Cost Behavior Analysis Using Method of Least Squares. Elisko Inc. is a major book distributor that ships books throughout the United States. Elisko’s Shipping Department consists of a manager plus 10 other permanent positions—four supervisors and six loaders. The four supervisors and six loaders provide the minimum staff and frequently must be supple¬ mented by additional workers during weeks when the volume of shipments is heavy. Thus the number of persons shipping the orders frequently averages over 30 per week—10 permanent plus 20 temporary workers. The temporary workers are hired through a local agency.

Elisko must use temporary workers to maintain a minimum daily shipment rate of 95% of orders pre¬ sented for shipping. The loss of efficiency from using temporary workers is minimal, and the $10.00-per-hour cost of temporary workers is less than the $15.00 per hour paid for the loaders and $22.50 per hour paid for the supervisors on Elisko’s permanent staff. The agency requires Elisko to utilize each temporary worker for at least four hours each day.

Jim Locter, shipping manager, schedules temporary help based on forecasted orders for the coming week. Supervisors serve as loaders until temporary help is needed. A supervisor stops loading when the ratio of loaders to supervisors reaches 7 to 1. Locter knows that he will need temporary help when the forecasted aver¬ age daily orders exceed 300. Locter frequently requested from two to four extra temporary workers per day to guard against unexpected rush orders. If there is not enough work, he dismisses the extra people at noon after four hours of work. The agency is not pleased with Locter’s practice of overhiring and notified Elisko that it is changing its policy. From now on, if a worker is dismissed before an eight-hour assignment is completed, Elisko will still be charged for an eight-hour day plus mileage back to the agency for reassignment. This policy is to go into effect the following week.

Paula Brand, general manager, called Jim Locter to her office when she received the notice from the agency. She told Locter, “Your staffing levels have to be better. This penalty could cost us up to $500 per week in labor cost for which we receive no benefit. Why can’t you schedule more accurately?”

Locter replied, “I agree that the staffing should be better, but I can’t do it accurately when there are rush orders. By being able to lay off people at noon, I have been able to adjust for the uncertain order schedule without cost to the company. Of course, the agency’s new policy changes this.”

Locter and Brand contacted Elisko’s controller, Mitch Berg, regarding the problem of how to estimate the number of workers needed each week. Berg realized that Locter needs a quick solution until he can study the work flow. Berg suggested a regression analysis using the number of orders shipped as the independent vari¬ able and the number of workers (permanent plus tem¬ porary) as the dependent variable. Berg indicated that data for the past year are available and that the analysis could be done quickly on the Accounting Department’s microcomputer.

Berg completed the two regression analyses that fol¬ low. The first regression is based on the data for the entire year. The second regression excludes the weeks when only the 10 permanent staff persons worked; these weeks were unusual and appear to be out of the relevant range.

Regression Equation W = a + bS where: W = total workers (permanent plus temporary) S = orders shipped a.

b.

Standard error (s) of the estimate.

Coefficient of determination (r2).

Regression 1 (Daily Data for 52 Weeks)

Regression 2 (Daily Data for 38 Weeks)

5.062 .489

.023 .028 2.012 .432

.962 .998 Locter is not familiar with regression analysis and is, therefore, unsure how to implement this technique. He wonders which regression data he should employ; that is, which data are better. When Loctor recognized that the regression is based on actual orders shipped by week, Berg told him he can use the forecasted ship¬ ments for the week to determine the number of work¬ ers needed.

Required:

(1) Using Regression 1 based on data from a full year, calculate the number of temporary workers who should be hired for a forecast of 1,200 shipments.

(2) Which one of the two regressions appears to be better? Explain.

(3) Explain the circumstances under which this regres¬ sion should be used in planning for temporary workers.

(4) Explain how the regression might be improved.