# How to find a model for data with anomalous error

I have some data which seems to be distributed along a line with large negative erros

$$Y \sim X - \epsilon \,\,$$ with $$\, \, \epsilon \in [0, \infty)$$.

Somehow, the error is not gaussian and there are some levels which are more probable than others. A OLS fit of the corresponding tangent does not return the correct slope of the lines. Do you have any ideas how to deal with this data?