Applies to:  StatTools; @RISK for Excel; @RISK For Project; @RISK Developer Kit

Multicollinearity in StatTools

 

What is Multicollinearity?
Multicollinearity occurs when two or more independent (explanatory) variables in a regression model are highly linearly related. It makes it difficult to distinguish the individual effects of each variable on the dependent (response) variable, potentially leading to misleading coefficient estimates, wrong signs, low t-values, or high p-values.

Testing for Multicollinearity in StatTools

1. Open the Regression dialog in StatTools.

2. On the Options tab, tick Check Multicollinearity and Show Correlation Matrix.

3. StatTools calculates a Variance Inflation Factor (VIF) for each independent variable.

   • Large VIFs indicate multicollinearity.

   • Check the correlation matrix to see which pairs of variables are highly correlated.

   • If a pair has high VIF and high correlation, consider excluding one from the regression.

Understanding VIF

• The VIF measures how much larger the standard error of a coefficient is compared to if the variable were uncorrelated with other predictors.

• Example: VIF = 5.27 → √5.27 ≈ 2.3 → the standard error is 2.3× larger.

• Rule of thumb: VIF > 4 → investigate further; VIF > 10 → serious multicollinearity.

Example: Height vs. Foot Length

• Dependent variable: Height

• Independent variables: Right foot length (Right) and Left foot length (Left)

• Right and Left are nearly perfectly correlated.

Analysis Steps:

1. Correlation matrix shows strong correlations between Height and both Right and Left, and between Right and Left themselves.

2. Regression with both Right and Left:

   • R² = 0.817 → suggests strong relationship.

   • Coefficients can be misleading: Left has a negative coefficient and low significance, despite being truly positively related to Height.

   • Coefficients sum (Right + Left) ≈ true effect.

3. Regression with only Right or only Left:

   • Right alone: Predicted Height = 31.546 + 3.195*Right

   • Left alone: Predicted Height = 31.526 + 3.197*Left

   • Both give nearly identical predictions and correct coefficient signs.

Key Points:

• Multicollinearity affects coefficient interpretation, not overall prediction.

• Symptoms: wrong coefficient signs, low t-values, high p-values.

• Solution: remove or combine highly correlated variables when possible.

• Sometimes diagnosis is less obvious, e.g., salary predicted by age, experience in company, and industry experience. Removing one variable may stabilize coefficients without hurting model fit.

Summary:
Multicollinearity is the presence of strong linear relationships among explanatory variables. Use StatTools’ VIF and correlation matrix to detect it and consider removing or combining variables to improve interpretability.

 

Attachments:
height.xls