What is a consequence of multicollinearity in regression?

Prepare for the Pearson Revel Test with multiple-choice questions and detailed explanations. Ace your exam with confidence!

Multiple Choice

What is a consequence of multicollinearity in regression?

Multicollinearity makes the individual effects of predictors hard to pin down. When predictors are highly correlated, the information each one adds about the outcome is redundant, so the design matrix X becomes nearly singular. In OLS, the variance of a coefficient estimate is proportional to the inverse of X'X, so as X'X becomes ill-conditioned, those variances explode. That inflates the standard errors, making the coefficients imprecise and highly sensitive to small changes in the data. As a result, the estimated coefficients can wiggle in sign or magnitude across samples, even though the overall model fit may still look good. This is the core issue: inflated standard errors and unstable coefficient estimates.

Multicollinearity makes the individual effects of predictors hard to pin down. When predictors are highly correlated, the information each one adds about the outcome is redundant, so the design matrix X becomes nearly singular. In OLS, the variance of a coefficient estimate is proportional to the inverse of X'X, so as X'X becomes ill-conditioned, those variances explode. That inflates the standard errors, making the coefficients imprecise and highly sensitive to small changes in the data. As a result, the estimated coefficients can wiggle in sign or magnitude across samples, even though the overall model fit may still look good. This is the core issue: inflated standard errors and unstable coefficient estimates.

More practice questions