Cost Accounting (14th Edition)

352 CHAPTER 10 DETERMINING HOW COSTS BEHAVE
Regression Analysis Method
Regression analysis is a statistical method that measures the average amount of change in
the dependent variable associated with a unit change in one or more independent variables.
In the Elegant Rugs example, the dependent variable is total indirect manufacturing
labor costs. The independent variable, or cost driver, is number of machine-hours.
Simple regression analysis estimates the relationship between the dependent variable and
one independent variable. Multiple regression analysis estimates the relationship
between the dependent variable and two or more independent variables. Multiple regression
analysis for Elegant Rugs might use as the independent variables, or cost drivers,
number of machine-hours and number of batches. The appendix to this chapter will
explore simple regression and multiple regression in more detail.
In later sections, we will illustrate how Excel performs the calculations associated
with regression analysis. The following discussion emphasizes how managers interpret
and use the output from Excel to make critical strategic decisions. Exhibit 10-6 shows the
line developed using regression analysis that best fits the data in columns B and C of
Exhibit 10-3. Excel estimates the cost function to be
y = $300.98 + $10.31X
The regression line in Exhibit 10-6 is derived using the least-squares technique. The leastsquares
technique determines the regression line by minimizing the sum of the squared vertical
differences from the data points (the various points in the graph) to the regression line.
The vertical difference, called the residual term, measures the distance between actual cost
and estimated cost for each observation of the cost driver. Exhibit 10-6 shows the residual
term for the week 1 data. The line from the observation to the regression line is drawn perpendicular
to the horizontal axis, or x-axis. The smaller the residual terms, the better the fit
between actual cost observations and estimated costs. Goodness of fit indicates the strength
of the relationship between the cost driver and costs. The regression line in Exhibit 10-6 rises
from left to right. The positive slope of this line and small residual terms indicate that, on
average, indirect manufacturing labor costs increase as the number of machine-hours
increases. The vertical dashed lines in Exhibit 10-6 indicate the relevant range, the range
within which the cost function applies.
Instructors and students who want to explore the technical details of estimating the
least-squares regression line, can go to the appendix, pages 367–371 and return to this
point without any loss of continuity.
The estimate of the slope coefficient, b, indicates that indirect manufacturing labor
costs vary at the average amount of $10.31 for every machine-hour used within the relevant
range. Management can use the regression equation when budgeting for future indirect
manufacturing labor costs. For instance, if 90 machine-hours are budgeted for the
upcoming week, the predicted indirect manufacturing labor costs would be
y = $300.98 + ($10.31 per machine-hour * 90 machine-hours) = $1,228.88
Exhibit 10-6
Regression Model for
Weekly Indirect
Manufacturing Labor
Costs and Machine-
Hours for Elegant Rugs
Indirect Manufacturing Labor Costs (Y)
$1,600
1,400
1,200
1,000
800
600
400
200
8
12
Relevant Range
Residual
term 1
20 40 60 80 100 110
Cost Driver: Machine-Hours (X)
5
3
11
4
7
9
2
10
Regression line
y $300.98 $10.31X
6