# Using standardized Y in Elastic Net

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)?

-