Stat 401B
Lab 8
Fall 2006
1
Due November 7, 2006
1. A question was raised about salary levels for men and women employed by a particular company. Some
women thought that their salaries were lower than men’s. The company responded that other factors,
for example the number of years with the company, could have an effect and explain some of the
perceived differences. A random sample of 25 employees was selected from the company. Information
on annual salary ($1000s), years with the company and sex are given below.
Employee
Adams
Brown
Carter
Davis
Eaves
Ford
Green
Higgins
Irvin
Jones
King
Lane
Martin
Salary
45
37
55
32
35
40
47
35
27
38
53
35
32
Years
15
17
25
13
2
10
17
17
1
4
25
15
1
Sex
m
f
m
f
m
m
m
f
f
m
m
f
m
Employee
North
Owen
Pitt
Quincy
Roberts
Smith
Turner
Underwood
Vance
Wilson
Young
Ziegler
Salary
38
39
29
39
48
29
32
49
50
31
38
40
Years
6
20
3
21
19
5
1
20
22
10
7
8
Sex
m
f
f
f
m
f
m
m
m
f
m
m
(a) Plot annual salary versus years with the company. Describe the general relationship between
years with the company and annual salary.
(b) Fit a simple linear regression of annual salary on years with the company for all 25 employees.
Give the prediction equation and comment on the adequacy of the fit of the model by looking at
R2 and a test of significance for the slope. Report the value of the Root Mean Square Error and
comment on the plot of residuals versus years with the company.
(c) Using the prediction equation in (b), what is the predicted salary for an employee who has 17
years experience with the company? Will this prediction tend to be over or under the true value
for a female employee? for a male employee?
(d) Using a different symbol for men and women, plot the annual salary versus the years with the
company.
• Do starting salaries appear to be different for males and females? If so, describe how.
• Do the rates of change in salary as years increase appear to be different for males and females?
If so, describe how.
(e) Fit a multiple regression model of annual salary versus years with the company, an indicator
variable, X, for sex and an interaction term, Years*X. Define X to be 0 if the employee is male
and define X to be 1 if the employee is female. Give the prediction equation. Give an interpretation
of each of the estimated slope coefficients and the intercept. Comment on the adequacy of the fit
of the model. Also, report the value of the Root Mean Square Error and comment on the plot of
residuals versus years with the company.
(f) Using the prediction equation in (e), what is the predicted salary for a male employee with 17
years with the company? for a female employee with 17 years with the company?
(g) Test to see if the mean starting salaries for men and women are the same. State your conclusions.
(h) Give a 95% confidence interval for the difference in mean starting salaries for males and females.
(i) Test to see if the rate of change in salary per year is the same for males and females. State your
conclusions.
(j) Give a 95% confidence interval for the difference in the rates of change in salary per year for males
and females.
(k) Summarize your findings in one page. Your audience for this summary is the Equal Opportunity in
Employment Commission who is looking into whether employees of this company are being fairly
compensated. This summary should be handed in to Dr. Stephenson on a separate
sheet of paper. It should be word processed and printed with a laser quality printer.