Question

In an OLS regression with severe multicollinearity, R² = 0.94 but no individual coefficient is significant at 5%. The researcher drops one collinear variable. Which consequence should she anticipate?

Q: Answer-In an OLS regression with severe multicollinearity, R² = 0.94 but no individual coefficient is signi...

Classic multicollinearity remedy trade-off If the dropped variable truly belongs in the model, its omission causes OMITTED VARIABLE BIAS in remaining coefficients. However, standard errors fall multicollinearity reduced. The researcher faces Option A ignores OVB. Option C is wrong BLUE requires correct specification dropping a relevant variable violates this. Option D is wrong R generally falls when a variable is dropped.

A Remaining coefficients unbiased, standard errors fall — model now correctly specified

B If the dropped variable is relevant (non-zero true coefficient), remaining coefficients will be biased (omitted variable bias), but standard errors will fall — a bias-variance trade-off

C Dropping the variable eliminates multicollinearity and restores BLUE properties without any cost

D R² will rise because the model is more parsimonious