How to improve your linear regression with basis functions and regularization

This post is a part of a series of posts that I will be making. You can read a more detailed version of this post on my personal blog by clicking here. Underneath you can see an overview of the series. We say that a model is linear if it's linear in the parameters not in the input variables. However, (1) is linear in both the parameters and the input variables, which limits it from adapting to nonlinear relationships.