Updated July 28, 1999
The following equations describe the calculations accountants can use to compute a variety of measures from operating data. This discussion assumes an accountant wants to estimate the fixed amount of cost per time period and the variable cost per unit of output. The basic equation is:
We compute the estimated variable cost per unit with this formula.
Basically, this formula takes the difference between the individual unit values, Xi, and the mean unit values X-bar and multiplies them by the similar values for the individual cost values, Yi. The total of these values is divided by the total of the squared differences between the mean number of units per period and the individual units per period.
Once the accountant has the variable cost per unit, he or she can multiply it by the average number of units per time period to compute the estimated total variable cost per time period. Subtracting this from the average period cost gives an estimate of the fixed cost as the following formulation shows.
Another useful measure for assessing the usefulness of the fixed and variable costs estimated from the regression equation is the Standard Error of the Estimate. This value gives some idea of how much a total cost estimate computed with the fixed and variable cost estimates may miss the actual cost incurred. Roughly speaking, this value gives an accountant some idea of how much a cost variance might be when using the fixed and variable costs as budget amounts. The formula for this calculation is:
Accountants can compute a similar value for the variable cost estimate, B, to give an idea of how much the estimated variable cost might be off from the actual variable cost. This formula shows how to compute the Standard Error of the Estimate for the variable cost estimate.
To help put the variable cost and its associated standard error in perspective, accountants can compute the ratio of the variable cost to its standard error to get the t value. Accountants find this ratio handy because it provides a quick way to relate the size of the variable cost to its associated standard error. For example, a variable cost estimate of $50 with a standard error of $2 gives a t of 25, but a $6 variable cost with the same $2 standard provides a t of only 3.
The standard error for the intercept gives the same kind information about the fixed cost as the standard error gives for the variable cost. Its calculation is described in the following formula.
The F Statistic is another measure provided by the regression analysis, and its calculation is provided by this formula.
Finally, the r-square provides an index of the closeness of the plotted points to the regression line, and the following formula shows its calculation.
