Balancing data-sets for regression problems
First, the histogram you plotted is that of the marginal distribution. The residuals might look perfectly fine once you regress on the variables. Linear regression is an estimation of Y conditional on the variables X; thus, in order to determine whether the distribution is a good fit, you examine the residuals which are assumed to be gaussian.

If you have data that is bounded between an interval, one approach would be modeling it using a beta regression. If the data is constrained to be positive, assuming a gamma distribution could work as well. You must, however, check the diagnostic plots afterwards to ensure that the distribution assumptions that you are making are correct.

See Beta Regression by Ferrari, A Better Lemon Squeezer by Smithson '06, and Extending the General Linear Model by Faraway. Also, for Bayesian implementations of regression models, you could look at Gelman's book.