Include residual standard deviation in text report

[strengejacke]

Related to https://github.com/easystats/parameters/issues/305, I'd say once insight is updated and provides a get_sigma() function, we should include the residual standard deviation in the (long) text-output from report().

[DominiqueMakowski]

What would be a good sentence to report and interpret it?

[strengejacke]

It's a bit tricky. Its direct interpretation is best described in relation to the SD(y), however, that is what R2 tells us. On the other hand, sigma tells us the precision of model predictions and can be "constant" across models when only a subset of the data is used, while R2 can vary in such cases (so sigma^2 is constant, SD(y) changes for subsets of data, so does R2).

Some formal interpretations are here: https://easystats.github.io/insight/reference/get_sigma.html

The more I think about this, I would say:

1. just report the value "as is", w/o interpretation
2. don't report it.

[mattansb]

just report the value "as is", w/o interpretation

Seems best, at least for starters, as with everything, interpretation becomes harder with mixed models...

[DominiqueMakowski]

I would argue not including it for now (as it is fairly rarely mentioned/required), and also because like I am worried it would clutter the information with something is hard to interpret by most people... In other words, I'd give priority to indices and values that are used more by users no?