The Essence of Logistic Regression

Logistic Regression aim is to assign a probability to an event occuring or a sample belonging to a certain class given some features. This is analogous to a boolean valued output. An example problem is determining whether a student passes an exam or not. Let's assign a pass (success) as 1 and a fail as 0. Now, let's assume we know how long they have spent studying for their exam, call this X_1, and whether they passed their previous exam, X_2. Where Y is the target, that should take values between 0 and 1, and the β values are the unknown coefficients that we need to compute to fit the model.