Cost Accounting (14th Edition)

370 CHAPTER 10 DETERMINING HOW COSTS BEHAVE
Exhibit 10-15
Constant Variance of Residuals Assumption
PANEL A:
Constant Variance
(Uniform Scatter of Data
Points Around Regression Line)
PANEL B:
Nonconstant Variance
(Higher Outputs Have
Larger Residuals)
Indirect Manufacturing
Labor Costs (Y)
$4,000
$3,000
$2,000
$1,000
Indirect Manufacturing
Labor Costs (Y)
$4,000
$3,000
$2,000
$1,000
50 100 150 200 250
Machine-Hours (X)
50 100 150 200 250
Machine-Hours (X)
areas that have higher machine-hours and higher indirect manufacturing labor costs. There would not be a uniform
scatter of data points about the regression line (see Exhibit 10-15, Panel B). Constant variance is also known
as homoscedasticity. Violation of this assumption is called heteroscedasticity.
Heteroscedasticity does not affect the accuracy of the regression estimates a and b. It does, however, reduce
the reliability of the estimates of the standard errors and thus affects the precision with which inferences about the
population parameters can be drawn from the regression estimates.
3. Independence of residuals. The assumption of independence of residuals is that the residual term for any one
observation is not related to the residual term for any other observation. The problem of serial correlation (also
called autocorrelation) in the residuals arises when there is a systematic pattern in the sequence of residuals such
that the residual in observation n conveys information about the residuals in observations n + 1, n + 2, and so on.
Consider another production cell at Elegant Rugs that has, over a 20-week period, seen an increase in production
and hence machine-hours. Exhibit 10-16 Panel B is a scatter diagram of machine-hours and indirect manufacturing
labor costs. Observe the systematic pattern of the residuals in Panel B—positive residuals for extreme (high
and low) quantities of machine-hours and negative residuals for moderate quantities of machine-hours. One reason
for this observed pattern at low values of the cost driver is the “stickiness” of costs. When machine-hours are
below 50 hours, indirect manufacturing labor costs do not decline. When machine-hours increase over time as
production is ramped up, indirect manufacturing labor costs increase more as managers at Elegant Rugs struggle
Exhibit 10-16
PANEL A:
Independence of Residuals
(No Pattern in Residuals)
Independence of Residuals Assumption
PANEL B:
Serial Correlation in Residuals
(A Pattern of Positive Residuals for
Extreme Machine-Hours Used;
Negative Residuals for Moderate
Machine-Hours Used)
Indirect Manufacturing Labor
Costs (Y)
$3000
$2500
$2000
$1500
$1000
$500
Indirect Manufacturing Labor
Costs (Y)
$3000
$2500
$2000
$1500
$1000
$500
50 100 150 200 250
Machine-Hours (X)
50 100 150 200 250
Machine-Hours (X)