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This lecture covers the concept of regularization in linear models, focusing on Ridge Regression and the Lasso. It explains how to make linear models less flexible by fixing parameters or favoring small ones. The instructor discusses the analytical solutions for simple linear regression, the alternative formulations of regularization, and the standardized inputs for regularization. The lecture also delves into polynomial ridge regression, multiple logistic ridge regression, and the Lasso path for weather data. It concludes with a summary highlighting the benefits of regularization in model flexibility and interpretability.