Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 218 6 b Solution Created 2026-10-03 Updated 2026-10-05
The two predictors have correlation coefficient , so there is severe multicollinearity. Their centered slope Gram matrix isThus either partial slope has variance . Relative to a univariate regression with the same error variance, the two-predictor variance inflation factor and standard-error factor areThe small eigenvalue makes the contrast between the two slope effects particularly poorly estimated. The univariate regressions test marginal association with the response; the bivariate tests ask whether one predictor adds an effect while holding its nearly identical companion fixed. Their much larger standard errors therefore make the partial tests insignificant without contradicting the marginal significance. The two fits also estimate slightly different residual variances, explaining why the reported standard-error ratio is not exactly 5.21.