Consider the regression estimating the impact of several explanatory variables o
ID: 3331838 • Letter: C
Question
Consider the regression estimating the impact of several explanatory variables on Washington State University's annual undergraduate enrollment in number of students. 5. Enrollment-a+ BiTuition + BGraduate Salary+ B Amenities + Balncome+ BsIncome?+ BeApple 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. Coefficients Standard -83.84 645.11 1,002.57 3.91 0.03 762.85 Enrollment at WSU (number of T-Stat 7.33 2.15 2.56 2.71 3.11 1.97 P- value 0.000 0.034 0.008 students) Tuition (dollars per credit hour) Graduate Salary (1,000s dollars) Amenities (1,000s dollars) Income (1,000s dollars per household) Income Squared Error 11.44 300.05 391.63 1.44 -0.01 387.23 0.007 0.002 0.090 Apple Cup Before looking at the estimated regression, what would you expect the signs (positive or negative) of coefficients B1 and B2 to be? Why? a) 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? Interpret the coefficient associated with the variable Apple Cup. Is the estimate statistically significant? d)Explanation / Answer
a) B1 would be negative ofcourse as more the tuition fee, lesser will be the enrollment. B2 will be positive as if salary after graduation is more, more number of students will enroll for the program.
b) Enrollment = -83.84 * tuition + 645.11* Grad salary + 1002.57 * amenities + 3.91 * Household income - 0.03 * income^2 + 762.85 * apple cup
c) If income of household increases by 1000 dollars, enrollment increases by a factor of 3.91.
When income is squared, the effect becomes negative.
d) If alpha = 0.05, then the coefficient is significant but if alpha is 0.01 then coefficient is not significant.
So, if last season game is won, then enrollment increases by 762.85.