linear regression Johnson Transformation

If two predictor variables transformed by the Johnson Transformation (see Minitab or Johnson 1949) are used in separate linear regressions (assuming the same response variable and sample sample size of predictors in each single predictor variable model) can the R-squared output of separate linear regression using each of these variables be compared? My concern is that the Johnson transformation uses an ever so slightly different function/equation to bring each predictor to a normal distribution.

I know Aikaike's Weight Criterion is an option to compare models, but I am still interested in the R-squared comparison; i.e. is it possible?

Thanks for your help! Thanks for reading!


Ambassador to the humans
Your predictor variable doesn't need to be normally distributed to do a regression so I don't see the point. All you're doing is creating a new variable in my mind and if all you're saying is that you're running two different univariate linear regressions using a different predictor but the same response variable then sure it's fine to compare the r-squares of the models. But maybe I'm misinterpreting what you're saying.