1. Consider a multiple regression;
, 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 b_{1} , b_{2} , and b_{3} for the model coefficients.
(b) An estimate for the error variance (sigma hat squared).
(c) An estimate for the variance for b_{2} .
(d) R^{2}, 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
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
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).