Question

1. The regression equation below describes a multivariable linear regression model for average salary among faculty who received initial K Award funding in 2000-2003 (Jagsi, et al, JAMA, June 13, 2012—Vol 307, No. 22, Table 3) Average Salary = 166 094 + 13,399*Male + 48,205*(Full Professor) + 17,007*(Associate Professor) + 60,379*(Surgical Specialties) – 10,190*(Hospital-based Specialties) – 1,317*(Specialties for Children, Women and Families) + 393*(Number of Publications – 30) +31,232*(Leadership position) – 361*(Percent Research Time) +19,070*(Moderate Paying Specialty) + 51,204*(High-paying Specialty) + 100,734*(Extremely High-paying Specialty)

A. What is the predicted salary of a male associate professor in hospital-based, moderate paying specialty, non-leadership position, with 31 publications and 50 percent research time?

B. What is the predicted salary of a female associate professor in hospital-based, moderate paying specialty, non-leadership position, with 31 publications and 50 percent research time?

C. What is the interpretation of the slope for gender in the model?

D. What is the predicted salary of a male assistant professor in medical, moderate paying specialty, non-leadership position, with 10 publications and 60 percent research time?

E. What is the interpretation of the intercept? Does it make sense?

Answer 1

Given Regression equation

Average Salary = 166 094 +
13,399*Male +
48,205*(Full Professor) +
17,007*(Associate Professor) +
60,379*(Surgical Specialties) –
10,190*(Hospital-based Specialties) –
1,317*(Specialties for Children, Women and Families) +
393*(Number of Publications – 30) +
31,232*(Leadership position) –
361*(Percent Research Time) +
19,070*(Moderate Paying Specialty) +
51,204*(High-paying Specialty) +
100,734*(Extremely High-paying Specialty)

a. A. What is the predicted salary of a male associate professor in hospital-based, moderate paying specialty, non-leadership position, with 31 publications and 50 percent research time?
The values given are as follow we put them in the equation.
(Note - Percent is taken as a whole number)

Male = 1
Full Professor = 0
Associate Professor = 1
Surgical Specialties = 0
Hospital-based Specialties =1
Specialties for Children, Women and Families=0
Number of Publications = 31
Leadership position = 0
Percent Research Time = 50
Moderate Paying Specialty = 1
High-paying Specialty =0
Extremely High-paying Specialty=0

"Average Salary" = 166094 +
13399*1 +
48205*(0) +
17007*(1) +
60379*(0) –
10190*(1) –
1317*(0) +
393*(31 – 30) +
31232*(0) –
361*(50) +
19070*(1) +
51204*(0) +
100734*(0) = 187723

b. What is the predicted salary of a female associate professor in hospital-based, moderate paying specialty, non-leadership position, with 31 publications and 50 percent research time?
The values given are as follow we put them in the equation.
(Note - Percent is taken as a whole number)

Male = 0
Full Professor = 0
Associate Professor = 1
Surgical Specialties = 0
Hospital-based Specialties =1
Specialties for Children, Women and Families=0
Number of Publications = 31
Leadership position = 0
Percent Research Time = 50
Moderate Paying Specialty = 1
High-paying Specialty =0
Extremely High-paying Specialty=0

Average Salary = 166094 +
13399*0 +
48205*(0) +
17007*(1) +
60379*(0) –
10190*(1) –
1317*(0) +
393*(31 – 30) +
31232*(0) –
361*(50) +
19070*(1) +
51204*(0) +
100734*(0) = 174324

C. What is the interpretation of the slope for gender in the model?
When the gender changes for female to male, the salary increases by 13399

D. What is the predicted salary of a male assistant professor in medical, moderate paying specialty, non-leadership position, with 10 publications and 60 percent research time?

Male = 1
Full Professor = 0
Associate Professor = 1
Surgical Specialties = 0
Hospital-based Specialties =1
Specialties for Children, Women and Families=0
Number of Publications = 10
Leadership position = 0
Percent Research Time = 60
Moderate Paying Specialty = 1
High-paying Specialty =0
Extremely High-paying Specialty=0

Average Salary = 166094 +
13399*1 +
48205*(0) +
17007*(1) +
60379*(0) –
10190*(1) –
1317*(0) +
393*(10 – 30) +
31232*(0) –
361*(60) +
19070*(1) +
51204*(0) +
100734*(0) = 175860

E. What is the interpretation of the intercept? Does it make sense?

If all the parameter are zero, then the base salary is 166094
This does not make sense in the context because if the person is not from the medical field and not a professor than he cannot qualify for the study.