Betareg, seems pretty straightforward, but I have some questions:

The **scale **variable, aka precision, phi: seems to be like dispersion Poisson regression. What does it specifically represent? Just the dispersion around the mean. What do I need to consider in regards to it?

I see the scale can be **constant or variable** if I associate model variables with it. If I do the later, do I just keep them in the model if the phi value goes up or AIC or based on a LR test or if the coefficients are significant in that part of the model?

Also, when presenting results, do I need to do anything to account for the **Scale** parameter in regards to estimates or talk about its impact on estimates beyond just describing the final model that I used, right?

Lastly, I have not seen a good description of how to present results. Is the **R^2** values even important? How do you describe the **model coefficients** for continuous and categorical variables, since the model uses a beta distribution and lets say a logit link. is it just something like:

-for every increase in the continuous variable the mean dependent proportion increases blank; and

-mean dependent proportion is blank higher for the categorical variable group in comparison to the reference

categorical group.

Does the **partial R^2** come into play at all for effect estimates?

Also, the demo example in betareg has the following, which I don't exactly know what they represent, are they just the model equation parts:

omega <- mu * phi

tau <- phi - mu * phi

Thanks!!