HW6_sol

HW6_sol - ECON 414 SOLUTION TO HOMEWORK 6 Spring 2011 4.6...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECON 414 SOLUTION TO HOMEWORK 6 Spring 2011 4.6 (i) With df = n 2 = 86, we obtain the 5% critical value from Table G.2 with df = 90. Because each test is two-tailed, the critical value is 1.987. The t statistic for H : = 0 is about -.89, which is much less than 1.987 in absolute value. Therefore, we fail to reject = 0. The t statistic for H : 1 = 1 is (.976 1)/.049 -.49, which is even less significant. (Remember, we reject H in favor of H 1 in this case only if | t | > 1.987.) (ii) We use the SSR form of the F statistic. We are testing q = 2 restrictions and the df in the unrestricted model is 86. We are given SSR r = 209,448.99 and SSR ur = 165,644.51. Therefore, (209,448.99 165,644.51) 86 11.37, 165,644.51 2 F- = which is a strong rejection of H : from Table G.3c, the 1% critical value with 2 and 90 df is 4.85. (iii) We use the R-squared form of the F statistic. We are testing q = 3 restrictions and there are 88 5 = 83 df in the unrestricted model. The F statistic is [(.829 .820)/(1 .829)](83/3) 1.46. The 10% critical value (again using 90 denominator df in Table G.3a) is 2.15, so we fail to reject H at even the 10% level. In fact, the p-value is about .23. (iv) If heteroskedasticity were present, Assumption MLR.5 would be violated, and the F statistic would not have an F distribution under the null hypothesis. Therefore, comparing the F statistic against the usual critical values, or obtaining the p- value from the F distribution, would not be especially meaningful. 4.8 (i) We use Property VAR.3 from Appendix B: Var( 1 - 3 2 ) = Var ( 1 ) + 9 Var ( 2 ) 6 Cov ( 1 , 2 )....
View Full Document

Page1 / 4

HW6_sol - ECON 414 SOLUTION TO HOMEWORK 6 Spring 2011 4.6...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online