In a multivariable model, what indicates multicollinearity, and how can you detect it?

• A. Predictors are highly correlated; detect via p-values.
• B. Predictors are highly correlated; detect via correlation matrix only.
• C. Detect multicollinearity with the Variance Inflation Factor (VIF) and tolerance; high VIF (>5-10) indicates concern.
• D. Multicollinearity improves model stability, so no action is needed.

Answer: (C)

Multicollinearity shows up when predictors are so interrelated that they share the same information, which inflates the variance of each coefficient and makes it hard to disentangle the individual effect of a predictor.

A practical way to detect it is to use the Variance Inflation Factor and tolerance for each predictor. For every predictor, you regress it on all the other predictors and look at how well it’s explained by them (that is, the R-squared from that regression). The VIF is 1 divided by (1 minus that R-squared). A large VIF means that the predictor’s variance is being inflated by its linear relationship with the others. Common guidance flags VIF values above about 5 or 10 as potential problems, and corresponding tolerance values below 0.2 or 0.1 as warnings.

Relying only on a correlation matrix isn’t enough, because high pairwise correlations don’t always capture the broader, multivariate structure that causes multicollinearity. Conversely, you can have multicollinearity without any single pair of predictors being highly correlated, but still have inflated variances due to their combined relationships.

If multicollinearity is present, you might address it by removing or combining correlated predictors, or by using regularization techniques that handle multicollinearity, such as ridge regression.