Regression Analysis—
Instructional Resource for
Cost/Managerial
Accounting
David E. Stout
Lariccia School of Accounting & Finance
2014 Annual Meeting of the American Accounting Association
Effective Learning Strategies (ELS) Forum
*Please Do Not Quote Without Permission of the Author*
ABSTRACT
The ability to generate accurate forecasts of costs is fundamental to the work of the managerial
accountant. Experience of the author suggests difficulty on the part of managerial accounting and
cost accounting students—graduate as well as undergraduate—in applying in an accounting
context statistical concepts related to the use of regression analysis for cost-estimation purposes.
This paper describes a classroom-tested instructional resource, grounded in principles of active
learning and a constructivism, that embraces two primary objectives: one, “demystify” for
accounting students technical material from statistics regarding ordinary least-squares (OLS)
regression analysis—material that students may find obscure or overly abstract; and, increase
student knowledge regarding the use of Excel for cost-estimation purposes. The resource consists
of a set of seven PowerPoint slides, Word documents, and Excel files meant for distribution to
students and divided into two major parts: four files that deal with simple (i.e., one-variable)
linear regression, and three files related to the incremental unit-time learning-curve model. A
separate Word file, meant for instructors, provides detailed guidance regarding the use of the
student-based files. The resource is flexible in that it can be: used at both graduate and
undergraduate courses in cost/management accounting; customized to meet the needs of
individual instructors (coverage of the entire resource requires approximately 7 hours of in-class
time); and, used in conjunction with any cost/management accounting textbook. Throughout the
resource many references to related online supplemental materials are provided, including links
to relevant online video clips. Survey evidence obtained from recent applications of the resource,
in both undergraduate cost accounting and in MBA managerial accounting, indicates positive
reception on the part of students: students perceive significant value in using the resource; the
vast majority of students recommend continued use of the resource in future offerings of the
course in question. Pre-test vs. post-test results from three classes over two recent semesters,
though limited in scope, provide evidence of student learning.
Keywords:
Instructional resource
Regression analysis
Excel-based applications
Cost/management accounting
Cost estimation
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1. Introduction
Among foundational concepts in cost/managerial accounting, the topic of cost estimation
is arguably the most important. Knowledge of cost behaviour, and the ability to provide
relatively accurate estimates of cost, is related directly to the ability of a cost system to provide
relevant data to support managerial functions of planning, control, and decision-making. In this
sense, knowledge of cost behaviour and cost-estimation techniques may be considered of critical
importance to the management accountant’s ability to add value to the organization.
Students in cost/management accounting courses are typically exposed first to relatively
simplistic methods of estimating cost functions, e.g., graphing (“eyeballing”) and the use of the
“high-low” method.1 They then typically transition to a discussion of ordinary least-squares
(OLS) regression as a “superior” method for estimating simple (i.e., one-variable) cost functions.
Depending on time devoted by the instructor to the topic, students in cost/managerial accounting
courses may be exposed to a variety of advanced considerations, including multiple-regression
models, the use of dummy variables, and the estimation of learning-curve (i.e., non-linear)
functions. Depending on the background of the instructor, various topics in regression analysis
could be covered via available software, such as SPSS, Minitab, or Excel.
By the time undergraduate accounting students cover cost estimation in a junior-level2
cost accounting class or by the time MBA students take a course in managerial accounting, they
have typically had at least one statistics course, usually (but not always) taught by a faculty
member outside of the business school. Over many years of teaching, I have observed that few of
my students retain much from these classes beyond perhaps a vague notion or rudimentary
knowledge of what “measures of central tendency” or “measures of variability” are. Even
students who have in one or more statistics classes covered regression analysis and/or the use of
a statistics package, seemed ill-equipped to apply this material in the courses I teach. There are,
of course, exceptions. For example, some of my students who have taken one or more “business
statistics” courses, which provide a context for covering basic statistical concepts, seem better
prepared for the discussion of this material within the context of cost estimation and cost
analysis, topics that—as noted above—can be considered fundamental to the managerial
accountant’s toolkit.
The “high-low” method fits a linear equation through two data points in a set of data: the high point in the data set
and the low point. The slope coefficient (variable cost rate) is estimated first, as the change in total cost (Y) divided
by the change in activity variable/cost driver (X) between these two points. The estimated slope coefficient (b) is
then used to estimate the fixed-cost component (a) by subtracting from the total cost at either the high point or the
low point the estimated variable cost.
1
In the U.S., “junior-level” refers to the third year of a typical four-year undergraduate (i.e., baccalaureate) degree
program; “senior-level” refers to the fourth year of a four-year undergraduate degree program.
2
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Cost and management accounting textbooks in general do a very good job of covering
what I would consider to be the basics of cost behaviour estimation and regression analysis. My
sense, however, is that many of these authors view the topic as more under the purview of
statistics professors than (cost or managerial) accounting professors. For this reason, coverage of
regression analysis in cost/management accounting textbooks is, in my opinion, incomplete and
superficial.3 For this reason, over the past few years I developed and class-tested, the
instructional resource described in this manuscript.
The rest of this paper is divided as follows. Section 2 contains an overview of the
components of the learning resource. This is followed in Section 3 by a statement of the
conceptual underpinnings and expected educational benefits of using this resource. Section 4
presents alternative implementation strategies that instructors might pursue in using the resource.
Section 5 contains student assessment results (both direct and indirect) from two recent
semesters in which the resource was used, while Section 6 provides a discussion of the
limitations of the resource in terms of its scope. A short conclusion is offered in Section 7.
2. Overview
This section provides an overview of an instructional resource that can be used—at both
the undergraduate and graduate cost/managerial accounting level—to cover both the underlying
theory behind ordinary least-squares (OLS) regression analysis and the use of Excel to estimate
both simple linear and non-linear cost functions. As such, the resource is meant to complement
available text material and can be used, at different levels of intensity, to reinforce and
“demystify” technical statistical material to which students in upper-level (and MBA) managerial
accounting classes may have been exposed to. The resource may be particularly valuable in
situations where a textbook for the course is not required or where a textbook is used but with
little-to-no coverage of material covered in this resource.
The resource package consists of PowerPoint slides, Word documents, and Excel files,
divided into two major parts: linear and non-linear cost-function estimation. These files, or userbased adaptations thereof, are meant for distribution to students. Coverage and use of the entire
resource would consume approximately seven (7) hours of in-class meeting time, split between
lecture-type (i.e., text) material and hands-on Excel-based work by the students. However, as
I am cognizant of the argument some instructors in the area would make, to the effect that there are “more
important topics” to cover. This, of course, is a judgment call. The critique referenced above in no way is meant to
denigrate an alternative viewpoint regarding the importance of cost estimation, regression analysis, and the use of
Excel in this regard, relative to other cost/management accounting-related topics. Those instructors who desire
relatively minor coverage of these topics will likely find the material in existing cost/managerial accounting texts to
be sufficient for their needs. As will be argued, instructors who desire more in-depth coverage of these topics should
find significant value in the present instructional resource, including the set of files available on request from the
author.
3
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noted above, the resource has built-in flexibility: based on the instructor’s goals and available
time in the course, individual components of the resource package could be used.4 An overview
of the seven files comprising the entire two-part instructional resource, along with estimated inclass coverage time for the material in each file, is provided in Exhibit 1. A supplemental file for
instructors, “Reference Document (Regression Analysis—Instructional Resource),” provides a
detailed discussion of the content of the seven student-related files as well as tips and
recommendations for using these files in class. 5 This supplemental file complements the
overview provided herein.
--Insert Exhibit 1 here—
As indicated in Exhibit 1, Part One deals with the use of regression analysis to estimate
simple linear cost functions, the use of Excel for estimating these functions, interpretation of
regression-related output associated with cost estimation, and alternatives for estimating costs
based on a regression model fit to a set of data. This portion of the resource consists of the
following four files: (1) a set of PowerPoint slides (“Estimating Linear Cost Functions”) that
provides an overview of simple (one-variable) cost functions and OLS regression analysis; (2) an
Excel file (“Estimating Linear Cost Functions Using Excel”) that discusses five Excel-based
methods that can be used to estimate a simple linear cost function; (3) a Word file (“Cost
Estimation and Statistical Issues—Regression Analysis”) that addresses three separate costestimation and statistical issues (five options in Excel for generating cost estimates after a
regression analysis has been performed; an analysis of changes in the standard error of the
regression, SE, as sample size, n, changes; and, constructing confidence intervals around point
estimates); and (4) an Excel file (“Change in SE as n increases”) that can be used in conjunction
with item (3) above.
Part Two of the resource module deals with estimating one form of non-linear cost
function: the incremental unit-time learning-curve model. This portion of the instructional
resource consists of the following three files: (1) a PowerPoint file (“Estimating Learning-Curve
Cost Functions”), which provides a review of logarithms and a discussion of common forms of
learning-curve models; (2) a Word file (“Example—Estimating a Learning-Curve Function”),
which provides a discussion of two procedures that can be used within Excel to estimate a
learning-curve model; and (3) an Excel file (“Learning-Curve Analysis [“Incremental Unit-Time
Model]), which provides a worked example of using Excel to fit a learning-curve model to a set
of data and a basis for discussing the interpretation and use of the estimated coefficients in this
model.
4
Implementation alternatives are discussed in Section 4, below.
5
All eight of these files are available on request from the author.
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3. Conceptual Underpinnings/Anticipated Benefits to Students6
Most (but not necessarily) all students in our accounting classes have been exposed to the
regression analysis and related statistical concepts (e.g., measures of dispersion or measures of
central tendency). Some might also have been exposed to the use of Excel as a cost-estimation
tool. Why, then, the need for coverage of these topics in an accounting class? Although the
underlying cause of this situation is likely multidimensional, one plausible explanation is that
many of our students may have adopted in their earlier studies what might be characterized as a
“shallow” (or “surface”), rather than a “deep,” learning approach.7
The importance of the above-referenced distinction rests on the assumption that students
do not have a fixed approach to learning; rather, it is the design of a learning opportunity that
motivates students to embrace a particular approach to learning. While there are alternative
strategies for motivating students to embrace a deep learning approach, one strategy is to use
interactive assignments, similar to the instructional resource discussed in this paper. Put
differently, because the present resource requires students to be actively (rather than passively)
engaged in the learning process a deeper (conceptual) understanding of the material is possible.8
4. Implementation Alternatives and Usage Strategies
The regression resource can be used in alternative ways. Below some thoughts are
offered regarding alternative usages based both on level of class/background of students and on
the textbook used by the professor. As noted earlier, the resource is very flexible and can be
customized (expanded upon or reduced in length) to meet the needs of individual instructors.
Thus, the thoughts below are meant to be suggestive in nature.
4.1. Alternative strategies based on course level and background of students
I have used Part One (simple linear regression) of the module at both the undergraduate
(cost accounting) and graduate (MBA managerial accounting) levels. In both cases, prior to in6
The author gratefully acknowledges an anonymous reviewer for comments that motivated the addition of this
section to the paper.
7
In a surface approach, students focus principally on the ability to reproduce material on a test or an exam. By
contrast, understanding of material is the primary aim of a deep approach to learning. Deep learning can lead to
long-term retention of concepts, which can be used for problem-solving in unfamiliar contexts. In a deep approach
to learning, the student analyses new facts and ideas critically, ties information into existing cognitive structures, and
makes links between ideas and facts.
Active learning is ultimately derived from what is called the “constructivist” approach to learning, that is, a belief
that learning occurs when students are actively involved in a process of meaning and knowledge construction, as
opposed to passively receiving information (e.g., traditional lecture format). In a “constructivist” classroom, students
are afforded the opportunity of testing, exploring, investigating, etc.; the principal role of the instructor is facilitator.
In short, constructivist teaching fosters critical thinking and motivated, independent learners.
8
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class coverage of the materials, files from the resource are made available to students via
Blackboard. At both levels, one full week (either two 75-minute day sessions or one 2 hour and
40-minute evening session) was devoted to the resource. I begin by presenting in class the entire
set of PowerPoint slides associated with Part One. Afterwards, I transition to the Excel file
“Estimating Linear Cost Functions Using Excel,” which contains five alternatives for
implementing regression analysis in Excel; all five methods are applied to the data set provided
at the top of the Excel file. I generally focus the discussion on method #2 (use of the Regression
routine in Excel), since this method provides opportunity for the most comprehensive discussion
of regression-related output. I then transition to the Word document “Cost Estimation and
Statistical Issues—Regression Analysis” and make sure that I cover at least one of the five
options for generating cost estimates from the regression-related cost functions. At the
undergraduate level, this typically concludes the discussion. At the MBA managerial accounting
level, I try to cover (in addition to the material discussed above) the topic of constructing
confidence intervals around point estimates generated by a regression equation. If covered, this
typically concludes the one-night presentation to my MBA students.
I have implemented the preceding plan successfully over the past five or six years. I
recognize, however, that alternative implementation strategies exist, based both on the quality
and background of students in the program and on the time the professor devotes to the module.
For example, in situations where the students (at either level) have better backgrounds in terms
of regression and the use of Excel to estimate cost functions, the deck of PowerPoint slides could
be reduced in length and nothing more than a quick “refresher” or review devoted to the process
of using Excel to generate cost estimates based on a regression model. In this situation,
discussion could focus on supplementary issues covered in Part One (analysis of changes in SE
as n [the sample size] changes and/or constructing confidence intervals around point estimates
generated by a regression-based cost model). Alternatively, after a quick review of some of the
material from Part One (based on the assumed knowledge and background of students), the
instructor may focus on the material in Part Two: learning-curve functions and how such
functions can be estimated using Excel.9 This plan might also be appropriate for students in an
alternative graduate course, for example, a course on “Strategic Cost Management” taken by
students in a Masters of Accountancy (MAcc) program.
It is possible to cover both Part One (simple linear regression) and Part Two (learningcurve analysis) of the module. In this case, the instructor could expect to devote up to seven (7)
hours of in-class time for the module. As noted earlier, flexibility is built into the module: the
instructor has the ability to customize the files by adding to or subtracting from the material
presented therein. If Part Two of the module is covered, and time permits, the case by Stout and
Juras (2009) could be assigned. Finally, should the instructor desire to do so, the material in Part
9
The educational case by Stout and Juras (2009) could also be assigned in conjunction with Part Two of the
resource.
Page 6 of 18
Two could be extended to covering topics beyond those included in the module. For example,
the module could be extended by covering the use of Excel for estimating and using multipleregression models of cost behaviour. In this case, the references provided below (in section 7)
should be helpful.
4.2. Alternative strategies based on textbook used
An examination of selected cost/management accounting textbooks reveals diversity in
terms of coverage of regression analysis and the use of Excel to estimate regression functions
and to use such functions for cost-estimation purposes. Exhibit 2 provides an overview of this
coverage.
–Insert Exhibit 2 here—
As seen from Exhibit 2, coverage of regression-related (including Excel-based) topics
varies from minor to no coverage (Datar and Rajan, 2014; Garrison et al., 2012; Hilton, 2011;
Maher et al., 2012; Noreen et al., 2014; and, Atkinson et al., 2012) to what might be considered
moderate/intermediate level coverage (Blocher et al., 2013; Horngren et al., 2012; and, Lanen et
al., 2011).10 Given coverage in popular textbooks, a legitimate question is whether and to what
extent the present instructional resource adds value.
The author asserts that this resource has wide applicability and can be used (albeit in
different ways) in conjunction with virtually any cost/managerial accounting text, as explained
below. As indicated by the notes provided in Exhibit 2, even when there is topical overlap
between textbooks and the present resource, textbook coverage can be considered relatively
light.11 For example, only the REGRESSION routine in Excel provides a full complement of
regression-related statistics. The last column in Exhibit 2 indicates that most cost/management
accounting texts do not discuss this approach.12 Further, even for those texts that do present the
REGRESSION routine as the method for estimating cost functions, there is very little (if any)
discussion of the supplementary regression-related output. As demonstrated above, the present
instructional resource provides a rich (and class-tested) discussion of this material within an
accounting context, thereby attempting to “demystify” this material for business and accounting
Classifications based on the author’s subjective assessment, based principally on the coverage dimensions
(columns) reflected in Exhibit 2.
10
11
This statement should not be construed as criticism of available textbooks, which by design or necessity are
limited in scope and coverage of some topics relative to others. The primary point is that the present instructional
resource extends and therefore adds value to the regression-related (including Excel-related) material contained in
popular cost/management accounting textbooks. It is, in fact, the reason that the resource was developed in the first
place.
12
It is interesting, too, that only one of the texts reviewed in Exhibit 2 (Blocher et al. 2013) discusses the issue of
building confidence intervals around point estimates generated by regression functions.
Page 7 of 18
students. Further, as indicated in Exhibit 2, coverage of the use of Excel for both cost-estimation
and cost-prediction purposes is relatively light compared to coverage contained in the present
instructional resource.13 Finally, even when there is textbook coverage of Excel, the discussion is
limited: the present instructional resource provides a rich set of alternatives in terms of using
Excel to generate cost functions (both linear and non-linear) and for using these functions for
cost-estimation purposes. Thus, the resource should be particularly attractive in those
cost/managerial accounting courses in which a heavy emphasis on Excel is placed.
In those classes where a textbook is not required, the module could be used as primary
source material for student learning of cost estimation using regression analysis, the use of Excel
for cost-estimation purposes, interpretation of regression-related output, and the use of Excel for
cost-prediction purposes.14 In situations where a textbook is used, the incremental value of the
module is a function of what is available in the textbook used by the instructor relative to the
goals of the instructor and the amount of available class time. Exhibit 2 is helpful in guiding the
discussion in this regard. As noted both by Exhibit 2 and the discussion above, in virtually all
cases (but to varying degrees) the present instructional resource provides a useful supplement to
the material covered in popular cost/managerial accounting textbooks.
5. Student Feedback
Student feedback in two forms was obtained: responses to a 12-item survey instrument
created by the author and administered to students, and scores on a five-item set of multiplechoice questions constructed by the author and administered by the author both prior to and
subsequent to in-class coverage of the material.15 The former provides indirect evidence
regarding the efficacy of the regression module, while the latter provides more direct (albeit
limited) evidence of student learning.
5.1. Survey response data
13
It is interesting to note that the perennial market leader in the cost accounting area (Horngren et al., 2012) has no
instructional material regarding the use of Excel for cost-estimation and/or cost-prediction purposes. As Exhibit 2
notes, a mathematical formula for estimating the slope and intercept of a linear cost function are presented (p. 367).
The text includes no discussion of the use of Excel, although the discussion does make reference to “output from
Excel.”
14
The text used by the author in MBA managerial accounting is Atkinson et al. (2012). As noted in Exhibit 2, this
text has no coverage of regression-based cost estimation and cost prediction, including Excel-based material. In this
course, therefore, the instructional resource discussed herein serves as the primary learning tool for this material.
15
The pre-test was administered during the first week of class. The regression instructional resource was covered
during the third week of class. The 12-item student survey (see Table 1) was administered after coverage of the
regression material but the week before the administration of the post-test. The post-test was administered to
students at the beginning of the fifth week of class, as part of an in-class exam that included additional material
covered during the first four weeks of class.
Page 8 of 18
Students responded to the survey instrument using a five-point Likert-type scale, with 1 =
“strongly agree” and 5 = “strongly disagree.” Response data for Fall semester 2013 (MBA
managerial accounting, n = 20, and undergraduate cost accounting, n = 25) and Spring semester
2014 (MBA managerial accounting, n = 31) are presented in Table 1. A comparison of responses
to Q11 and Q12 compared to Q1 and Q2 indicates an increase in perceived knowledge of both
regression concepts and the use of Excel to estimate regression functions.16 Responses to Q3 and
Q4 indicate a perception that the resource was effective in illustrating both important concepts
regarding regression analysis and the use of Excel for cost-estimation purposes. Responses to
Q5, Q6 (reverse-scored), and Q7 indicate that student in all three classes found value in the
material. Virtually all students in these classes agreed or strongly agreed that coverage of the
regression module was an effective use of class time (Q5) and that the material should be used in
future offerings of the course (Q7). Note that the wording of Q6 was reversed: the vast majority
of students disagreed or strongly disagreed with the statement that the regression resource did not
increase knowledge and understanding of regression.17 Items Q8 through Q10 were included to
help improve the measurement properties of the survey instrument: the present regression
resource has nothing to do with constructing a “profit-planning model” (Q8)18 or with “decisionmaking under uncertainty” (Q10). And since only Part One of the resource (simple linear cost
functions) was covered in these classes, there is no reason to expect a positive response to Q9,
which refers to “a better understanding of learning-curve functions.” Low scores on items Q8
through Q10 were therefore anticipated. As seen in Table 1, responses to each of these items
indicate little-to-no perceived effect of the learning resource on each of these three dimensions.
—Insert Table 1 here—
5.2. Pre- versus post-test results
At the beginning of the semester, the set of five regression-related multiple-choice items
constructed by the author (see the Appendix) was administered to students as a pre-test. The
same items were subsequently included on an in-class exam administered during week five of the
course. The exam included all material covered during the first four weeks of the course,
including the regression-related material covered in week four. Five-item aggregated pre-test
versus post-test results, from both MBA managerial accounting classes (Fall semester 2013 and
Spring semester 2014) and undergraduate cost accounting (Fall semester 2013) are reported in
16
As seen from the data in Table 1, roughly 70-80% of students perceived that prior to coverage of the regression
module their knowledge of regression fundamentals (Q1) and the use of Excel to estimate regression functions (Q2)
was “very minimal.” However, 80% or more of students in the sampled indicated a perception that, after covering
the regression module, their knowledge of regression concepts (Q11) and knowledge of the use of Excel to estimate
regression functions (Q12) was “very good.” The extent to which knowledge of regression concepts increased is
addressed, albeit in limited fashion, by the results reported in Table 2 below.
17
This is a common approach to guarding against (or detecting) response-set bias.
18
In my classes, CVP analysis (short-term profit planning) is covered after coverage of the topic of cost
estimation/regression analysis.
Page 9 of 18
Table 2, Panel A. As can be seen, there were statistically significant increases in mean scores and
a slight reduction in the score variability (measured by sample standard deviations) for all three
groups. Panel B in Table presents paired-sample t-test results for mean differences on each of the
five items (both under the assumption of equal and unequal variance in scores, pre-test vs. posttest). As can be seen, these results are generally (but not wholly) consistent with the five-item
aggregate-level results reported in Panel A.
--Insert Table 2 here—
While the data reported in Table 2 are consistent with a positive effect of the resource on
student learning, caution in interpreting these results is in order, for three reasons: one, data are
from a single semester at a single institution; two, only a subset of items covered in the
instructional resource were included on the test (i.e., the resource is much richer in terms of
content coverage—we simply do not have assessment results for these other learning
dimensions, such as the many Excel-based applications in the module); and three, there is no
comparison group, that is, no claims can be made regarding the effect of the learning resource
relative to other mechanisms for covering regression-related material. It is entirely possible that
greater (or lesser) levels of test-item scores would be observed through use of an alternative
resource.
6. Limitations and Extensions
While the author believes the present resource for regression analysis is rich, there are
certain important topics that are not covered. For example, the discussion of learning-curves (in
part two of the module) did not consider the cumulative average-time model. The extension of
the discussion to cover this topic is, however, straightforward. The instructor who wishes to
cover this alternative form of the learning curve model can use the same data set provided in the
Excel data file.
Another limitation relates to the focus of use of only a single approach for cost-estimation
purposes: fitting past observations to a function using regression analysis. As noted in Hilton
(2011, p. 251), Lanen et al. (2011, pp. 156-158), and Garrison et al. (2012, p. 35), non-statistical
approaches (such as account analysis and the engineering method), can be used for costestimation purposes. Thus, instructors using the present regression resource should make the
point to students that this statistical approach is but one of several available alternatives that can
be employed in practice.
In addition, the resource does not include coverage of several important regressionrelated topics, such as the use of dummy variables, the problem of statistical “outliers” (i.e.,
abnormal data observations), dealing with trend and/or seasonality in time-series regressions, and
the estimation of multiple-regression models of cost behaviour. At the same time, the foundation
provided by the present instructional resource should allow for a smooth transition to these
Page 10 of 18
topics, should the instructor be inclined to do so. In addition to material found in cost/managerial
accounting textbooks, much information regarding these topics is available on the web. For
example, the instructor who wishes to cover the use of Excel to generate multiple-regression
models can have students consult any of the following sources:
http://www.wikihow.com/Run-a-Multiple-Regression-in-Excel
http://www.real-statistics.com/multiple-regression/multiple-regression-analysis/
http://www.jeremymiles.co.uk/regressionbook/extras/appendix2/excel/
Pertinent video clips covering the topic of multiple-regression analysis and using Excel to
estimate multiple-regression models are available at:
http://www.youtube.com/watch?v=GHVL6aCpf2g
http://www.youtube.com/watch?v=2J8WBo2CKM4
http://www.youtube.com/watch?v=Ek4bIe-DuMA
http://www.youtube.com/watch?v=tlbdkgYz7FM
http://www.youtube.com/watch?v=IL7xukTdLyI
http://www.youtube.com/watch?v=HgfHefwK7VQ
7. Conclusion
Knowledge of cost behaviour is of fundamental importance to the areas of cost and
managerial accounting. Cost estimates, drawn from cost equations (or models), are used for
managerial functions related to planning, control, and decision-making. As such, one can make
the argument that in accounting curricula today extensive coverage of material related to the
cost-estimation process (including regression analysis and the use of spreadsheet software, such
as Excel, for this purpose) is appropriate, if not desirable.
Experience of the author over many years, at both the graduate and undergraduate levels
of cost/managerial accounting, suggests that many (if not most) students have difficulty applying
to an accounting context regression-related material covered in statistics classes. This paper
discusses a classroom-test instructional resource that has two primary objectives: “demystify”
technical material regarding regression and related statistical concepts both by providing
contextual richness to the discussion; expose students to an extensive array of Excel-based tools
and functions related to use of regression analysis for estimating cost functions. The module is
grounded conceptually in a constructivist/active-learning approach.
The resource is divided into two major sections: Part One deals with the estimation of
simple (i.e., one-variable) linear functions, while Part Two deals with the estimation of one type
of learning-curve (i.e., non-linear) function. The material contained in the module is designed to
supplement current textbook coverage of regression and the use of Excel for cost-estimation
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purposes. The entire resource consists of eight files, all of which are available on request from
the author. Extensive references to additional source material—both in print and in video-clip
form—are provided in a Word document for instructors named “Reference Document
(Regression Analysis—Instructional Resource)” and throughout the resource six files meant for
distribution to students.
The instructional resource discussed herein can be used at either the undergraduate (e.g.,
cost accounting) level or in an MBA managerial accounting class. Approximately two weeks of
class time (roughly six hours) would be needed to cover the entire resource. The resource is
flexible, however, and can be customized to meet the needs of individual faculty. Alternative
implementation strategies for the resource, based on the goals of the instructor, the amount of
class time available, and the textbook used in the course in question are possible.
Feedback, from both undergraduate cost accounting and MBA managerial accounting
students, regarding the module has been positive: students generally perceive that coverage of
the module increases both their knowledge of regression and their proficiency in using Excel to
do regression analysis. The vast majority of students who recently covered the module
recommended that the module be used in future offerings of the course in question. To
complement the discussion of simple (single-variable) models covered by the present resource,
references to multiple-regression models and the use of Excel to estimate such models—topics
not covered in the resource—are provided at the end of the paper.
References
Anderson, D. R., D. J. Sweeney, and T. A. Williams. (1987). Statistics for Business and
Economics, 3rd edition. New York: West Publishing Company.
Atkinson, A. A., R. S. Kaplan, E. M. Matsumura, and S. M. Young. (2012). Management
Accounting: Information for Decision-Making and Strategy, 6th edition. New York:
Pearson.
Blocher, E. J., D. E. Stout, P. E. Juras, and G. Cokins. (2013). Cost Management: A Strategic
Emphasis, 6th edition. New York: McGraw-Hill/Irwin.
Datar, S. M. and M. V. Rajan. (2014). Managerial Accounting: Making Decisions and
Motivating Performance. New York: Pearson.
Garrison, R. H., E. W. Noreen, and P. C. Brewer. (2012). Managerial Accounting, 14th edition.
New York: McGraw-Hill/Irwin.
Hilton, R. W. (2011). Managerial Accounting: Creating Value in a Dynamic Business
Environment, 9th edition. New York: McGraw-Hill/Irwin.
Page 12 of 18
Horngren, C. T., S. M. Datar, and M. Rajan. (2012). Cost Accounting: A Managerial Emphasis,
14th edition. Upper Saddle River: Prentice Hall.
Lanen, W. N., S. W. Anderson, and M. W. Maher. (2011). Fundamentals of Cost Accounting, 3rd
edition. New York: McGraw-Hill/Irwin.
Leininger, W. E. (1980). Quantitative Methods in Accounting. New York: D. Van Nostrand
Company.
Maher, M. W., C. P. Stickney, and R.Weil. (2012). Managerial Accounting: An Introduction to
Concepts, Methods, and Uses, 11th edition. South-Western, Cengage Learning.
Noreen, E. W., P. C. Brewer, and R. H. Garrison. (2014). Managerial Accounting for Managers,
3rd edition. New York: McGraw-Hill/Irwin.
Stout, D. E., and P. E. Juras. (2009). Instructional case: Estimating learning-curve functions for
managerial planning, control, and decision-making. Issues in Accounting Education, Vol.
24, No. 2 (May), pp. 195-217.
Page 13 of 18
Table 1
Student Feedback—Survey Results: Fall Semester 2013 and Spring Semester 2014
Item
Q1. Prior to this course, my knowledge of regression concepts was very
minimal.
Q2. Prior to this course, my knowledge of the use of Excel to estimate
regression functions was very minimal.
Q3. The regression resource used in this class was effective in terms of
illustrating important concepts associated with regression analysis.
Q4. The regression resource used in this class was effective in terms of
illustrating the use of Excel to estimate regression functions.
Q5. Coverage of the regression resource in this class was an effective use
of my time.
Q6. The regression resource did NOT increase my knowledge and
understanding regression analysis.
Q7. I would recommend the use of the regression resource in future
offerings of this course.
Q8. After completing the regression resource, I am now better able to
construct a profit-planning model.
Q9. After completing the regression resource I have a better understanding
of learning-curve functions.
Q10. Use of the regression resource has increased my understanding of
decision-making under uncertainty.
Q11. My knowledge of regression concepts is very good.
Q12. My knowledge of using Excel for estimating regression functions is
very good.
Fall Semester
2013
Undergraduate Cost
MBA Managerial
Accounting (n = 25)
Accounting (n = 20)
% Agree/
% Agree/
Mean
Strongly
Mean
Strongly
(Median)
(Median)
Agree
Agree
2.10
75
2.25
80
(2.00)
(1.50)
1.75
75
2.00
70
(2.00)
(1.50)
1.60
100
1.50
100
(2.00)
(1.00)
1.80
100
1.58
100
(2.00)
(1.50)
1.60
90
1.58
100
(1.50)
(2.00)
4.10
8
4.25
0
(4.00)
(4.00)
1.80
100
1.50
100
(2.00)
(1.00)
3.75
12
4.00
5
(4.00)
(4.00)
3.50
12
3.75
10
(4.00)
(4.00)
3.75
8
4.25
5
(3.50)
(4.00)
1.85
80
1.80
90
(2.00)
(2.00)
1.70
90
1.50
100
(2.00)
(2.00)
Legend: (1) = Strongly Agree, (2) = Agree, (3) = Neutral, (4) = Disagree, (5) = Strongly Disagree
Spring
Semester 2014
MBA Managerial
Accounting (n = 31)
% Agree/
Mean
Strongly
(Median)
Agree
2.25
71
(2.00)
1.75
77
(1.75)
1.70
100
(1.75)
1.45
100
(1.50)
1.50
97
(1.50)
4.25
6
(4.00)
1.50
97
(1.00)
4.10
9
(4.00)
3.60
9
(4.00)
3.75
13
(4.00)
1.60
90
(1.50)
1.75
97
(2.00)
Table 2
Panel A: Five-Item Aggregate Pre-test vs. Post-test results: Fall Semester 2013 and Spring Semester 2014
Statistic
Mean
Median
SD
Fall Semester
2013
MBA Managerial Paired-Sample t(n = 20)
test
Pre-test Post-test
p*
df**
0.40
0.68
< 0.0001
19
0.40
0.70
0.23
0.16
Fall Semester
2013
Undergraduate
Cost (n = 25)
Pre-test Post-test
0.50
0.70
0.60
0.80
0.19
0.13
Paired-Sample ttest
p*
df**
< 0.0001
24
Spring Semester
2014
MBA Managerial
(n = 31)
Pre-test Post-test
0.47
0.74
0.60
0.80
0.21
0.17
Paired-Sample
t-test
p*
df**
< 0.0001 30
* Based on a two-tailed distribution
**df = n −1
Panel B: Individual Item Analysis—Pretest vs. Post-test Results: Fall Semester 2013 and Spring Semester 2014
Question #*
1
2
3
4
5
Fall 2013: MBA Managerial
(n = 20)
p-value on mean difference**
Equal variance Unequal variances
0.048
0.058
0.015
0.011
0.035
0.013
0.048
0.060
0.086
0.060
Fall 2013: Undergraduate Cost
Accounting (n = 25)
p-value on mean difference
Equal variance
Unequal variances
0.052
0.094
0.067
0.071
0.055
0.045
0.106
0.132
0.015
0.045
Spring 2014: MBA Managerial
(n = 31)
p-value on mean difference
Equal variance
Unequal variances
0.001
0.003
0.009
0.013
0.022
0.021
0.016
0.034
0.052
0.021
*See Appendix.
**Based on a two-tailed distribution.
Page 15 of 18
Exhibit 1: Overview of Resource Components
Part One: Estimating Simple Linear Cost Functions
File
Type
File
Name
PPT
Estimating Linear
Cost Functions
Estimating Linear
Cost Functions
Using Excel
Cost Estimation
and Statistical
Issues—
Regression
Analysis
Change in SE as n
increases
Excel
Word
Excel
Estimated InClass Time
Description
Introduction/Overview of Simple (One-Variable)
Cost Functions and OLS Regression
Five Excel-Based Methods for Estimating a
Simple Linear Cost Function
Cost-Estimating Procedures using Excel (Five
Options); Analysis of Changes in the SE as n
(Sample Size) Changes; Constructing Confidence
Intervals Around Point Estimates
Analysis of How the Standard Error of the
Regression (SE) Can Change/Be Improved
0.75 hour
1.75 hours
1.50 hours
0.5 hour
Total
4.50 hours
Part Two: Estimating a Learning-Curve Function
File
Type
PPT
Word
Excel
File
Name
Estimating LearningCurve Cost Functions
Example—Estimating a
Learning-Curve
Function
Learning-Curve
Analysis (“Incremental
Unit-Time Model”)
Description
Introduction (Review of Logarithms and
Common Forms of Learning Curves)
Overview of Two Procedures in Excel for
Estimating the “Incremental Unit-Time
Model”
Using Excel to Fit a Learning-Curve Model
to a Data Set
Total
Estimated InClass Time
0.75 hours
1.00 hours
0.75 hours
2.50 hours
Exhibit 2: Overview of Selected Textbook Coverage of Regression Analysis and Use of Excel by Subjective Assessment of
Extent of Coverage
Panel A: Slight (or No) Coverage
Text
Atkinson et al. (2012)
Datar and Rajan (2014)
Topical Coverage
R
SE MR
LC
2
X
X
Excel Coverage
CE CP MR
LC
X
Garrison et al. (2012)
X
X
Hilton (2011)
X
X
X
Maher et al. (2012)
X
X
X
Noreen et al. (2014)
X
X
Notes
MR and LC given very light coverage
Excel material covered in Appendix 2A (pp. 67-69);
INTERCEPT, SLOPE, and RSQ functions in Excel covered
Excel material covered in Appendix to Chapter 6 (pp. 256-257);
INTERCEPT, SLOPE, and RSQ functions in Excel covered
LC analysis covered in Appendix 5.1 (pp. 160-161)
Excel material covered in Appendix 2A (pp. 64-66);
INTERCEPT, SLOPE, and RSQ functions in Excel covered
Panel B: Moderate/Intermediate-Level Coverage
Text
Topical Coverage
R
SE MR
LC
Blocher et al. (2013)
X
X
X
X
Horngren et al. (2012)
X
X
X
X
Lanen et al. (2011)
X
X
X
2
Excel Coverage
CE CP MR
LC
X
X
Notes
Confidence intervals covered; REGRESSION routine covered;
six-page online supplement covering regression-related output
is available
Regression formula, not functions in Excel, used (footnote 3, p.
367), although reference is made to “output from Excel”
Use of REGRESSION routine in Excel covered in Appendix
5A (pp. 175-180); learning-curve functions covered in
Appendix 5B (pp. 180-181)
Legend: SE=standard error of the regression; MR = multiple-regression; LC = learning-curve functions; CE = cost-function
estimation; CP = cost prediction (from a regression equation).
Appendix: Test Items
1. OLS (Ordinary Least-Squares) regression:
(A) Cannot be used to estimate nonlinear cost functions, such as learning-curve functions
(B) Cannot handle multiple cost drivers (independent variables)
(C) Assures us of the “line of best fit” using the Mean Absolute Error (MAE) criterion
(D) Is sensitive to outliers (abnormal data points) because of the “squaring” procedure that is used for
cost-estimation purposes
(E) None of the above is correct
2. In estimating cost functions, including linear cost functions, the analyst can calculate a statistic referred
to as the “coefficient of determination” (that is, R2). This statistic refers to:
(A) The percentage variation in cost, Y, that can be explained by the variation in the independent
variable, X (e.g., units produced)
(B) The slope of the cost function at the highest point on the curve
(C) The amount of variance in cost, Y, that is not explained by the output variable, X
(D) An amount equal to “1 minus the explained variation in Y given changes in X”
(E) None of the above
3. The standard error of the regression (SE):
(A) is an absolute measure of “goodness-of-fit” for a cost function
(B) is equal to the sum of the squared deviation between each Y value and the mean of the Y’s
(C) cannot be calculated for cost functions containing more than a single independent variable
(D) represents the estimated value of Y when X (the independent variable) is zero
(E) is defined as 1 – R2 (where R2 = the coefficient of determination)
4. Regression analysis can be used, with past (historical) observations, to estimate linear cost functions. In
what sense does OLS regression analysis result in the line of best fit through any set of data points?
(A) It minimizes the variance of the actual observations around the mean value of Y
(B) It disregards sunk costs when calculating an estimate of the fixed cost component
(C) It minimizes the sum of the squared deviations of the actual observations around the mean value
of Y
(D) It smooths out the effect of atypical or abnormal observations
(E) None of the above
5. The standard error of the regression (SE) is best interpreted as:
(A) the estimated slope coefficient of a linear cost function
(B) the estimated slope coefficient of a non-linear cost function
(C) the percentage of the variability of the dependent variable (e.g., cost) associated with changes in
the cost driver (activity variable)
(D) a relative measure of goodness-of-fit between the dependent variable and the independent
variable in a regression equation
(E) None of the above