PCA used for regression



Hello, I am new here. thank you for the opportunity to post. I had a question from an earlier post. titled Practical Guide to Principal Component Analysis (PCA) in R & Python

a few responses are below.

“Really informative Manish, Also variables derived from PCA can be used for Regression analysis. Regression analysis with PCA gives a better prediction and less error.”

“Rightly said. PCA when used for regression takes a form of supervised approach known as PLS (partial least squares). In PLS, the response variable is used for identification of principal components”

I am having trouble finding a good illustration of this. other blogs seemed to indicate that it is not too common for PCA to improve regression (compared to using the original x’s as independent variables).

can anybody advise for a good example, perhaps complete with data that compares using PCA components as independent variables compared to the original x’s (where there is collinearlity) and PCA fares better in predicting (such as comparing by way of RMSE)? thanks John