I have a question regarding the validity of transforming the predicted response from a regression model when the response has been log-transformed.
I'm completing an exercise geared towards fitting different model types to training data to predict a response variable (price) in the test data. The distribution of price in the training data made it obvious that a log-transform would help, so this was done. We then fit a variety of models (ordinary ols, glm, gam, pls) in R, computed the training RMSE, and the validation RMSE. I now must take the test data, predict the response, and submit it for the evaluator to check my test RMSE.
My question comes to the prediction itself - is it safe to assume that I can just exponentiate my predicted response since it will be in terms of $\log(x)$? Or do I need to perform some other kind of transformation?