Research scientists at the Educational Testing Service (ETS) used multiple regression analysis to model y, the final grade point average (GPA) of business and management doctoral students. A list of the potential independent variables measured for each doctoral student in the study follows:
(1) Quantitative Graduate Management Aptitude Test (GMAT) score
(2) Verbal GMAT score
(3) Undergraduate GPA
(4) First-year graduate GPA
(5) Student cohort (i.e., year in which student entered doctoral program: year 1, year 3, or year 5)
a. Identify the variables as quantitative or qualitative.
b. For each quantitative variable, give your opinion on whether the variable is positively or negatively related to final GPA.
c. For each of the qualitative variables, set up the appropriate dummy variable.
d. Write a first-order, main effects model relating final GPA, y, to the five independent variables.
e. Interpret the B's in the model, part d.
f. Write a first-order model for final GPA. y, that allows for a different slope for each student cohort.
g. For each quantitative independent variable in the model, part f, give the slope of the line (in terms of the B's) for the year 1 cohort.