I have a very urgent question. Do I center a regressor before I exclude outliers from the dependent variable or after? It would change the mean of the regressor because the data points that are an outlier for the dependent variable, their value of the regressor wil not be included in the mean of the regressor that is used to center it. Is there a convention in what order it should be done?

I hope I put my question in words correctly.

I would apppreciate every hint very much.