Tolerance in regression analysis indicates multicollinearity. Which statement is true?

Tolerance in regression analysis indicates multicollinearity. Which statement is true?

• A. Values below 0.9 indicate serious multicollinearity problems.
• B. Tolerance is identical to VIF.
• C. Values below 0.1 indicate serious problems, though values below 0.2 are worthy of concern.
• D. Tolerance measures model fit.

Answer: (C)

Tolerance shows how much of a predictor’s variance is left after accounting for the other predictors. It’s computed as 1 minus the R^2 from regressing that predictor on the other predictors, so a small tolerance means the predictor is almost a linear combination of the others, signaling multicollinearity. Values below 0.1 indicate serious multicollinearity; values below 0.2 are a warning sign worth investigating. This makes the statement true. Tolerance is not identical to the Variance Inflation Factor (VIF)—VIF is the reciprocal of tolerance (VIF = 1 / tolerance). It also isn’t a measure of overall model fit; it’s a diagnostic for multicollinearity. The other descriptions—tolerance needing to be below 0.9 for problems, or tolerance measuring model fit—don’t fit the concept.

Tolerance shows how much of a predictor’s variance is left after accounting for the other predictors. It’s computed as 1 minus the R^2 from regressing that predictor on the other predictors, so a small tolerance means the predictor is almost a linear combination of the others, signaling multicollinearity.

Values below 0.1 indicate serious multicollinearity; values below 0.2 are a warning sign worth investigating. This makes the statement true. Tolerance is not identical to the Variance Inflation Factor (VIF)—VIF is the reciprocal of tolerance (VIF = 1 / tolerance). It also isn’t a measure of overall model fit; it’s a diagnostic for multicollinearity. The other descriptions—tolerance needing to be below 0.9 for problems, or tolerance measuring model fit—don’t fit the concept.