Which statement regarding the effect of the tuning parameter λ in ridge regression is true?

The correct statement regarding the effect of the tuning parameter λ in ridge regression is that as λ approaches zero, the penalty term has no effect. This means that when λ is very small (approaching zero), the ridge regression formula behaves similarly to ordinary least squares regression because the penalty for larger coefficients becomes negligible. Essentially, the model relies on the regular least squares fitting method, allowing the coefficients to be estimated without any regularization. When the penalty is non-existent, the model freely fits the training data, potentially leading to overfitting if the model complexity is not appropriately managed.

This understanding highlights the importance of λ in balancing the trade-off between fitting the training data well and regularizing to prevent overfitting. Higher values of λ introduce a greater penalty for large coefficients, leading to more shrinkage of the coefficients compared to traditional linear regression, but as it goes to zero, that penalty fades away, returning to the standard regression model behavior.