test3-3u03-2011w - ECON 3U03 Test 3 Instructor Shintaro...

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Unformatted text preview: ECON 3U03: Test 3 Instructor: Shintaro Yamaguchi March 29, 2011 • Do not start or read problems starting from the next page until you are told to do so (or get 10% penalty on this test). • Only university calculator (Casio FX991) is allowed. • There are 5 questions. The marks for each question are indicated. • Your answer must be supported by a clear explanation unless otherwise noted. • Answer concisely. Writing something that is not directly related to the right answer may result in deduction. • No mark may be awarded if your answer makes little sense or if it is not comprehensible to the marker, even if it includes some words which should appear in the correct answer. • When finished, submit only the answer sheet to the place assigned by the invigilator. Invigi- lators do not pick it up from you. Keep this sheet for your study. • A student who does not respect the time limits during the test will get a 10% penalty on this test. 1 1. (25 marks) Consider the following regression model, S t = β + β 1 P t + β 2 A t + e t , where S t is sales, P t is price, A t is advertising, and e t is an error term. Assume that e t ∼ N ( , σ 2 ) . The following table summarizes the results. Variable Coefficient Std. Error Intercept 118.91 6.35 P t-7.90 1.09 A t 1.86 0.68 T = 75, R 2 = . 44, SSE = 1718 . 94, ˆ σ = 4 . 88, ˆ σ s = 6 . 49 Note that T is sample size and ˆ σ s is the estimate for standard deviation of S calculated by the unbiased estimator. Test the significance of the model at 5% level by the following steps. (a) (5 marks) Construct the null hypothesis. (b) (5 marks) Construct the alternative hypothesis. (c) (10 marks) Calculate the test statistic. Also state what distribution the test statistic follows. (d) (5 marks) State critical value and conclusion of the test. If the exact critical value is not in the statistic table, approximate it by the critical value with closest DF....
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test3-3u03-2011w - ECON 3U03 Test 3 Instructor Shintaro...

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