Using Ridge weights on original X matrix

[dunrokay]

My question:

If you have a set of features/variables for which you perform ridge regression (X features with a Y dependent variable), to generate weights/scores,

which is the most statistically sound approach of applying the ridge weights to the original standardized (mean = 0, SD=1) X matrix so that you can perform other downstream analyses?

Is it okay to just apply the ridge weights directly: |ridge weights| * Xmatrix? Where you multiply the i_th row of X by ridge weights [i].

Just to be clear, I am aware of Rick's response here https://communities.sas.com/t5/Statistical-Procedures/Ridge-regressions-with-weights-proc-reg/td-p/3...  BUT I need some clarity..got a little confused with the square root explantion.

I'm trying to understand how to make use of the weights in the most appropriate manner/multiply the original X matrix with the weights.

Many thanks!

[Rick_SAS · Accepted solution]

I'm sorry, but I cannot understand your question. Please provide data and output from the ridge regression (PROC REG) so that we can clarify what you are trying to do.

If you want to understand how to formulate ridge-regression in terms of matrix operations on centered and scaled data, see the article "Understanding ridge regression in SAS," which shows the matrix formulation and how to reproduce the output of PROC REG by using the matrix equations.