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Unformatted text preview: ECON 414 Answers to Homework 2 Answers to Homework 2 Chapter 3 Exercise 3.5 • a. False X values being closer to their mean implies that S xx is smaller. From equations 3.18 and 3.19 in the textbook, we see that a smaller S xx means a larger variance. Thus estimates are less precisely estimated. • b. False We need Assumptions 3.3 and 3.4 for unbiasedness. Violation of Assumption 3.4 implies that unbisedness is no longer valid. • c. False Assumption 3.8, i.e., normality of error terms is needed only for hypothesis tesing. Thus BLUE still holds when Assumption 3.8. is not satisfied. • d. True t- and F- distributions for the test statistics were derived from the assumption of nor- mality (Assumption 3.8) which is a must for hypothesis tesitng. • e. True The width of a confidince interval directly depends on the standard error of an estimate. • f. True If V AR ( X ) is large, then from equations 3.18 and 3.19, the variances of an estimate will be smaller and hence confidence intervals will be narrower. • g. False A high p-value means that rejection of H might result in a high probability of type-I error. So we should not reject, implying that we should not conclude that the coefficent is significant. • h. True Higher level of significance means a lower value for t * and hence actual | t c | is more likely to be to the right of t * . Also, a higher level of significance meand a greater chance for p- value to be low it and hence more likely for the null hypothesis to be rejected, implying significance of a coefficent. 1 ECON 414 Answers to Homework 2 • i. Partly True Violation of Assumptions 3.5 and 3.6 only affects the BLUE property. Thus estimators are still unbiased and consistent but NOT BLUE....
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This note was uploaded on 02/28/2008 for the course ECON 414 taught by Professor Rashidian during the Spring '07 term at USC.
- Spring '07