Question

Recall "It's what you learn, not where" from The Economist in Lecture 22. Consider a multiple regression to explain the percentage returns to education (R) using the percentage of applicants a university admits (U) and program of study. As seen in the figure in lecture, a high value of R would be 15 (a great return) but some programs and schools have an R close to zero. U also varies across universities where a value of 20 is a selective university (hard to get into) but some have a value of U near 100 (almost everyone gets in). Consider three programs of study: A, B, and C, which are included via dummy variables.
The multiple regression also allows for interaction effects between university admissions and programs. Consider this equation of multiple regression results: R-hat = 7.5239 - 0.0594*U - 0.2581*Program_A + 0.5587*Program_C + 0.0141*Program_A*U + 0.0089*Program_C*U. For Program C at a university that admits 75 percent of applicants, what is the predicted value of R? (Record your answer accurate to at least the nearest first decimal place with standard rounding.)

Answer 1

The estimated regression model is

where

U=the percentage of applicants a university admits

There are three programs of study: A, B, and C, and hence we need 3-1=2 dummy variables to represent these 3

• Program_A=1, Program_C=0, if the program of study is A
• Program_A=0, Program_C=0, if the program of study is B
• Program_A=0, Program_C=1, if the program of study is C

he predicted value of R, given U=75 and for Program C (that is Program_A=0, Program_C=1) is

ans: the predicted value of R is 4.3