Robin Cleveland, the career counselor at Meadville College , has modified the re
ID: 388230 • Letter: R
Question
Robin Cleveland, the career counselor at Meadville College , has modified the regression model she built to predict a recent graduate’s starting salary with the hope of providing a more accurate prediction. In addition to the student’s GPA and whether or not the student has completed an internship, Robin has incorporated the student’s major into the model. The three most popular majors at Meadville College are General Studies (i.e., no specific major), Natural Sciences, and Business Management. As the student’s major is a categorical variable with three levels, Robin has created two indicator variables, SCIENCE and BUSINESS, that are equal to 1 if the student majored in the respective field and 0 otherwise. Her modified regression model is as follows:
SALARY ˆ = 6,491.78+5,204.54 GPA+1,927.39 INTERNSHIP+ 904.11 GPA INTERNSHIP+8,329.81 SCIENCE+6,765.06 BUSINESS.
Based on Robin’s revised model, what is the estimated difference in salary if a student who is currently majoring in Natural Sciences decides to switch his or her major to Business Management? Assume that the student’s GPA and his or her propensity to complete an internship is the same regardless of the major.
Explanation / Answer
Refer the modified regression model is as follows:
SALARY ˆ = 6,491.78+5,204.54 GPA+1,927.39 INTERNSHIP+ 904.11 GPA INTERNSHIP+8,329.81 SCIENCE+6,765.06 BUSINESS.
In the above regression model, the coefficient of SCIENCE in 8329.81 and that of BUSINESS is 6765.06. The coefficient of SCIENCE is higher than that of BUSINESS.
Keeping all other variables same for both situations,, the estimated difference in salary if a student switches from Natural Sciences to Business Management is equal to the difference in respective objective coefficients
= 8329.81 - 6756.06
= 1573.75
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