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When is Ridge regression favorable over Lasso regression?

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Final answer:

Ridge regression is better when there are many small or moderate effects and you have more predictors than samples, as it shrinks the coefficients but keeps all features. Lasso regression is better for simpler models, shrinking some coefficients to zero, offering feature selection and interpretability.

Step-by-step explanation:

Ridge regression is generally favored over Lasso regression in scenarios where there are many small or moderate-sized effects. In cases where the number of predictors (variables) is greater than the number of observations, Ridge regression tends to perform better because it includes all predictors in the final model, just shrinking their coefficients towards zero. Ridge regression uses L2 regularization which adds a penalty equivalent to the square of the magnitude of coefficients. This discourages large coefficients, but does not set any of them to zero, and thus preserves all features in the model.

Lasso regression, on the other hand, is preferable when we are trying to build simpler and more interpretable models since it uses L1 regularization, which can shrink some coefficients to zero, effectively performing feature selection by removing non-important features. It typically works well when we have a smaller set of significant predictors.

To sum up, choose Ridge when dealing with many small-sized effects and when model complexity is not an issue. Choose Lasso when interpretability is a priority and you suspect only a subset of predictors truly matter.

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