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Beta regression is used when the output $y\in[0,1]$. Common examples include the fraction of employees participating in a company 401k plan or any response that is a percentage. Such data is usually heteroskedastic: they show more variation around the mean and less variation as we approach the boundaries 0 and 1. Also, the distributions are usually asymmetric and Gaussian-based approaches are often inaccurate. Instead, beta regression assumes the response to follow a \textit{beta distribution}. The beta distribution is usually given by   \begin{equation}  {f(y;p,q)} = {\frac{\Gamma(p+q)}{\Gamma(p)\Gamma(q)}}y^{p-1}(1-y)^{q-1}, \quad 0  \end{equation} Where the two parameters are $p$ and $q$.