What is multicollinearity and why is it a problem in regression analysis?

• A. Low correlation among predictor variables; leads to biased estimates
• B. Nonlinearity between predictor and outcome; causes model to fail to converge
• C. Small sample size; increases the risk of overfitting
• D. High correlation among predictor variables; inflates standard errors and makes estimates unstable

Answer: (D)

Multicollinearity happens when predictor variables are highly correlated with each other, making it hard to separate their individual effects on the outcome. In regression, the goal is to estimate how each predictor uniquely contributes, holding the others constant. When predictors carry similar information, the model struggles to attribute changes in the outcome to one predictor versus another, and the mathematics amplifies this ambiguity. This shows up as inflated standard errors for the coefficient estimates, which means wider confidence intervals and less precise tests of whether those predictors matter. The estimates can also become unstable—small changes in the data can lead to large swings in the estimated coefficients or even changes in their signs—while the overall model fit might look fine. This is why the situation is described as high correlation among predictors that inflates standard errors and makes estimates unreliable. Remedies include removing or combining redundant predictors, or using techniques like regularization or dimensionality reduction to reduce the impact of the collinearity.