Applies to:
@RISK for Excel 5.x and Up

Interpreting Regression Coefficients in @RISK Tornado and Sensitivity Reports

 

Overview

Regression coefficients on tornado diagrams and sensitivity reports in @RISK indicate how much each input affects the output. They are calculated using stepwise multiple regression.

• Longer bars or larger coefficients = greater impact

• Positive coefficient (bar to the right) → increasing input increases output

• Negative coefficient (bar to the left) → increasing input decreases output

Types of Regression Coefficients

@RISK provides three types of regression coefficients, depending on the function or graph:

Type	Description
Regression Coefficients	Scaled or normalized by standard deviations of input and output (unitless).
Regression Coefficients — Mapped Values	Scaled to output units per standard deviation of input.
Unscaled Regression Coefficients	Actual coefficients used in the regression equation (units of output per unit of input).

1. Regression Coefficients (Standardized)

• Expressed in standard deviations (SD).

• Example: Input A has a coefficient of 0.78 → for every k SD increase in Input A, the output increases by 0.78 × k SD.

• To convert to actual units:

[
\text{Actual coefficient} = \text{Standardized coefficient} \times \frac{\text{SD of output}}{\text{SD of input}}
]

Example Calculation:

• SD(Output) = 12,784

• SD(Input A) = 1,000

• Coefficient = 0.78

[
0.78 \times \frac{12784}{1000} \approx 10
]

A 1-unit increase in Input A corresponds to a 10-unit increase in output.

2. Regression — Mapped Values

• Expressed as units of output per standard deviation of input.

• Example: Mapped coefficient of 10,023.53 → increasing Input A by 1 SD increases output by 10,023.53 units.

• Multiple SDs:

[
\text{Change in output} = \text{Mapped coefficient} \times k
]

Example:

• SD(Input A) = 1,000

• k = 2 SD increase → output increases: 10,023.53 × 2 = 20,047.06 units

Mapped values are easier to interpret in terms of real-world units, rather than standard deviations.

3. Using the Regression Tornado Graphs

• In Browse Results or with the RiskResultsGraph function, you can choose “regression coefficients” or “regression coefficients — mapped values”.

• With the RiskSensitivity function, you can also access unscaled regression coefficients.

• The tornado graph shows the impact visually: bar length represents magnitude, direction represents positive/negative effect.

Tip: Always check whether the coefficients are standardized or mapped before interpreting them in real-world units.

Actual (Unscaled) Regression Coefficients

Related Article:

Regression Coefficients in Your Worksheet

 

Attachments:
KB138_Sensitivity.docx
KB138_TornadoCoefficients.xlsx