Cost Accounting (14th Edition)

372 CHAPTER 10 DETERMINING HOW COSTS BEHAVE
Exhibit 10-18
Comparison of Alternative Cost Functions for Indirect Manufacturing
Labor Costs Estimated with Simple Regression for Elegant Rugs
Cost Function 2:
Cost Function 1:
Direct Manufacturing
Machine-Hours as
Labor-Hours as
Criterion Independent Variable Independent Variable
Economic plausibility A positive relationship between A positive relationship between
indirect manufacturing labor
indirect manufacturing labor costs
costs (technical support labor) and and direct manufacturing labormachine-hours
is economically hours is economically plausible,
plausible in Elegant Rugs’ highly
automated plant
but less so than machine-hours in
Elegant Rugs’ highly automated
plant on a week-to-week basis.
Goodness of fit a
Significance of
independent
variable(s)
r 2 = 0.52; standard error of
regression = $170.50.
Excellent goodness of fit.
The t-value of 3.30 is significant
at the 0.05 level.
r 2 = 0.17; standard error of
regression = $224.60.
Poor goodness of fit.
The t-value of 1.43 is not significant
at the 0.05 level.
Specification analysis of Plot of the data indicates that Plot of the data indicates that
estimation assumptions assumptions of linearity, constant assumptions of linearity, constant
variance, independence of residuals variance, independence of
(Durbin-Watson statistic = 2.05), and residuals (Durbin-Watson
normality of residuals hold, but statistic = 2.26), and normality of
inferences drawn from only
residuals hold, but inferences
12 observations are not reliable. drawn from only 12 observations
are not reliable.
a If the number of observations available to estimate the machine-hours regression differs from the number of observations
available to estimate the direct manufacturing labor-hours regression, an adjusted r 2 can be calculated to take this difference
(in degrees of freedom) into account. Programs such as Excel calculate and present adjusted r 2 .
Multiple Regression and Cost Hierarchies
In some cases, a satisfactory estimation of a cost function may be based on only one independent variable, such as
number of machine-hours. In many cases, however, basing the estimation on more than one independent variable
(that is, multiple regression) is more economically plausible and improves accuracy. The most widely used equations
to express relationships between two or more independent variables and a dependent variable are linear in the form
where,
y = a + b 1 X 1 + b 2 X 2 + ... + u
y = Cost to be predicted
X 1
,X 2
, ... = Independent variables on which the prediction is to be based
a, b 1
, b 2
,... = Estimated coefficients of the regression model
u = Residual term that includes the net effect of other factors not in the model as well as measurement errors in the dependent
and independent variables
Example: Consider the Elegant Rugs data in Exhibit 10-19. The company’s ABC analysis indicates that indirect manufacturing
labor costs include large amounts incurred for setup and changeover costs when a new batch of carpets is
started. Management believes that in addition to number of machine-hours (an output unit-level cost driver), indirect
manufacturing labor costs are also affected by the number of batches of carpet produced during each week (a batchlevel
driver). Elegant Rugs estimates the relationship between two independent variables, number of machine-hours
and number of production batches of carpet manufactured during the week, and indirect manufacturing labor costs.