# Ordinary linear regression vs penalized regression: predictive MSE

Does predicting on a test set with an ordinary linear regression model result in a smaller predictive MSE compared to a penalized regression model (LASSO or ridge)?

• if that were the case, why would we have Lasso or Ridge? – user75138 Oct 21 '15 at 1:56
• I was under the impression that using ridge reduces the variance of the estimates – K23 Oct 21 '15 at 2:02
• That is correct, but that will also increase the bias. The goal is to minimize the MSE by adding a little bias and reducing the variability substantially. – user75138 Oct 21 '15 at 2:37