# 45 - Chapter 3 Exercise Solutions Principles of...

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Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 45 EXERCISE 3.8 (a) We set up the hypotheses H 0 : β 2 = 0 versus H 1 : β 2 < 0. The alternative β 2 < 0 is chosen because an inverse relationship is one where the dependent variable increases as the independent variable decreases, and visa versa. Thus, a negative β 2 suggests an inverse relationship between variables. The test statistic, given H 0 is true, is 2 (182) 2 ~ se( ) b tt b = The rejection region is (0.05,182) 1.653 <= . The value of the test statistic is 194.233 19.031 10.2061 t == Since t = 19.03 < 1.653, we reject the null hypothesis that 2 0 β = and accept the alternative that 2 0 β< . We conclude that there is a statistically significant inverse relationship between the number of house starts and the 30-year fixed interest rate. (b) We set up the hypotheses 02 : 150 H β =− versus 12 : 150 H β ≠− . The test statistic, given H 0 is true, is 22 (182) 2 ~ se( ) b b −β = The rejection region is 1.973 t <− and 1.973 t > , with (0.975,182) 1.973 t = . The value of the test statistic is 194.233 150 4.334 10.2061 t −+ Since t = 4.334 < 1.973, we reject the null hypothesis
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## This note was uploaded on 11/23/2011 for the course ECON MPBE taught by Professor Jansveceny during the Spring '11 term at Metropolitní Univerzita Praha.

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