Question

18-E3.

Results of multiple regression for expend

Summary measures

Adj R-Square	71.5%
Model Error	4.877

Regression coefficients

	Coefficient	Std Err	t-value	P-value
Constant	-7.53	4.27	-1.76	0.08
Age	3.786	0.260	14.56	0.000
Age 2	-0.041	0.004	-10.72	0.000

1. What is the formula relating salary to age? What would be the predicted salary of someone of age 30?
2. According to this model, what age is associated with the highest salary?
3. How well can you predict salary from someone’s age alone?
4. If these data were used in an age discrimination case, then how might one explain the apparent association with age and claim that there is, in fact, no age discrimination?

Answer 1

a) The regression equation is:
Salary = -7.53 + 3.786*Age - 0.041*(Age)^2

Predicted Salary (Age = 30) = -7.53 + 3.786*30 - 0.041*30*30
Pred. Salary = 69.15

b) Age associated with highest salary:
Differentiating Salary wrt Age,
dS/dA = 3.786 - 2*0.041*age
Age = 3.786/0.082 = 46.17

Double differentiation is negative, hence it is a maxima
Therefore, the age associated with highest salary is 46

c) The model explains 71.5% variation in the salary. Hence, the model is pretty good in predicting salary from someone's age alone.

d) If this data was used in an age discrimination case, the arguments one could provide are that the model is not an exact fit for predicting salary by age. Hence, we cannot say that age predicts an individual's salary at all times. There are exceptions when an individual has higher than expected salary irrespective of their age. Therefore, there is no age discrimination of salary, this purely depends on the individual