= Solution
Choose $\lambda$ to minimize an estimate of out-of-sample <mean squared prediction error>, commonly <K-fold cross-validation> or a separate <validation set>. As $\lambda$ increases, the coefficient vector is shrunk toward zero. This generally increases <bias of an estimator> but decreases <variance of an estimator>; the minimizing value balances the two contributions in the <bias-variance tradeoff>. The independent test set in the question can assess the final choice, but repeatedly selecting $\lambda$ on that same set would cause <data leakage>.
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