Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 6 / d

The nearly identical predictor columns create severe multicollinearity. Their sum is well identified, as shown by the excellent fitted response, but their difference is weakly identified, allowing ordinary least squares to choose huge opposite coefficients with huge standard errors. The independent $N(0,1)$ priors impose the ridge penalty from part c, shrinking that unstable difference toward zero and producing the stable estimates near $(1,1)$.