Question

22 The cost of College (15 points) The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which return of only low you and your parents are not pleased. One of the ministrator at your writy college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of other Tom a te this h ot collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 US News and World Report antal rankings Next you perform the following region Gert 7.311.173.985.20 - reputation-0.20 - sine +8.406.79dpiv - 416.38 .dlibart+2.376.51.dreligion R = 0.72 SER= 3,773.35 where cost is Tuition, Fees, Room and Board in dollars, reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 ("marginal") to 5 ("distinguished"), size is the number of undergraduate students, and dpriv, dlibart, and dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parents are heterorkedasticity-robust standard errors. (a) (3 points) Indicate whether or not the coefficients are significantly different from zero. (b) (2 points) What is the p-value for the null hypothesis that the coefficient on sise is equal to zero? Based on this, should you eliminate the variable from the regression? Why or why not? (c) (5 points) You want to test simultaneously the hypotheses that i = 0 and aberta 0. Your regression package returns the F-statistic of 1.23. Can you reject the null hypothesis? (d) (2 points) Eliminating the size and dliburt variables from your regression, the estimation regression becomes cost=5, 450.35 +3.538.84 -reputation + 10.335.70 dpiv-2.783.31 religion R 0.72 SER3.792.68 Why do you think that the effect of attending a private institution has increased now? (e) (3 points) You give a final attempt to bring the effect of size back into the equation by forcing the assumption of homoskedasticity onto your estimation. The results are as follows: cost=7.311.17 +3. 5.20 reputation - 0220 - Sie religion +8.406.79.dpriy - 416.38 .dlibart-2.736,51 (1.25) R=0.72 SER = 3,682.02 Calculate the t-statistic on the side coefficient and perform the hypothesis test that its coefficient is zero. Is this test reliable? Explain.

Answer 1

In part c, we are to conduct a joint hypothesis F- test.

The null hypothesis is:

Ho: ​​​​​​

Bsize = Bdlibart = 0

And alternate hypothesis is:

H1:​​​​​​

Bsize = Bdlibart +0

The F-statistics is calculated using R² but we are given the F-statistic as 1.23

We are to calculate F-critical value from the table.

Since we are not given a significance level, we assume it to be 5%.

The degrees of freedom will be Fq, n-k-1 where q is the number of restrictions (here 2) and n is sample size(here, 100)amd k is number of independent variables in the regression in unrestricted case (here, 5)

Thus, F - critical value is 3.093

Since F-statistic

*The table provided by you for F- distribution will not be used. F- table has two degrees of freedom, one for numerator and another for denominator.