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{p(y;\beta)} = \frac{1}{1 + e^{-(\beta_0+\beta_1x)}}  \end{equation}  In order to fit this function to the data, we must find the parameters $\beta_i$ that maximize the \textit{likelihood function}, $L(\beta;y)$. The \textit{likelihood function} is algebraically the same as the joint probability density function $f(y;\beta)$ except that the change in notation reflects a shift of emphasis from the random variables \textit{y}, \textit{y_i},  with parameters $\beta$ fixed, to parameters $\beta$ with \textit{y} \textit{y_i}  fixed.