Econometrics - Midterm Exam

ECON7020x by H. Morita

Econometrics

- Midterm Exam -

Due August 12, 2013

Part I

Suppose that you collected the following sample.

X 1 2 3 4 5

Y 100 85 90 60 45

(1) In Regression Yi = β0 + β1Xi + ui: find the estimated intercept (β̂0) and the estimated slope (β̂1).

(2) Find the predicted values for each observation.

(3) Find the residuals for each observation.

(4) Find an adjusted R2. Interpret the number in this adjusted R2

Part-II

Suppose that the tuition of your college has once again gone up, and you are interested in what determine cost of attending college. In this investigation, you collect data randomly for 100 national universities and liberal arts colleges from the 2008-2009 U.S. News and World Report annual rankings. Then, you run 3 regressions and the results are shown in Table 1.

In Table 1, Cost is tuition, textbook cost, etc., including living cost 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, i.e. Dpriv = 1 for private college, 0 otherwise. Dlibart = 1 for liberal art college, 0 otherwise. Dreligion = 1 for religion-affiliated college, 0 otherwise.

Numbers in parentheses are homoskedasticity-only standard errors.

(1) Which regression has the best fit to the sample? Why?

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Table 1: Regression Summary

Dependent Variable: Cost

Regressors (A) (B) (C)

Dpriv (X1) 11123 10935 8407 (835) (875) (2155)

Reputation (X2) 3539 3985 (590) (664.6)

Dreligion (X3) -2377 (1508)

Size (X4) -0.20 (0.13)

Dlibert (X5) -416.4 (206.1)

Intercept 6311 5450 7311 (1864) (1772) (2058)

Summary Statistics

R2 0.700 0.705 0.730

R 2

0.697 0.699 0.705

(2) Suppose that the number of undergraduates at College A is 20,000 and its Reputation is 4. Us- ing (C), Find a predicted value of Cost. College A is also a public, liberal-art, and non-religious college.

(3) In (B), is Reputation statistically significant at the 5% level?

(4) In (C), are Dlibart, Size, and Dreligion jointly statistically significant at the 5% level?

(5) Which regression (A), (B), or (C) is the best model to predict Cost?

Part-III Explain the questions as fully as possible.

(1) Explain the difference between homoskedastic and heteroskedastic error terms. Also, explain why heteroskedasticity is more general than homoskedasticity

(2) What are four assumptions in OLS estimation? Also, explain why these assumptions are re- quired.

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Table 2: Critical Value of t

Level of Significance 10% 5% 1% C.I. 90% 95% 99%

Critical Value 1.645 1.960 2.576

Table 3: Critical Values of F

Degrees of Freedom 10% 5% 1%

1 2.71 3.84 6.63 2 2.30 3.00 4.61 3 2.08 2.60 3.78 4 1.94 2.37 3.32

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