Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 5J / a / i / Solution

The individual t-tests only test each regression coefficient after adjusting for the other covariate. Here neither covariate is individually significant at conventional levels, but from the abbreviated coefficient table alone one cannot conclude that neither explains the response: strong multicollinearity can make both standard errors large even when the covariates are jointly useful.