Cost Accounting (14th Edition)

APPENDIX 371
to manage the higher volume. How would the plot of residuals look if there were no auto-correlation? Like the
plot in Exhibit 10-16, Panel A that shows no pattern in the residuals.
Like nonconstant variance of residuals, serial correlation does not affect the accuracy of the regression estimates
a and b. It does, however, affect the standard errors of the coefficients, which in turn affect the precision
with which inferences about the population parameters can be drawn from the regression estimates.
The Durbin-Watson statistic is one measure of serial correlation in the estimated residuals. For samples of 10
to 20 observations, a Durbin-Watson statistic in the 1.10–2.90 range indicates that the residuals are independent.
The Durbin-Watson statistic for the regression results of Elegant Rugs in Exhibit 10-14 is 2.05. Therefore, an
assumption of independence in the estimated residuals is reasonable for this regression model.
4. Normality of residuals. The normality of residuals assumption means that the residuals are distributed normally
around the regression line. The normality of residuals assumption is frequently satisfied when using regression
analysis on real cost data. Even when the assumption does not hold, accountants can still generate accurate estimates
based on the regression equation, but the resulting confidence interval around these estimates is likely to
be inaccurate.
Using Regression Output to Choose Cost Drivers of Cost
Functions
Consider the two choices of cost drivers we described earlier in this chapter for indirect manufacturing labor costs (y):
y = a + (b * Number of machine-hours)
y = a + (b * Number of direct manufacturing labor-hours)
Exhibits 10-6 and 10-8 show plots of the data for the two regressions. Exhibit 10-14 reports regression results for
the cost function using number of machine-hours as the independent variable. Exhibit 10-17 presents comparable
regression results (in Excel) for the cost function using number of direct manufacturing labor-hours as the independent
variable.
On the basis of the material presented in this appendix, which regression is better? Exhibit 10-18 compares
these two cost functions in a systematic way. For several criteria, the cost function based on machine-hours is
preferable to the cost function based on direct manufacturing labor-hours. The economic plausibility criterion is
especially important.
Do not always assume that any one cost function will perfectly satisfy all the criteria in Exhibit 10-18. A cost analyst
must often make a choice among “imperfect” cost functions, in the sense that the data of any particular cost function
will not perfectly meet one or more of the assumptions underlying regression analysis. For example, both of the
cost functions in Exhibit 10-18 are imperfect because, as stated in the section on specification analysis of estimation
assumptions, inferences drawn from only 12 observations are not reliable.
Exhibit 10-17
Simple Regression Results with Indirect Manufacturing Labor Costs as Dependent
Variable and Direct Manufacturing Labor-Hours as Independent Variable (Cost Driver)
for Elegant Rugs
1
2
3
4
5
6
7
8
A B C D E F G H
Coefficients Standard Error t Stat
(1) (2) (3) = (1) ÷ (2)
Intercept $ 744.67 $ 217.61
3.42
Independent Variable:
Direct Manufacturing
Labor-Hours (X ) $ 7.72 $ 5.40
Regression Statistics
R Square 0.17
Durbin-Watson Statistic 2.26
1.43
= Coefficient/Standard Error
= B4/C4
= 7.72/5.40