I have an Elastic Net model that is selecting a number of variables from X, for prediction of Y. The assumption for Elastic Net is that X is standardized (I'm using Z-Scores), and Y is centered around zero (I'm using Y-mean(Y)). So, I am wondering if my Elastic Net model will act differently if I use both standardized X and Y (i.e., z-scores for both X and Y)?
I figured out that one should stick with the assumption of ElasticNet, and use standardized predictors and CENTERED outcome. Standardized outcome should not be used and it will lead to different results.