Implications of Constant Activity Levels

Asymmetric Cost Variation Economies of Scale or Learning Effects Most regression analyses assume that a linear, or directly proportional, relationship exists between the dependent variable and the independent variables. The regression analysis could be badly flawed if a linear equation were fitted to an inherently nonlinear relationship. Nonlinearity could arise in the presence of learning or experience curve effects. Total or average costs vary nonlinearly with cumulative output, since the learning effect causes more recently produced items to have lower production costs than items produced much earlier. A second example of a nonlinear relationship between the dependent variable and the underlying activity variable occurs if economies of scale exist. If the firm is able to produce products more efficiently at higher levels of production, a simple linear model will not capture this phenom-enon. Changes in the Nature of the Production Process Regression analysis assumes a single, stable, and continuing relationship between the dependent variable and the independent variable(s). This assumption is violated if some aspect of the production process is changed, such as when a new piece of important production equipment is installed. The environment of the firm is constantly changing, and if the assumption of constancy were to be taken literally, regression analysis would never be possible. We can only require that there be no major changes in the production process. Changes in the quality or mix of materials used, the labor classification employed, or the type of equipment used are all examples of changes that would need to be explicitly recognized in the modeling process. If a major change in the production process has oc moteneroe regression analysis should analyze hee expations before aured then the nge separately or else model the change explicitly within the regression model. Operating at a Constant Level of Activity Operating at a constant level of activity, the production scheduler's ideal, is the worst possible situation for applying regression analysis. It would be impossible to uncover a relationship between cost and the activity level, since there would be observations on only one activity level. Regression analysis will be most effective when the dependent and independent variables are observed over a wide range of values. Unfortunately, this goal for wide variation in data conflicts with the normal data accrual process. There may be significant day-to-day changes in activity levels, an ideal situation for regression analysis. But if data are accrued and reported on only a monthly basis, then the analysis must be limited to monthly data. Over this period of time, daily variations will average out to much more stable monthly data. Practices Relating to Adjustment to Expansion or Contraction Many businesses can expand more responsively than they can contract. Costs, therefore, tend to follow expansion up much more closely than they follow contraction down, since it may be difficult to dispose of excess plant and equipment and many firms are reluctant to lay off skilled or highly valued employees. The asymmetry of costs varying during expansions but remaining fixed during contractions creates problems for regression analysis, since a simple linear relationship will not exist between current costs and current activity levels. The history of how we got to the present level of activity will also help to explain the current level of costs. Choosing the Underlying Activity Measure Units of production and direct labor-hours are two activity measures often used in cost analysis. In highly automated production processes, measures such as the machine-hours, amount of raw materials handled, average production flow rate, and number of production-run setups have also been suggested. These latter measures, however, may not be recorded in the official accounting system. As organizations attempt to shift from a direct-labor to a machine-hour basis for distributing overhead, entirely new measurements have to be made and recorded. All of these attributes of the practical environment of business create potential pitfalls for the application of regression analysis. The analyst must be sensitive to violations of the regression assumptions caused by these phenomena.