Regularized least squares

Have you ever tried to solve a jigsaw puzzle and found that some pieces don't fit together perfectly? You might have to push them in or pull them out a little bit to make them fit. This is similar to what happens when we try to use a linear regression model to fit data.

Linear regression is a method used to predict an output value based on input variables. It draws a straight line through some points on a graph to make predictions. But sometimes, the points are not perfectly aligned with the line. This means that the model is not accurately capturing the relationship between the input and output variables.

This is where regularized least squares comes in. It's like adding some extra pieces to the puzzle to help the line fit better. The regularized least squares method adds an extra term to the linear regression model, which punishes the model for having large coefficients.

Think of this extra term as a "penalty" for making the line too steep or too wiggly. It helps the model prioritize finding a more simple solution that still fits the data well.

So in summary, regularized least squares is a method to help linear regression models fit data more accurately by adding a penalty term to keep the solution simpler. It's like adding extra puzzle pieces to help the line fit better, even if some points don't perfectly align with it.