We have seen how linear regression models allows us to predict a numerical outcome. Logistic regression models, however, allow us to predict a categorical outcome by predicting the probability that an outcome is true.
As with linear regression, in logistic regression models, we also have a dependent variable y and a set of independent variables x1, x2, …, xk. In logistic regression however, we want to learn a function that provides the probability that y = 1 (in other words, that the outcome variable is true) given this set of independent variables, as follows:
This function is called the Logistic Response function, and provides a number between 0 and 1, representing the probability that the outcome-dependent variable is true, as illustrated in Figure 4.3:
Positive coefficient values βk increase the probability...