HomeTechniques and Tips@RISK Simulation: Graphical ResultsInterpreting Regression Coefficients in Tornado Graphs

# 7.8. Interpreting Regression Coefficients in Tornado Graphs

Applies to:
@RISK for Excel 5.x–7.x

How can I interpret the regression coefficients on the tornado diagram or sensitivity report produced by @RISK?

The regression coefficients are calculated by a process called stepwise multiple regression.

The main idea is that the longer the bar or the larger the coefficient, the greater the impact that particular input has on the output that you are analyzing. A positive coefficient, with bar extending to the right, indicates that this input has a positive impact: increasing this input will increase the output. A negative coefficient, with bar extending to the left, indicates that this input has a negative impact: increasing this input will decrease the output.

In Browse Results and with the RiskResultsGraph function, you can get "regression coefficients" or "regression coefficients—mapped values". With the RiskSensitivity function, you can get either of those measures and also the unscaled coefficients that would be used in a regression equation. Please open the attached workbook and click Start Simulation. It shows both types of regression tornados and all three types of coefficients.

Regression Coefficients

The graph labeled simply "regression coefficients" does not express them in terms of actual dollars or other units. Rather, they are scaled or "normalized" by the standard deviation of the output and the standard deviation of that input.

For the output, Input A has a regression coefficient (standard b) of 0.78. That means that for every k fraction of a standard deviation increase in Input A, the output will increase by 0.78k standard deviations (SD). To get from that coefficient to the actual coefficient in terms of units of input and units of output, multiply by the SD of the output and divide by the SD of the input. 0.78 × 12784 / 1000 = about 10,and therefore a 1-unit increase of A corresponds to a 10-unit increase of the output.

Regression – Mapped Values

Regression coefficients—mapped values are in units of output per standard deviation of input. For example, Input A has a mapped coefficient of 10013.4, meaning that an increase of k fraction of a standard deviation in Input A produces an increase of 10013.4k units (not standard deviations) of the output. The standard deviation of Input A is 1001, and therefore every unit increase in Input A is 1/1001 of a standard deviation and impacts the output positively by 10013.4 × (1/1001) = 10.003 units of output.

Actual (Unscaled) Regression Coefficients

There is no option to show these on the graph, but you can get them from the worksheet function RiskSensitivity. The attached workbook shows examples in row 26; for more information please see Regression Coefficients in Your Worksheet.