# Log transformation for percentages or proportion in regression

I am doing a study understanding impact of vehicle registration fee on vehicle miles travelled. I am using linear regression and figured out that log transformation of dependent variable and some of the control variables improves the R2 and reduces standard error. I have a few control variables that are in percentages / proportions. I checked them for normality and their are normally distributed, but I still have to log transform them as R2 improves by it as compared to when they are not log transformed. Can someobody explain me why this happens?

• Adding to gel_b's answer, after nonlinearly transforming the R2 will be on another scale, so not directly comparable. – kjetil b halvorsen Feb 26 '17 at 10:35

However, if you're trying transformations and choosing one with higher $R^2$ and then using the same data for hypothesis tests or confidence intervals or prediction intervals among other things (i.e. using the same data on which you chose a model to evaluate the model or predict from it) then the statistical procedures don't have the properties they're intended to -- among other things, p-values are too low, standard errors are too small.