Reverse Regression, Fairness, and Employment Discrimination

Possible salary discrimination can be studied by comparing mean salaries of, say, males and females, after statistical adjustment for differences in job qualifications. The adjustment is often made by regression, with salary as dependent variable, and job qualifications and sex as independent variables. One might also regress job qualifications on salary and sex, a procedure called reverse regression. Ideas about fairness as well as technical concepts are relevant to discrimination studies. There are two distinct aspects of fairness, one based on comparisons of salary and the other based on comparisons of qualifications. Both concepts are needed to evaluate fairness.