I'd like to conduct a regression analysis using the entire population's data which I have at my disposal. However, the data of the dependant (Y) variable is not normally distributed (I have run a chi-squared test for normality to confirm this). How do I deal with this situation? Since it cannot be a case of sampling error (the data represents the entire population), I'm not sure what to do. I have eliminated any outliers, but that hasn't made a difference.

Can I go ahead and run the regression analysis even though the Y-variable's data isn't normally distributed? I have of course done this already, for curiosity, and I found that the residuals from that analysis were also not normally distributed, which is not surprising I guess.

Any advice at all would be appreciated.

Thanks!