Under which condition does ridge regression outperform lasso regression?

Under which condition does ridge regression outperform lasso regression?

• A. When the response variable is unrelated to the predictors.
• B. When there are fewer predictors than observations.
• C. When the response is a function of all predictors.
• D. When the variables are not collinear.

Answer: (C)

Ridge regression tends to outperform lasso regression in scenarios where the response variable is a function of all predictors, particularly when the predictors exhibit multicollinearity. Ridge regression is designed to handle situations where there are many correlated predictors by applying a penalty to the size of the coefficients, which helps to stabilize estimates and reduce variance. In cases where the underlying relationship involves all variables, ridge regression distributes the coefficient shrinkage across all predictors. This means that even if predictors contribute similarly to the response variable, ridge regression will retain all predictors in the model and provide more robust estimates. By contrast, lasso regression can force some coefficients to be exactly zero, potentially excluding predictors that are indeed informative but might not stand out due to the correlations present among the variables. Thus, when the response is truly related to all predictors, utilizing ridge regression allows for retaining all information without arbitrary exclusion, making it the preferable choice in this context.

Ridge regression tends to outperform lasso regression in scenarios where the response variable is a function of all predictors, particularly when the predictors exhibit multicollinearity. Ridge regression is designed to handle situations where there are many correlated predictors by applying a penalty to the size of the coefficients, which helps to stabilize estimates and reduce variance.

In cases where the underlying relationship involves all variables, ridge regression distributes the coefficient shrinkage across all predictors. This means that even if predictors contribute similarly to the response variable, ridge regression will retain all predictors in the model and provide more robust estimates. By contrast, lasso regression can force some coefficients to be exactly zero, potentially excluding predictors that are indeed informative but might not stand out due to the correlations present among the variables.

Thus, when the response is truly related to all predictors, utilizing ridge regression allows for retaining all information without arbitrary exclusion, making it the preferable choice in this context.