Multiple regression is used by accountants in cost analysis to shed light on the factors that cause costs to be incurred and the magnitudes of their effects. Sometimes, it is desirable to use physical units instead of cost as the dependent variable in a cost analysis (e.g., if the cost associated with the activity of interest is a function of some physical unit, such as hours of labor). The advantage of this approach is that the regression model will provide estimates of the number of labor hours required under different circumstances, and these hours can then be costed at the current labor rate (Horngren, Foster, and Datar, Cost Accounting, 2006). The sample data shown in the table below have been collected from a firm's accounting and production records to provide cost information about the firm's shipping department. These data are saved in the file. Consider the model
y = β0 + β1x1 + β2x2 + β3x3 + ε
a. Find the least squares prediction equation.
b. Use an f-test to investigate the usefulness of the model specified in part a. Use α = .01 and state your conclusion in the context of the problem.
c. Test H0: β2 = 0 versus Ha: β2 ≠ 0 using α = .05. What do the results of your test suggest about the magnitude of the effects of x2 on labor costs?
d. Find R2 and interpret its value in the context of the problem.
e. If shipping department employees are paid $7.50 per hour, how much less, on average, will it cost the company per week if the average number of pounds per shipment increases from a level of 20 to 21? Assume that x1 and x2 remain unchanged. Your answer is an estimate of what is known in economics as the expected marginal cost associated with a 1-pound increase in x3.
f. With what approximate precision can this model be used to predict the hours of labor?
g. Can regression analysis alone indicate what factors cause costs to increase? Explain.