Consider the problem of modeling the completion of a stat course by students based on their Scholastic Assessment Test in the subject of mathematics SAT-M scores at the time of their admission. After the completion of the final exams we know which students successfully completed the course and which of them failed. Here, the output pass/fail may be represented by a binary number 1/0. It may be fairly said that higher the SAT-M scores at the time of admission to the course, the more likelihood of the candidate completing the course. This problem has been discussed in detail in Johnson and Albert (1999) and Tattar, et. al. (2013).
Let us begin by denoting the pass/fail indicator by Y and the entry SAT-M score by X. Suppose that we have n pairs of observations on the students' scores and their course completion results. We can build the simple linear regression model for the probability of course completion pi = P(Yi = 1) as a function of the SAT-M score with ....