I am trying to decide whether to use a square root transformed dependent variable in multiple linear regression. Transforming $y$ leads to more normally distributed residuals and also to less heteroskedasticity. However, coefficient of determination is reduced compared to the model using the non-transformed dependent variable.
What criterion is most important when deciding whether to use a transformation?
Edit (Background and goal of regression):
I have a large panel data set and I am running a pooled OLS regression. The main goal is to spot how the dependent variable (electricity consumption) differs with different independent variables, so I am mainly interested in the actual parameter estimates.
However, the model should also be useful for prediction, both on individual as well as aggregated level. In my context, aggregated means the sum of individual $y$'s for each day. I suspect modeling aggregated $y$ using the panel model might not be entirely correct. Back-transformation of $y$ when comparing aggregated metered and modeled values still causes some headache... But this is probably yet another question.