I am working with GLS linear models. I have a transformed dependent variable (log) and 2-3 independent variables. Now I am aware of the basic ideas surround scaling and/or centering variables. I am attempting to center independent variables so all variables have a mean of 0 but retain the original units. My question is: if I have centered my independent variables when building the model (coefficients remain the same, but intercept changes) should I be doing anything to new input variables when running the model to make predictions? i.e., should I also center input variables when running the model with the parameters that were generated from building the initial model with centered variables?