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{Var(y) = \frac{\mu(1-\mu)}{1+\phi}}  \end{equation}  The parameter $\mu$ $\phi$  is known as the precision parameter since, for fixed $\mu$, the larger $\phi$ the smaller the variance of y; $\phi$ $\phi^{-1}$  is the dispersion parameter. The main motivation for using beta regression is that the beta distribution can take on many different shapes through the adjustment of the parameters $\mu$ and $\phi$. Some examples of beta distributions are shown below.