The business valuation, lost profits expert will need to forecast or project the revenues and related expenses to determine the value of a company or the lost profits or damages in a case. There are multiple techniques for making the forecasts or projections. One of the techniques used in business valuations and lost profits cases is regression analysis. In reality, it is seen very often.
Coefficient of Determination or r squared (r2)
The coefficient of determination or r squared (r2) is a key component in preparing and understanding the results of the business valuation or lost profits forecasted or projected results. The math to perform the forecast or projection is relatively easy. The analyst can input the data into Excel, or some other program, and with a few keystrokes, there is an answer. The question becomes, how reliable is the answer for the forecast of projection?
The coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event.[1]
The values can range from 0.0 to 1.00.
The coefficient of determination is an overall measure of accuracy of the regression model.
It helps to describe how well a regression line fits (a.k.a, goodness of fit).
An r2 value of 0 indicates that the regression line does not fit the set of data points.
A value of 1 indicates that the regression line perfectly fits the set of data points.
Reasonable Certainty
Reasonable certainty refers to the requirement forecast and projection results must be estimated using reliable methods and evidence. In the world of business valuations and lost profits, we are wanting results that are more than likely than not. This is an r squared of greater than .50. If the r squared is greater than .50, it will provide a more than likely result. If the r squared is less than .50, the result will not be more likely than not and has no predictive power. If there is no predictive power in the r squared, the regression model method should be rejected.
Business Valuation and Lost Profits: How Reliable Are The Experts Forecast?
The regression model is commonly used. If it is not used, the attorney should vet the expert to verify how they have calculated variable costs, cost that will change in relationship to revenues.
Questions:
Ask the expert if they have used a regression model to forecast or project future revenues and or expenses.
Answer:
No. If no, inquire as to how variable costs are determined.
Yes. Ask them to produce their calculations to determine the r squared.
Question: Ask the expert to provide the formula for the r squared.
Question: Ask the Expert to provide a copy of the ANOVA table that is prepared when the r squared is calculated,
No. Follow up and get the ANOVA table after the deposition
Yes. Have someone knowledgeable verify the calculations in the ANOVA table
The ANOVA table is calculated and prepared by EXCEL when the r square is calculated
[1] https://www.statisticssolutions.com/coefficient-of-determination/