# How and when: ridge regression with glmnet

@drsimonj here to show you how to conduct ridge regression (linear regression with L2 regularization) in R using the glmnet package, and use simulations to demonstrate its relative advantages over ordinary least squares regression.

## Ridge regression

Ridge regression uses L2 regularisation to weight/penalise residuals when the parameters of a regression model are being learned. In the context of linear regression, it can be compared to Ordinary Least Square (OLS). OLS defines the function by which parameter estimates (intercepts and slopes) are calculated. It involves minimising the sum of squared residuals. L2 regularisation is a small addition to the OLS function that weights residuals in a particular way to make the parameters more stable. The outcome is typically a model that fits the training data less well than OLS but generalises better because it is less sensitive to extreme