interpretation of square roots coefficient

[Damian CHP]

Dear Statalist Members

I have ran linear regression and I have used square root to deal with the skewed distribution of my dependent variable, my independent variable is a dummy variable (After transformation, sweked, normality and heterocedasticity issues was solved)
Now, I would like to know how to interpret coefficients of independent variables when dependent variable is square rooted or how to transform my regression coefficients back to original values

Thanks for your time

[Rich Goldstein]

for back-transformation, see the following article: Miller, DM (1984), "Reducing tranformation bias in curve fitting", The American Statistician, 38 (2): 124-126

re: interpretation, why do you think that interpretation is different for transformed variables? or, is it that you are uncomfortable dealing with a one-unit change in the transformed metric?

[Nick Cox]

Consider also a generalised linear model with power link.

[Maarten Buis]

Probably the easiest solution is to use glm with power .5 link function. That way you are modeling \(\sqrt{\mathrm{E}(y)}\) instead of \(\mathrm{E}(\sqrt{y})\). This means you can easily use margins afterwards.

sysuse nlsw88, clear
glm wage i.union grade ttl_exp hours, link(power .5)
margins, dydx(*)

[Nick Cox]

I'd consider also log link, e.g. (or according to some i.e.) Poisson regression.

It's common to obsess about marginal distributions, but the biggest deal is getting a good model for the systematic structure in the data. That need not mean normal conditional distributions.

As you have a response and one independent variable (at least according to the first sentence of #1) you should able to show us a plot of the data (e.g. side by side dotplots) and perhaps even list them here is the dataset is not large.