The name logistic regression comes from the fact that the dependent variable of the regression is a logistic function. It is one of the widely used models in problems where the response is a binary variable (for example, fraud or not-fraud, click or no-click, and so on).
A logistic function is defined by the following equation:
It has the particular feature that, as y varies from to , the function value varies from 0 to 1. Hence, the logistic function is ideal for modeling any binary response as the input signal is varied.
The inverse of the logistic function is called logit. It is defined as follows:
In logistic regression, y is treated as a linear function of explanatory variables X. Therefore, the logistic regression model can be defined as follows:
Here, is the set of basis functions and are the model parameters as explained in the case of linear regression in Chapter 4, Machine Learning Using Bayesian Inference. From the definition of GLM in Chapter...