Q. 12.24 (Data for 12.24) a. - d. (or part d, use adjusted R²⁾

12.24 Cost analysis for a shipping department. Multiple regres- 12.22 #' and model fit. Because the coefficient of determination sion is used by accountants in cost analysis to shed light R' always increases when a new independent variable is SHIP on the factors that cause costs to be incurred and the Results for Exercise 12.23 Independent Variables Bota Estimate Standard Error * = Vintage year .03 x2 = Average growing season temperature ( *C) .60 120 ry = Sept /Aug. rainfall (cm) -.004 x. = Rainfall in months preceding vintage ( cm) .0015 .0005 Is an Average Sept. temperature ("C) 550 R- = .85 7 = .30 Data for Exercise 12.24 Pounds Shipped, Percentage of Units Average Shipment Weight, Week Labor, y (hr) * (1,000s) Shipped by Truck, X2 100 5.1 20 3.8 99 22 108 5.3 19 116 7.5 16 15 92 4.5 54 20 3 3 12 26 79 12 25 101 5.9 32 21 88 4.0 56 24 10 71 4.2 64 29 11 122 6.8 78 10 12 85 3.9 90 301 13 50 3.8 74 28 14 114 7.5 14 15 104 4.5 90 21 16 111 40 20 17 110 8.1 55 16 18 100 2.9 64 19 19 4.0 35 23 30 85 4.3 25 magnitudes of their effects, Sometimes, it is desirable to c. Test Hy: B = 0 versus 1/,: By 7 0 using a = .05. What use physical units instead of cost as the dependent vari- do the results of your test suggest about the magnitude able in a cost analysis (eg., if the cost associated with the of the effects of x, on labor costs? activity of interest is a function of some physical unit, d. Find A" and interpret its value in the context of the such as hours of labor). The advantage of this approach problem. is that the regression model will provide estimates of the c. If shipping department employees are paid $750 per number of labor hours required under different circum- hour, how much less. on average, will it cost the com- stances, and these hours can then be costed at the current pany per week if the average number of pounds per labor rate (Horngren and Datar, Cost Accounting, 2014). shipment increases from a level of 20 to 21? Assume The sample data shown in the table above have been col- that a and xy remain unchanged. Your answer is an lected from a firm's accounting and production records estimate of what is known in economics as the expected to provide cost information about the firm's shipping marginal cost associated with a I-pound increase in x3. department. These data are saved in the file. Consider the E With what approximate precision can this model he model used to predict the hours of labor? [Note: The preci- sion of multiple regression predictions is discussed in Section 12.4.] a. Find the least squares prediction equation. H. Can regression analysis alone indicate what factors h. Use an F-test to investigate the usefulness of the model course costs to increase? Explain. specified in part a. Use a = .01 and state your conclu sion in the context of the