I keep telling people in my profession who didn't really learn important things in school: "regression" should really be called "iid regression".
For example: time-series econometrics is a whole field dedicated to try to squeeze iid information from stuff that's not iid. So you can use regression.
But they're receptive to my message because they were repetitively warned that curve fitting was not regression analysis. Somehow this is lost in our "data" culture.
There is more than certainly forms of regressions that can work on heteroskedastic errors, i.e. non-iid (can be clustering, autoregressive, or more), but part of the general ordinary least squares assumptions and interpretations is iid. errors.
If you do not have iid. errors, any interpretations of the model will be skewed.
There are however other heteroskedasticaly robust interpretations of regressions.
For example: time-series econometrics is a whole field dedicated to try to squeeze iid information from stuff that's not iid. So you can use regression.
But they're receptive to my message because they were repetitively warned that curve fitting was not regression analysis. Somehow this is lost in our "data" culture.