Ridge regression uses an L2 penalty on coefficients.

Ridge regression uses an L2 penalty on coefficients.

• A. True
• B. False
• C. Uses an L1 penalty
• D. Uses no penalty

Answer: (A)

Ridge regression adds a penalty that is proportional to the sum of squares of the coefficients. This L2 penalty discourages large coefficient values, shrinking them toward zero to stabilize estimates when predictors are correlated. The objective becomes the usual residual sum of squares plus lambda times the sum of squared coefficients: RSS + lambda * sum(beta_j^2). As lambda grows, all coefficients are pulled toward zero, but they are typically not driven exactly to zero, keeping the model dense. This behavior helps reduce variance from multicollinearity, unlike doing nothing (no penalty) or using an L1 penalty (which can drive some coefficients to zero, producing a sparse model).

Ridge regression adds a penalty that is proportional to the sum of squares of the coefficients. This L2 penalty discourages large coefficient values, shrinking them toward zero to stabilize estimates when predictors are correlated. The objective becomes the usual residual sum of squares plus lambda times the sum of squared coefficients: RSS + lambda * sum(beta_j^2). As lambda grows, all coefficients are pulled toward zero, but they are typically not driven exactly to zero, keeping the model dense. This behavior helps reduce variance from multicollinearity, unlike doing nothing (no penalty) or using an L1 penalty (which can drive some coefficients to zero, producing a sparse model).