Transforming highly left skewed x with log((-1)*x+max(x)) in linear regression I have a highly left skewed variable  (see plot) in a linear regression model for inference. Transforming right skewed data is rather easy by applying the log, for lewft skewed I could not find a suitable transformation which still lets me easily interpret my estimated coefficients so I thought about applying log((-1)*x+max(x)) which would leave me with the following:

Does that makes sense at all and if so how would could you interpret the estimated cooefficients? Scaling by (-1) would just invert the interpretation? And how does the shift by max(x) would change the interpretation?
Thanks in advance a lot for your answers and help!
Best regards
 A: Linear regression features do not have to be normal.
Transforming features to achieve (rough) normality does not make sense to me. It can be useful to do a $\log$ transform to put the interpretation in terms of percent change, yes, but that has nothing to do with feature distribution and everything to do with wanting that interpretation in terms of percent change. It might be that applying the $\log$ transformation brings your feature closer to normality, but that need not occur for the $\log$ transformation to be useful.
You want to transform if that aids your interpretation or model fit, not to satisfy a nonexistent assumption that the features be normal. It is a common misconception that linear regression features have to be normal, I suspect because of the assumption about model errors being normal in order to do the usual inferences (t-test, F-test, confidence intervals). However, that is a misconception, nonetheless. Linear regression features do not have to be normal.
(The normality assumption comes from doing maximum likelihood estimation with a Gaussian/normal likelihood, and that derivation never concerns itself with feature distributions.)
If you like the $\log$ transform because of the interpretation in terms of percent, then $\log$-transform your feature.
