# If you standardize X, must you always standardize y?

Background:

I am comparing the effectiveness of various forms of linear regression machine learning, such as sklearn.linear_model.Ridge, sklearn.linear_model.Lasso, sklearn.svm.SVR.

Question:

The linked questions above discuss various reasons to standardize, center, or neither the predictor variables in regression settings. If I standardize the X matrix do I have to then standardize the y array? If I center the X matrix do I have to center the y array?

For either of those situations, would failing to standardize/center give me incorrect results?

• NO, just because you standardized $X$ (or some of them) do not force you to standardize $y$ also. Ask yourself: Why do I standarize? and see what the standarization is doing. Otherwise see: stats.stackexchange.com/questions/244507/… Commented May 9, 2017 at 20:02
• So I know that for simple linear regression you do not need to standardize y (or x for that matter). I am asking about various other methods, like ridge, lasso, and SVR. It is not clear to me that the argument you linked applies to those methods. Commented May 9, 2017 at 20:10
• They applies. ridge and lasso are not invariant, so needs standardization. But they only need it for $X$, not $y$ (but standardizin $y$ do no harm). I do not know about SVR, but the same principles apply. Commented May 9, 2017 at 20:13

NO, just because you standardized the predictors $X$ do not force you to standardize the response $y$. Ask yourself "Why do I standardize?" and see what the standardization is doing. Some answers to that can be found at: What algorithms need feature scaling, beside from SVM? As to the additional question in comments: The arguments in my answer linked at above do also apply for ridge and lasso. The arguments to standardize $X$ in those cases do not apply to $y$ (but if you want you can standardize $y$ too, it does no harm, but can complicate interpretations). The same principles apply to SVR, but I do not know the answer in that case.