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. The independent variables of such a regression model are the factors believed to be related to cost, the dependent variable. In some instances, however, it is desirable to use physical units instead of cost as the dependent variable in a cost analysis. This would be the case if most of 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, 1994). 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. The EXCEL computer printout for fitting the model  is provided on page 592.

a. Find the least squares prediction equation.

b. Use an F-test to investigate the usefulness of the model specified in part a. Use a = .01, and state your conclusion in the context of the problem

c. Test H₀:  ß₂ = 0 versus H_a: ß₂ ≠ 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 7 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 one pound increase in x₃.

f. With what approximate precision can this model be used to predict the hours of labor'? [Note: The precision of multiple regression predictions is discussed in Section 10.6.1]

g. Can regression analysis alone indicate what factors cause costs to increase? Explain.