How do we detect multicollinearity?

How do we detect multicollinearity?

• A. Tolerance smaller than 0.1 and/or Variance Inflation Factor greater than 10.
• B. p-values all below 0.01.
• C. Residuals are normally distributed.
• D. R-squared equals 1.

Answer: (A)

Multicollinearity shows up when independent variables are highly related to each other, making it hard to assess the unique effect of each predictor. The standard diagnostic tools are tolerance and the variance inflation factor (VIF). Tolerance is the portion of a predictor’s variance that is not explained by the other predictors; when tolerance is very small (less than 0.1), it signals that the variable shares a lot of variance with others. VIF, the reciprocal of tolerance, directly measures how much the standard error of a coefficient is inflated because of multicollinearity; a VIF above 10 is a common rule-of-thumb threshold indicating problematic multicollinearity. The other options don’t diagnose multicollinearity. P-values below a certain level reflect whether predictors are statistically significant, not whether predictors are interrelated. Normality of residuals relates to another regression assumption (distribution of errors). An R-squared of 1 would mean perfect fit, but it doesn’t specify whether multicollinearity is present or how it affects individual coefficient estimates.

Multicollinearity shows up when independent variables are highly related to each other, making it hard to assess the unique effect of each predictor. The standard diagnostic tools are tolerance and the variance inflation factor (VIF). Tolerance is the portion of a predictor’s variance that is not explained by the other predictors; when tolerance is very small (less than 0.1), it signals that the variable shares a lot of variance with others. VIF, the reciprocal of tolerance, directly measures how much the standard error of a coefficient is inflated because of multicollinearity; a VIF above 10 is a common rule-of-thumb threshold indicating problematic multicollinearity.

The other options don’t diagnose multicollinearity. P-values below a certain level reflect whether predictors are statistically significant, not whether predictors are interrelated. Normality of residuals relates to another regression assumption (distribution of errors). An R-squared of 1 would mean perfect fit, but it doesn’t specify whether multicollinearity is present or how it affects individual coefficient estimates.