This week, I am discussing the using of regression analysis to make projections or forecasts of revenues and determining fixed and variable or saved costs in a damages model.  However, before I get started I want to reiterate again that the example I am showing is from actual cases and this is what business valuation experts are actually doing.  I have found these errors in large and small firms.

### What is the Coefficient of Determination (r2)?

The coefficient of determination is the proportion of variability or difference between two variables that are being used to make a projection or forecast.  The less the difference in the two variables, the projection or forecast result is more reliable.  The coefficient of determination (r2) can range from zero to one with zero representing no reliability on the predictive power of the results and 1, representing a 100% reliability of the predictive power of the result.

### Interpretation of the Coefficient of Determination (r2)

When making a projection of forecast for a business valuation or damages or lost profits case, we want to use data that will provide the higher coefficient of determination.  In the world that business valuation or damages expert practices in, the coefficient of determination (r2) results should indicate a result having a strong relationship and a good predictive power.

The ability to have predictive power is indicated by having a coefficient of determination greater than 0.50 or 50%.

The same is true in the area of damages or lost profits cases.  These types of cases dictate that the expert determine the fixed costs and the saved costs.  The same coefficient of determination (r2) can be used and should use the same criteria of greater than .50 to have a greater than 50% chance of the data having a strong predictive ability.

In the expert’s business valuation report, they used 0.02 for the coefficient of determination.  The table and chart below indicates the there is no useful pattern of the historical data with a 0.02 coefficient of determination.

As indicated by the line graph, the data using a 0.02 coefficient of determination is extremely erratic and has no pattern that can be used for making projections using regression analysis.

I changed some of the historical and obtained a 0.8 coefficient of determination (r2).  The table and chart below indicates the pattern of the historical data with a 0.8 coefficient of determination.  There is an obvious trending of the data.  The 0.8 coefficient of determination indicates that there is a good fit of the data and could be used for making projections or forecasts using regression analysis.

### Comment

When attorneys notice that the coefficient of determination, typically indicated by r2, is less than .50, there is no predictive power in the data that is being used.  The dataset should not be used for making predictions using regression analysis.  It is important for the attorney to have a basic understanding of this concept so that they can easily recognize and understand the issues at hand.

Why should the attorney care?

The attorney will be advised of a result that does not have a basis for reliability.

The unreliable value or damage amount may be to the detriment of your client and this may be embarrassing to explain to a client.

I provide a more thorough analysis in a report so it will withstand scrutiny.

I provide calculations imbedded in the report for most analysis instead of just stating a result.

I have earned the most difficult business valuation designations for valuations of closely held companies.

I have earned a Master’s Degree in Business Valuations and apply those skills to my everyday business valuations.

Because you as the attorney need to detect the deficiencies in business valuation (damages reports).  The better informed you are, the better the outcome of your cases…for you and your clients!

Richard Claywell has been valuing closely held companies since 1985.  He has earned two of the highest designations in the business valuation field , the Certified Business Appraiser (“CBA”) and Accredited Senior Appraiser (“ASA”),  Richard is a Certified Public Accountant, has a Master’s in Business Valuation (MBV)  and holds the ASA, CBA, ABV, ICVS, CVA, MAFF, CFD, CVGA, ICVS-A credentials.