Multicollinearity and Variance Inflation Factor Quiz

Answers and explanations appear as you take the quiz.

1. In an auxiliary regression for a predictor, R-squared equals 0.8. What VIF follows from 1 divided by (1 minus R-squared)?
   • 1.25
   • 4
   • 5
   • 0.2
2. Two predictors are exact unit conversions of the same measurement. What issue does this create in an ordinary design matrix?
   • Perfect linear dependence
   • Near dependence that leaves coefficients estimable but unstable
   • A large but imperfect correlation between the two columns
   • Different measurement units for the same predictor
3. A model predicts well, but the signs of two correlated predictors' coefficients change across samples. Which interpretation fits?
   • Prediction quality proves the coefficients are stable
   • Overlapping predictor information can destabilize individual effects
   • The response must have been measured in the wrong unit
   • The VIF measures only residual normality
4. A VIF is large. What conclusion is justified by that value alone?
   • The predictor must be removed
   • The model is unusable for every purpose
   • The predictor has strong linear overlap with other included predictors
   • The model has poor held-out accuracy
5. For a VIF of 5, by what factor is the coefficient standard error inflated under the stated comparison?
   • 5
   • The square root of 5
   • 25
   • 0.2
6. Why might dropping a high-VIF feature be a poor automatic response?
   • It can change the research question or create omitted-variable bias
   • The VIF of every remaining predictor must be unchanged after removal
   • Removing a predictor guarantees that all remaining coefficients are unbiased
   • A large VIF directly proves held-out predictions will be poor
7. What can centering help with in a polynomial regression?
   • Nonessential correlation between a raw predictor and its powers
   • Every form of substantive predictor overlap
   • Dependence between successive time observations
   • Incorrect outcome measurements
8. If the goal is prediction and correlated predictors are useful, which remedy can be considered?
   • Ridge regularization with evaluation on appropriate data
   • Use lasso and expect it to retain every correlated feature together
   • Use unregularized coefficients and interpret each as stable
   • Replace predictors with principal components while preserving their original coefficient meanings