# Analysis with total overhead costs as the dependent

• Homework Help
• 37

This preview shows page 33 - 35 out of 37 pages.

analysis with total overhead costs as the dependent variable and the number of academic programs and number of enrolled students as the two independent variables.2. Solution Exhibit 10-33 evaluates the multiple regression model. Hanks should use the multiple regression model rather than the two simple regression models of Problem 10 32. The multiple regression model appears economically plausible and the regression model performs very well when estimating overhead costs. It has an excellent goodness of fit, has significant t-values on both independent variables, and meets all the specification assumptions for ordinary least squares regression.The adjusted R2 value = 0.766 is higher than the Problem 10 32 simple linear regression model R2 values.There is some correlation between the two independent variables, but multicollinearity does not appear to be a problem here. The significance of both independent variables (despite some correlation between them) suggests that each variable is a driver of overhead cost. Of course, as the chapter describes, even if the independent variables exhibited multicollinearity, Hanks should still prefer to use the multiple regression model over the simple regression models of Problem 10 32. Omitting any one of the variables will cause the estimated coefficient of the independent variable included in the model to be biased away from its true value.3. The Durbin-Watson statistic = 1.91, so serial correlation in the residuals is not apparent. Caution:The sample size of 12 is small. Possible uses for the multiple regression results include:a. Planning and budgeting at Eastern University. The regression analysis indicates the variables (number of academic programs and number of enrolled students) that help predict changes in overhead costs.b. Cost control and performance evaluation. Hanks could compare actual performance with budgeted or expected numbers and seek ways to improve the efficiency of the university operations, andevaluate the performance of managers responsible for controlling overhead costs.c. Cost management. If cost pressures increase, the university could save costs by closing down academic programs that have few students enrolled.SOLUTION EXHIBIT 10-33Evaluation of Cost Function for Overhead Costs Estimated With Multiple Regression for Eastern University
CriterionNumber of Academic Programs andNumber of Enrolled Students asIndependent Variables1. Economic Plausibility A positive relationship between overhead costs and number of academic programs and number of enrolled students is economically plausible at Eastern University.2. Goodness of Fitr2 = 0.81, Adjusted R2 = 0.766Excellent goodness of fit3. Significance of Independent Variable(s)t-values of 3.46 on number of academic programs and 2.02 on number of enrolled students are both significant, at 99% and 90% C.L.s respectively.MLR d.f. = n − k = 12 − 2 = 10 degrees offreedomAt 95% C.L. t-critical = 2.23Therefore t-stat of 2.02 for # of studentsenrolled is only statistically significant at 90% C.L. t-critical re 90% C.L. = 1.81 with 10 d.f.