How to Interpret coefficients of a beta regression model with logit link I'm running a beta regression in R where the outcome variable is continuous but bounded between 0-1. I need the results to be understandable to an audience with a very basic stats background. I need some help interpreting the coefficients. My model is very basic and look like:
betareg(Y ~ ANE + factor(Year) +factor(Month) +factor(Sector))
I'm not sure how to interpret the coefficient on ANE. Below are the results I got for the ANE variable:

Coefficients (mean model with logit link):
              Estimate  Std. Error  z value  Pr(>|z|) 
(Intercept) 1.036e+00 : 7.735e-02 : 13.395 : < 2e-16 ***
ANE        -1.693e-05 : 6.948e-06 : -2.437 : 0.014803 *


 A: I know this question is kind of old, but it has hundereds of views (including myself, as I went hunting for an answer to this very question today), so maybe someone else might find this information useful. I came across this post: interpretation of betareg coef , which helped me a lot, but I still had to make the leap to understand how to translate the coefficients into the original proportional space.
Essentially, you can express your coefficients in terms of 
$$x/(1-x)=exp(\text{coefficient or sum of coefficients})$$ and solve for x, so that $$x=exp(\text{coefficient})/(1+exp(\text{coefficient}))$$ so for the above example, the intercept would equal $exp(1.036)/(1+exp(1.036))$, or $2.817923/3.817923$, which equals $0.7380775$. Then ANE would be $exp(1.036-0.00001693)/(1+exp(1.036-0.00001693))$, or $0.7380742$, which is an absolute difference of $-0.0000033$.
It then gets trickier to figure out absolute values for slopes for year or month, which you haven't shown, but would be of the form $$exp(1.036-0.00001693+\text{year_coefficient}*Year)/(1+exp(1.036-0.00001693+\text{year_coefficient}*Year))$$
and then you have to figure out how to deal with Year. I decided to calculate a change in 1 from the intercept for the local rate of change, and then additionally calculate the max and min for the overall scope of change.
