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I'm putting the "x"s in lower-case because they are typically treated as non-random. |
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The model takes the form
:<math>\operatorname{logit}(p)=\log\left(\frac{p}{1-p}\right) = \alpha + \beta_1
where
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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, ''X''<sub>1</sub> to ''X''<sub>''k''</sub>. This can be written equivalently as
:<math>p = \Pr(Y=1|X) = \frac{e^{\alpha + \beta_1
The interpretation of the <math>\beta</math> parameter estimates is as an additive effect on the log of the odds. In the case of a dichotomous explanatory variable, for instance sex, <math>e^\beta</math> (the antilog of <math>\beta</math>) is the estimate of the [[odds-ratio]] of having the outcome for, say, males compared with females.
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