Fundamentals of Addressing Assumptions

Addressing Regression Assumption In this chapter, we discuss five issues that arise when applying regression analysis to estimate cost functions: • What procedures in the recording and accounting process can cause problems for regression analysis? • What criteria exist to evaluate the output from a regression analysis? • What are the crucial assumptions of regression and why are they important? • How can we detect when a regression assumption has been violated? • What can we do when we find that a regression assumption has been violated? The discussion of these five topics can become quite technical, requiring expertise far beyond the reasonable capability of a practicing management accountant. Our discussions will be only of an introductory na-ture, to identify some of the sources, effects, diagnoses, and cures of the problems that might arise. Planning for Regression Analysis of Business Data Before embarking on a statistical analysis of historical data, the analyst needs to verify that the data have been gathered appropriately. Several factors in the business environment can create difficulties that need to be overcome or at least mitigated before the statistical analysis should pro-ceed: 1. Accuracy and honesty in recording data 2. Difficulties in ensuring proper accrual 3. Economies of scale or learning effects 4. Changes in the nature of the production process Accuracy and Honesty in Recording Data Regression analysis must be performed on accurate data. Data that are unreliable will cause the regression analysis to fail to uncover, or possibly to misrepresent, an underlying relationship that may exist. Inaccuracies can arise in two ways. First, there may be clerical errors in recording the data. This should not be a problem when data are extracted from the financial accounting system, since those data are subject to considerable integrity and validity checks. Frequently, however, the data for a regression analysis will be derived from informal production reports that contain considerable errors because • The importance of accuracy is not impressed on the recorder • The data are not subject to independent verification or calculation • The data may be used in either formal or informal performance evaluation schemes so that the recorder may present the data in the most favorable, rather than the most accurate, way Difficulties in Ensuring Proper Accrual Regression analysis, by its very nature, requires the comparison of data that relate to the same period of time. This in turn means that costs must be accurately accrued. Performing a statistical analysis on data generated from a cash, rather than an accrual, system will almost surely yield meaningless output. For example, if a regression analysis is undertaken to determine the effect of changes in the level of production activity on overhead costs, the overhead costs must be accumulated and properly accrued for the same time interval as the production data. Frequently, however, the cost accumulation and the production systems may be out of phase. Production activity may be recorded weekly, daily, or batch by batch, but costs may be accrued monthly or quarterly. Therefore, the analyst must data will be available. choose a time interval for which both accurate production and financial Improper accruals will lead to errors in two data points. A cost incurred in January but allocated to February because of a late billing will cause January's costs to be understated and February's to be overstated. A similar problem arises if a detected error in one month's report is corrected by adjusting the next month's report rather than restating the initial month's total correctly. Such adjustments may be satisfactory for financial reporting, but they undermine the value of the monthly data for analyzing cost behavior. When selecting an accounting period as the basis for a historical-cost analysis, good closings should occur at the end of each period; accruals of all incurred costs (including the hourly or weekly pay-roll) should be estimated carefully, all relevant costs incurred during the period should be counted, and errors detected subsequent to the closing should be closed back to the appropriate period rather than handled as an adjustment in some subsequent period. Problems can also arise from cost aggregation and allocation pro-cedures. For example, suppose the firm allocates corporate overhead in proportion to the level of production. A correlation of overhead cost with production activity will merely reflect this allocation procedure. It cannot be used to imply that corporate overhead is affected by the level of pro-duction. The data used in the regression analysis should only include items for which a cause-and-effect relationship is thought to exist. It should exclude arbitrary or formula allocations, such as corporate overhead, that might confuse the regression analysis.