What is a consequence of multicollinearity among predictors?

• A. It reduces residual variance
• B. It inflates standard errors, making it harder to detect unique predictor effects
• C. It increases the model's p-values but decreases R-squared
• D. It has no impact on the model interpretation

Answer: (B)

Multicollinearity happens when predictors are highly correlated, so the information each predictor adds overlaps with what another provides. This makes the estimated coefficients unstable across samples and, crucially, inflates their standard errors. With larger standard errors, the t-statistics drop, which leads to higher p-values and less evidence that a predictor has a unique effect while holding the others constant. In practice, you can still have a model that fits the data reasonably well overall, but you struggle to interpret the individual contributions of correlated predictors because their effects can trade off with one another. The residual variance—the portion of outcome variability not explained by the model—doesn’t get reduced by multicollinearity in itself. Similarly, R-squared, which reflects overall fit, can stay the same or even rise when adding correlated predictors, so it’s not a reliable indicator of multicollinearity’s presence. The key consequence, then, is the inflation of standard errors and the resulting difficulty in detecting and interpreting unique predictor effects. If needed, addressing it can involve removing or combining predictors or using regularization methods like ridge.