The cost of attending your university/college has once again gone up. One of the administrators at your university/college tells you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you estimate the following regression equation (p-values are in brackets). Cost = 7,311.17 + 3,985.20 Reputation - 0.20 Size (2,058.63) (664.58) (0.11) + 8,406.79 & Dpriv - 416.38 & Dlibart - 2,376.51 & Dreligion (2,154.85) (1,121.92) (1,007.86) R2 = 0.72 The numbers in parentheses (brackets) are standard errors. 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 Dpriv, Dlibart, and Dreligion are separate dummy variables indicating whether the institution is private or not private, i.e. public [Dpriv]; a liberal arts college or not liberal arts [Dlibart]; and has a religious affiliation or is not religious [Dreligion]. (a) Interpret the coefficients of the variables below and test to determine whether or not the coefficients are significantly different from zero at the alpha=5% level. (Show your work). What would be the problem if you could not claim the coefficients are different from zero? (i) Reputation (ii) Dpriv (b) To save money, you are willing to switch from a private university to a public university, which has a ranking of 0.5 less and 10,000 more students. What is the effect on your cost?(c) Does there seem to be a difference in cost between a liberal arts college and one that is not liberal arts? Explain