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)?