Question

Consider the regression estimating the impact of several explanatory variables on Washington State University’s annual undergraduate enrollment in number of students.

Enrollment = a + B₁Tuition + B₂Graduate Salary + B₃Amenities + B₄Income + B₅Income² + B₆Apple Cup

The variable Tuition is the in-state cost per credit hour charged, Graduate Salary is the average yearly salary of WSU alumni in 1,000s of dollars, Amenities is WSU’s total spending on amenities such as recreation and entertainment in 1,000s of dollars for its student body, Income is average household income in Washington in 1,000s of dollars, and Apple Cup is a dummy variable equal to one if the Cougs won the Apple Cup the previous season and zero otherwise. The Apple Cup is the rivalry football game between Washington State and University of Washington.

Enrollment at WSU (number of students)	Coefficients	Standard Error	T-Stat	P-value
Tuition (dollars per credit hour)	-83.84	11.44	7.33	0.000
Graduate Salary (1,000s dollars)	645.11	300.05	2.15	0.034
Amenities (1,000s dollars)	1,002.57	391.63	2.56	0.008
Income (1,000s dollars per household)	3.91	1.44	2.71	0.007
Income Squared	-0.03	-0.01	3.11	0.002
Apple Cup	762.85	387.23	1.97	0.090

a)      Before looking at the estimated regression, what would you expect the signs (positive or negative) of coefficients B₁ and B₂ to be? Why?

b)      Write down the estimated regression equation.

c)      Look at the regression output. What does this regression tell us about the relationship between household income and enrollment at WSU? At what income level does the effect of income on enrollment become negative?

d)      Interpret the coefficient associated with the variable Apple Cup. Is the estimate statistically significant?

BONUS: Suppose WSU has a budget of $100,000 to increase undergraduate enrollment. Suppose further that WSU could guarantee an Apple Cup victory by spending all of the $100,000 budget on the football program. The WSU administration can either spend the budget on student amenities or the football program. Which option should they choose? Why?

Answer 1