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Econ 141: Problem Set 3: Answers Fall 2007 Due Monday, October 1st in Class This problem set gives you questions very similar to those you will see on the ﬁrst midterm exam. Question 3 requires that you use SAS. In an exam, you won’t need to actually run SAS, but you may be given SAS output which you will use to answer questions similar to those in question 3. 1. (Wooldridge 4.4) i) Null hypothesis: H 0 : β 3 = 0 Alternative hypothesis: H 1 : β 3 6 = 0 ii) We should expect that β 1 is positive since larger populations will lead to higher demand, all else equal, thereby driving up rents. Similarly, we expect that β 2 is also positive since higher incomes will also lead to higher demand all else equal. iii) Note from page 49 of the text that in a log-log regression, the interpretation of the β s is that: y = β x . In this case, x = 10 and β = 0 . 066 , so this means that y = 0 . 066 * 10 = 0 . 66 . Therefore, a 10 percent increase in population is associated with about a 0.66 percent increase in rent. iv) Testing the hypothesis in (i) at the 1% level: 0 . 0056 / 0 . 0017 = 3 . 29 . The critical value of the t-distribution for a two-sided test with 60 degrees of freedom at the 1% level is

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