Are there predictive benefits to Box-Cox/Yeo-Johnson on an outcome/dependent variable?

Suppose we have a simple regression model with non-normal residuals. Transform the outcome variable with Box-Cox or Yeo-Johnson and fit a linear regression. Evaluating on a suitable test set, take the resulting response variable results, reverse the transformation, and find the R^2. Is there any reason to expect a better R^2 from this procedure than from a fit without transforming the response variable?

I'm under the impression that the most compelling reason to transform your response variable in a simple regression is to allow you to validly apply more statistical tests. I'm trying to see if I'm misguided on that front.

• Do not pre-emptively declare that your question is simple; it is for readers to judge this matter. (In the present case your question assumes reader familiarity with regression analysis, two types of variable transformations, and statistical prediction.)
– Ben
Feb 6, 2022 at 21:08
• That's fine. Change the wording however you like. I'm more interested in some kind of an answer, though. Feb 7, 2022 at 0:11
• The answer must depend in part on what you mean by "better" predictions: how do you propose to measure the goodness of the predictions?
– whuber
Feb 12, 2022 at 20:00
• A fair question. R^2 in addition to RMSE or MAE, depending on the data and how outlier heavy it is. Feb 13, 2022 at 0:49
• Yes, I should have been clearer; I will edit the question. The focus of my analysis is on R^2 of the response variable as originally expressed (evaluated on a suitable test set, not used to train the model). I was focused on training a model with a transformed response variable, fitting it on test data and then reversing the transformation to get results as originally expressed. Then, take R^2. I have not found a dramatically improved R^2 from this procedure in the wild on a variety of datasets. Feb 13, 2022 at 21:39