Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 13L / c / Solution

The nested-model $F$-test has hypothesesIts statistic isThe reported $p$-value $5.252\times 10^{-6}$ gives strong evidence against $H_0$: weight and width are jointly useful.

Neither individual coefficient is significant at $5\%$. This is consistent with the predictor correlation $0.877$: strong multicollinearity makes the two partial effects difficult to distinguish and inflates their individual standard errors, even though their joint contribution is clear.