Temple University
Department of Economics

Introduction to Econometrics

Hypothesis Testing Homework

 

1. Consider a multiple regression;

eqn01, with 17 observations given in the table:

 

Y

x2

x3

15

12

360

13

8

372

17

10

355

18

12

340

24

16

326

23

14

304

28

18

284

32

21

271

32

21

253

37

26

239

39

29

205

42

31

195

44

33

172

46

34

158

49

37

137

53

41

112

55

43

98

 

Based on computer estimation (attach a printout), find:

(a) The least squares estimates b1 , b2 , and b3 for the model coefficients.

 

(b) An estimate for the error variance eqn02 (sigma hat squared).

 

(c) An estimate for the variance for b2 .

 

(d) R2, SSE, SST, and SSR.

 

 

2. For this problem you will need the data in rdchem.wf1 for 32 firms in the chemical industry. This is an EVIEWS workfile. You will need the EVIEWS software to do the homework. The variable rdintens is is expenditures on research and development as a percent of company sales. Sales and R&D expenditures are both measured in millions of dollars. The variable profmarg is profits as a percent of sales; both in millions of dollars. From the data use EVIEWS to construct estimates of the model parameters of

 

R&D

 

A. Report your estimates of the coefficients and their standard errors.

 

B. How much of the variation in rdintens is explained by the two independent variables?

 

C. Interpret your estimate of the coefficient on the log of sales. In particular, if sales increases by 10%, what is the estimated percentage increase in rdintens? Is this and economically large effect?

 

D. At the 5% level, test the hypothesis that sales has no impact on rdintens.

 

E. Are sales and profmarg jointly significant in explaining rdintens?

 

3. Some cities are economically dominated by the universities that they host. Examples include University of Illinois in Champaign-Urbana, University of Wisconsin in Madison, University of MIchigan in Ann Arbor, or Penn State in Happy Valley. A perennial complaint in these towns is that the student population drives the monthly rent fo apartments. The data for 127 college towns is in the EVIEWS file rental .wf1. Let rent be average monthly rent paid on apartments in the town, pop denote the total city population, avginc the average city income, and pctstu the student population as a percent of the total population. A model of rental costs in such towns is

 

rent

 

A. What do you expect for the sign of the coefficient on log(avginc)?

B. Use the data to fit the stated model.

C. Was your supposition in part A. confirmed? (Note that your supposition is a testable hypothesis.)

D. Test the hypothesis, at the 1% level, that the effect of log(pop) is five times as great as the effect of pctstu on log(rent).