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I have a linear model which doesn't have any particular issues with its assumptions (diagnostics plots look well). However it has a slighly skewed response (skewness approx. 0.5) and few skew independent variables. Now I would like to try to transform these skewed variables (as well as response) and see if the transformed model is better (that is if it explain response better). However, as far as I know I can't use neither R^2 statistic or AIC/BIC criterion to compare model with different data as they differ in variance. What should I do to compare the new, transform model with the old one? What criterion can I use?

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