Standardizing the target variable aka the dependent variable

Question

I have standardized the independent variables(X) used in feature selection using Ridge regression. Do I need to also standardize the target variable(y)?

Answer 1

No.

Think about this example: if y is 10 times larger, we can make all coefficients 10 times larger.

In fact, if it is OLS but not ridge regression, i.e., without regularization, we even do not need to scale x.

In addition, a relevant post can be found here

Question about standardizing in ridge regression