Part 4: Longer Answers (30 points total, 5points each) The cost of attending col
ID: 3060828 • Letter: P
Question
Part 4: Longer Answers (30 points total, 5points each) The cost of attending college has increased. Although students are told that education s an investment in human capital, most students are not pleased about the increasing cost of college. College administrators claim that students have to pay more if their college's reputation is high. To investigate this hypothesis, you collect data on a random sample of 100 colleges and universities from the 2015-2016 U.S. News and World Report rankings. Next you estimate the following regression: 7,303,85 Repuation97Pria,4191 (2.059) (66s) (0.12) (2,155) (629) R2 =0.72 SER = 3,773 where Cost is yearly tuition, fees, room, and board in dollars at college c, Reputation is the index used in U.S. News and World Report (based on a survey of college adminis- trators), which ranges from 1 ("marginal") to 5 ("distinguished"), Size is the number of undergraduate students, and Private and LibArts are binary variables indicating whether the institution is private or a liberal arts college. Heteroskedasticity-robust standard errors appear in parentheses. (a) Interpret the results for Reputation in a sentence. Does the coefcient have the espected sign? (5 points) (b) What is the predicted cost for a student who attends a private liberal arts college, which has 1,500 students, and a reputation level of 4.5? (5 points)Explanation / Answer
Solution-
Regression equation is-
Cost = 7311 + 3985* Reputation -0.2 * Size +8407 * private -416 Lib arts
A. From the estimated regression equation - we have the slope of reputation variable equal to 3985. This is positive and implies that when reputation increases by 1 unit then costs increase by 3985 units. This is expected as higher reputation should lead to higher fees should be more too.
B. When reputation = 4.5 and size = 1500 and college is private lib arts, the expected cost-
= 7311 + 3985* 4.5 -0.2 * 1500+8407 * 1 -416 *1
= 32934.5
C. When reputation = 4 and size = 10000 and college is private non-lib arts, the expected cost-
= 7311 + 3985* 4 -0.2 * 10000+8407 * 1 -416 *0
= 29658
Thus change in costs = 32934.5 - 29658 = 3276.5
D. Standard error if size variable = 0.12 and cofficient = -0.2
Then t statistic = -0.2/0.12
= -1.667
critical value is given by - t0.975,100-5 = -1.985
As t statistic > critical value,
Hence null hypothesis is not rejected at 5% level of significance. Thus size cofficient is not statistically significant.
Thanks!