Logit function

If p is the probability of the occurring of an event, 1-p is the probability of the event not occurring. The odds of the event occurring are:

The log of the odds is the logit function, or the logit of p:

The logistic regression model, comprising q predictor variables, is given by:

 

Exponentiating both sides, we get:

Now, the interpretation of the beta coefficient is:

a unit increase (e.g., from 0 to 1) in , multiplies the odds of the event occurring by  .

To calculate the probabality estimate of an observation belonging to class 1 (vs. class 0), we use: