A regression approach to fairer grading

In this paper, we consider an issue of great interest to all students: fairness in grading. Specifically, we represent each grade as a student's intrinsic (overall) aptitude minus a correction representing the course's inherent difficulty plus a statistical error. We consider two statistical methods for assigning an aptitude to each student and, simultaneously, a measure of difficulty to each course: (1) we minimize the sum of squares of the errors, and (2) we minimize the sum of the absolute values of those errors. We argue that by accounting for course difficulty, we arrive at a measure of aptitude that is fairer than the usual gradepoint average metric. At the same time, the measures of course difficulty can be used to inform instructors as to how their courses compare to others. The two particular models presented are examples of least-squares and least-absolute-deviation regression and can be used in the classroom to motivate an interest in regression in general and to illustrate the pros and cons of these two approaches to the regression problem.