A newspaper based in the US is interested in studying the relationship between the cost of attending college and the reputation of the college. To investigate such relationship, the newspaper collects data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings, and performs the following 2 regressions:
R2=0.720, SER = 3,773.35
[Regression 2]
R2=0.712, SER = 3,792.68
where Cost is Tuition fees in dollars, Rep 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 Drelig are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parentheses are standard errors (assuming homoskedasticity).
You want to test simultaneously the hypotheses that ?size = 0 and ?Dilbert = 0. What is the F-test statistic? Report your answer with 2 significant digits.
Based on the F statistic computed in the previous question, can you reject the null hypothesis?
A newspaper based in the US is interested in studying the relationship between the cost of attending college and the reputation of the college. To investigate such relationship, the newspaper collects data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings, and performs the following 2 regressions: [Regression 1] = 7,311.17 + 3,985.20 Rep 0.20 Size + 8,406.79 Dpriv 416.38 Dlibart 2,376.51 Drelig (2,058.63) (664.58) (0.13) (2,154.85) (1,121.92) (1,007.86) R2=0.720, SER = 3,773.35 [Regression 2] = 5,450.35 + 3,538.84 Rep + 10,935.70 Dpriv 2,783.31 Drelig (1,772.35) (590.49) (875.51) (1,180.57) R2=0.712, SER = 3,792.68 where Cost is Tuition fees in dollars, Rep 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 Drelig are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parentheses are standard errors (assuming homoskedasticity). You want to test simultaneously the hypotheses that ?size = 0 and ?Dilbert = 0. What is the F-test statistic? Report your answer with 2 significant digits. Based on the F statistic computed in the previous question, can you reject the null hypothesis? No. Yes.
Yes we can reject the null hypothesis
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