Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 218 / 2 / a / Solution

Because the columns of the design matrix are centred, ridge regression with an unpenalized intercept solvesThe normal equations give, for $\lambda >0$,The fitted values are consequentlyIf the objective is normalized by $n$, the same formulas hold after replacing $\lambda$ by $n\lambda$.