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*Please Do Not Quote Without Permission of the Author*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 hoursof 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
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-level[2] 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.
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 aninstructional 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 user-based 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 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 in-class 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.
--InsertExhibit 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 cost-estimation 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.
3. Conceptual Underpinnings/Anticipated Benefits to Students[6]
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 in-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 (learning-curve 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 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 multiple-regression 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, alegitimate 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 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.