 24,750,000Gross profit $ 5,250,000Operating costsVariable 862,500Mixed 2,300,000Fixed 1,854,000Operating income $ 233,500USMI 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 withthe addition of these franchises. Jack estimates that 90% of the mixed costs shown are variable forpurposes of this analysis. He also suggests performing regression analyses on the various componentsof the mixed costs to more definitively determine their variability.Required1. Calculate the composite dealership profit if 2,000 units are sold.2. Assume that regression analyses were performed on the separate components of the mixed costs andthat a coefficient of determination value of .60 was determined as applicable to aggregate mixed costsover the relevant range.a. Define the term relevant range.b. Explain the significance of an R-squared value of .60 to USMI’s analysis.c. Describe the limitations that may exist in applying the composite-based relationships to specificnew dealerships that have been proposed.d. Define the standard error of the estimate.3. The regression equation that Jack Snyder developed to project annual sales of a dealership has anR-squared of 60% and a standard error of the estimate of $4,500,000. If the projected annual sales for adealership total $28,500,000, determine the approximate 95% confidence interval for Jack’s predictionof sales. (Hint: The 95% confidence interval uses 2 standard errors in determining the interval.)4. What is the strategic role of regression analysis for USMI?(CMA Adapted
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:
AVERAGE DEALERSHIP FINANCIAL PROFILE
Composite Income Statement
Sales $30,000,000
Cost of goods sold 24,750,000
Gross profit $ 5,250,000
Operating costs
Variable 862,500
Mixed 2,300,000
Fixed 1,854,000
Operating income $ 233,500
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. 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.
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.
a. Define the term relevant range.
b. Explain the significance of an R-squared value of .60 to USMI’s analysis.
c. Describe the limitations that may exist in applying the composite-based relationships to specific
new dealerships that have been proposed.
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 interval for Jack’s prediction
of sales. (Hint: The 95% confidence interval uses 2 standard errors in determining the interval.)
4. What is the strategic role of regression analysis for USMI?
(CMA Adapted
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