I have a continuous dependent variable that is non-normally distributed, skewed to the right (long right tail). I have fit two OLS regression models to this variable.
Model 1 - Regression model of un-transformed dependent variable regressed on the independent variable of interest, and other covariates.
Model 2 - Regression model of log-transformed (normally distributed) dependent variable regressed on the independent variable of interest, and other covariates.
As expected, the residuals of Model 1 are not normally distributed and their variance is heteroscedastic, while the residuals of Model 2 are normally distributed and variance is homoscedastic. However, the coefficient of my variable of interest in Model 2 is more difficult to interpret because of the dependent variable transformation. My understanding of the normal error distribution assumption of a regression model is that if it is violated, coefficient p-values may be biased.
My question - Are there any alternative inference options available for me to use Model 1 with interpretable coefficients, while still getting appropriate p-values for coefficient inference? Is bootstrapping an option here? Does residual variance heteroscedasticity come into play?