Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 205 / 5 / a / Solution

With the normalization used in the question, ridge regression solvesDifferentiating with respect to $\mu$ and using the centered columns $X^{T}1=0$ gives $\hat{\mu }=\overline{Y}$. The normal equation for $\beta$ issoThe push-through identity then gives the equivalent dual form