An expert witness in a case of alleged racial discrimination in a state universi

Question

An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.

Variable Coefficient t p
Intercept -3,816,521 -29.4 .000
Year 1,948 29.8 .000
YearHire -826 -5.5 .000
Race -2,093 -4.3 .000
Rank -6,438 -22.3 .000

R2 = 0.811 R2adj= 0.809 s = 3,318

Explanation / Answer

The regression equation is: Salary = -3,816,521 + 1,948*Year – 826*YearHire – 2,093*Race – 6,438*Rank The p-values with respect to all the coefficients are very small, i.e they give strong evidence against the null hypothesis H0 : ßj = 0. The coefficient of determination value is 0.811, which means that 81.1% of the variation in the salary is explained by the variation in the values of the independent variable. The remaining 18.9% of the variation remains unexplained.This is a very good regression, as the coefficient of correlation is R = sqrt(R2) = sqrt(0.811) = 0.9005. The year plays a positive role in the regression (as its coefficient is positive), but all the other variables have negative coefficients, indicating that as the value of these variables increase, the salary decreases.

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