Best regression correcting for non-normality, outliers and heteroskedasticity We are performing a regression on cross-sectional data for $Y$ = subjective well-being (scale 0-10) and $X$ = working hours (divided into 5 dummy categories; less than 27 hours, 27-32 hours etc). 
After having performed statistical tests we have the following: 


*

*Non-normality in the residuals 

*Heteroskedasticity (when control variables are included) 

*Outliers and leverage 
Our question is now whether OLS still can be applied to our regression, despite the high kurtosis in the residuals (violation of the non-normality assumption)?
In that case, which is the best OLS regression to run that corrects for all the violations mentioned above (e.g. PROCREG)?
We have read that quantile regression can be appropriate as it does not require normality in the residuals. We are however only familiar with OLS regressions, and thus we do not really know what implications it will have for the other tests. Would be great to get some tips about how to best proceed now. 
Furthermore, how do we perform a simple test for spatial regression in SAS (EG)?
 A: I am no expert of the wellbeing literature, but I guess that a viable route is to transform the outcome variable into a dummy variable.
It could equal 0 if the original y is lower than the median and equal 1 is it is higher than the median.
I think this transformation is good starting point. 
Usually, wellbeing is around 7.5/10 whatever country whatever study; this is why the distribution is skewed and dummy based on the median of y is better.
Of course, the second step would be to use the ordered logit model...but beware of all the related problems. As someone has already suggested, better to start from the UCLA website to seek for information on this econometric model.
A: I'm not familiar with quantile regression. However, a typical approach to the problems you are facing is to transform the data.
Have you tried transforming the outcome to get it to approximate a normal distribution?
Have you examined the bivariate relationships with the (transformed) outcome with the predictors and explored transforming the predictors in order to get a more linear relationship? (It would certainly by my inclination to start with the IV ungrouped and used as a continuous variable if that makes sense theoretically and practically.)
These operations do make interpretability of the result more difficult, but they may allow you to use OLS, which is well known by most producers (and consumers) of research.
Next, do you mean a test for spatial autocorrelation? There is an explanation for doing this in SAS here: http://support.sas.com/kb/22/944.html 
EDIT: I hope it's reasonable to say that there are almost always methods that better fit the theory, research question, dataset, and so on. However, better methods are sometimes beyond the technical capability of the analyst. If that is the case, and it is not remediable, a good practice is to be explicit about things like failures of assumptions and to use the best possible method. 
