A large variance inflation factor in a linear regression model indicates strong linear correlation among features and may lead to overfitting. In this chapter, we address this issue by regularizing the objective function with the \(l^2\) -norm of the parameter vector and introduce the ridge regression model. We also study the LASSO (least absolute shrinkage and selection operator) method, which employs \(l^1\) -regularization. Since the \(l^1\) -norm is not differentiable, we introduce the concept of the subdifferential and formulate the problem within the framework of convex optimization. An iterative algorithm is then derived to compute a numerical solution for linear regression with \(l^1\) -regularization.