Question

1. The NBA hires you to determine whether there is discrimination. You find the following results for a regression with Salary as the dependent variable:

Variable	Coefficient	t-statistic
Constant	320,000	20.43
Points per game	15000	5.23
Rebounds per game	9500	4.25
Assists per game	1223	1.95
Steals per game	-87.5	0.54
Plays Center	100,000	2.75
Plays Forward	-738	1.02
Player is Black	-99,000	1.14

1. What does the table tell you about the impact of “points per game” on a player’s salary?

2. According to this table, is there discrimination? Justify your answer.

Answer 1

Number of predictors = 7
df = n - p - 1
We will assume that the sample size is large enough and hence the degrees of freedom are large so that we can consider the t-distribution approximately as standard normal distribution.

t-statistic (Points per game) = 5.23
p-value (one-tailed) < 0.001

Hence, we can say that the coefficient of "points per game" is significantly different than zero and hence is a significant predictor of salary. Therefore, there is a positive impact of points per game on a player's salary, higher the points per game higher the salary.

t-statistic (Player is Black) = 1.14
p-value = 0.12

Hence, we can say that as the p-value = 0.12 > 0.05 (at significance level of 0.05), we can say that it is not a significant predictor of player's salary. There is no discrimination on the basis of race on a player's salary.