I am running multiple regression analysis and my dependent variable is not normally distributed (skewness=-1.794 and kurtosis: 4.643). In order to correct this, I applied log transformation but because it is negatively skewed I used this formula: $log(1+max value of DV - DV)$. The inversely and log transformed DV was closer to normally distributed (though inverse transformation was much closer, I still chose log transformation as there is literature on how to interpret log transformation, while none on how to interpret inverse transformation is available to me).
When I run the regression on the transformed DV, I got negative values for unstandardised b which implies that increase in one unit of the predictor would lead to beta*100% decrease in DV. But it is very well known in literature that the increase of that independent variable cannot cause decrease in the dependent variable. I also see reversal of the signs of beta coefficients for some of the other independent variables (as I would expect also to see the increase in both dependent and indepenent variables, not one increase and other decrease).
Does anyone know whether this formula applied to the negatively skewed variable can actually produce such a result (reversal of signs), or something else is wrong? Thank you.