Page 50 - Calculating Lost Profits

od may not be representative of the damage period, such as when labor or input costs per unit have risen,
like the cost of eggs or if the minimum wage rises (using the American Kitchen example).

Statistical Analysis

Another tool that may be used in evaluating the relationship between costs and revenue is statistical
analysis of the relationship between costs and revenue. Regression is a specific type of statistical analy-
sis, quantifying the relationship between two variables (for example, food expense and revenue). It is
typically performed by using a software package such as Microsoft Excel, SAS, Stata, or SPSS. In a re-
gression, there is a dependent variable (for example, food expense) and one or more independent or ex-
planatory variables. A regression with multiple independent or explanatory variables is referred to as a
multiple regression. The following is a regression output from Microsoft Excel for a single-variable re-
gression of executive compensation expenses regressed against revenue (executive compensation ex-
penses as explained by revenue).

Figure 7.4. Selected Regression Output: Exec. Comp. Expense Regressed Against Total Food and Bever-
age Revenue

Per the preceding table and the data in the regression, for every $1 increase in revenue, all else equal,
there is a $0.04 increase in executive compensation expense. The intercept value of $808,811.68 means
that there would be executive compensation expense of $808,811.68 with no revenue, based on the data
in the regression. The t-score of the revenue variable provides an indication of the strength of the ex-
planatory power of revenue as an indicator of executive compensation expense (a higher t-score means
that the data show a stronger relationship between the variables). The R-squared value of 0.82 indicates
that a high portion of the variation in executive compensation expense is explained by changes in reve-
nue. fn 5

In consideration of the regression output, the beta value of 0.04 is not unreasonable because it indicates
that with higher revenue, there is more executive compensation expense (but not much), all else equal.
Likewise, the t-score and R-squared value suggest that it may be appropriate to treat executive compen-
sation expense as having some variable component. But the intercept value suggests that there is also a
fixed component of the expense. When a cost has both fixed and variable components, it is often re-
ferred to as a semi-variable expense (also called semi-incremental). Or, there can be costs that are step-

fn 5 R-squared values range from 0 to 1, where values close to 1 indicate that the regression explains much of the variation in the de-
pendent variable, and an R-squared value close to 0 indicates that the regression explains very little of the variation in the dependent
variable.

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