Question

WEEK 5 DUE DATE: 12/28/2018 Assignment: Regression Modeling Regression modeling is a foundational skill for those conducting secondary data analysis, much like you will encounter in the completion of the Doctor of Healthcare Administration (DHA) program. Additionally, regression modeling assists in finding connections among multiple variables and one dependent variable. Consider, for example, a healthcare administrator who may be asked to develop or interpret models of patient satisfaction based on other quantitative or dichotomous variables. For this Assignment, review the resources for this week. Then, review your course text, and complete Case Study 11.2 on page 536 The case study is based on a real-world problem. The Assignment: (3 pages) • • Complete Case Study 11.2, “Heating Oil at Dupree Fuel Company” on page 536 of your course text using SPSS. Note:This case study is real. The name of the company is changed for purposes of anonymity. CASE 11.2 DEVELOPING A FLEXIBLE BUDGET AT THE GUNDERSON PLANT The Gunderson Plant manufactures the industrial product line of FGT Industries. Plant management wants to be able to get a good, yet quick, estimate of the manufacturing overhead costs that can be expected each month. The easiest and simplest method to accomplish this task is to develop a flexible budget formula for the manufacturing overhead costs. The plant’s accounting staff has suggested that simple linear regression be used to determine the behavior pattern of the overhead costs. The regression data can provide the basis for the flexible budget formula. Sufficient evidence is available to conclude that manufacturing overhead costs vary with direct labor hours. The actual direct labor hours and the corresponding manufacturing overhead costs for each month of the last three years have been used in the linear regression analysis. The three-year period contained various occurrences not uncommon to many businesses. During the first year, production was severely curtailed during two months due to wildcat strikes. In the second year, production was reduced in one month because of material shortages, and increased significantly (scheduled overtime) for two months to meet the units required for a one-time sales order. At the end of the second year, employee benefits were raised significantly as the result of a labor agreement. Production during the third year was not affected by any special circumstances. Various members of Gunderson’s accounting staff raised some issues regarding the historical data collected for the regression analysis. These issues were as follows. the monthly data could include efficiencies and inefficiencies, they believed these efficiencies and inefficiencies would tend to balance out over a longer period of time. ■ Other members of the accounting staff suggested that only those months that were considered normal should be used so that the regression would not be distorted. ■ Still other members felt that only the most recent 12 months should be used because they were the most current. ■ Some members questioned whether historical data should be used at all to form the basis for a flexible budget formula. The accounting department ran two regression analyses of the data—one using the data from all 36 months and the other using only the data from the last 12 months. The information derived from the two linear regressions is shown below (t-values shown in parentheses). The 36-month regression is OHt = 123,810 + 1.60 DLHt, (1.64) The 12-month regression is OHt = 109,020 + 3.00 DLHt, (3.01)

Questions 1. Which of the two results (12 months versus 36 months) would you use as a basis for the flexible budget formula? 2. How would the four specific issues raised by the members of Gunderson’s accounting staff influence your willingness to use the results of the statistical analyses as the basis for the flexible budget formula? Explain your answer. R2 = 0.32 R2 = 0.48

Answer 1

Solution:

Given:

The 36-month regression is OHt = 123,810 + 1.60 DLHt, (1.64) R2 = 0.32

The 12-month regression is OHt = 109,020 + 3.00 DLHt, (3.01) R2 = 0.48

Explanation:

R squared tells us the proportion of variance of a dependent variable that's explained by an independent variable.

R² = 0.32 in the first case explains 32% of variation is explained by DLHt (independent variable) and remaining 68% of variation is explained by the error term.

Similarly in the second case, R² = 0.48 implies that 48% of variation is explained by DLHt and remaining 52% of variation is explained by the error term.

So, more the R² better is the regression model.

In this case the 12 month regression is better than the 36 month regression model since R² is better or significant. Also it tells the line of best fit.

NOTE: R² can be used to compare the goodness of two regression models.