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:<math>\operatorname{logit}(p)=\ln\left(\frac{p}{1-p}\right) = \alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i}</math>,
:<math>i = 1, \dots, n
where
:<math>p = \Pr(Y_i = 1)
The logarithm of the [[odds]] (probability divided by one minus the probability) of the outcome is modelled as a linear function of the explanatory variables, <math>X_1</math> to <math>X_k</math>. This can be written equivalently as
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