exam98s - q s 2 [1 + z ( Z Z )-1 z ], which is...

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THE UNIVERSITY OF CHICAGO Graduate School of Business Business 424-01, Spring Quarter 1998, Mr. Ruey S. Tsay Solutions to Midterm I used the current textbook as reference to answer the questions (4/29/02). 1. Answer: (a) Yes, based on Result 4.7(a) on page 163. (b) False, based on Result 4.6 on page 160. The correct variance is σ 11 - σ 2 12 σ 22 . (c) The expectation is σ 12 22 . (d) Yes, based on Result 4.3 on page 157 and Result 4.6 on page 160. (e) N m ( μ , 1 n Σ ) based on Result 4.3. 2. Answer: (a) Apply Result 7.1 on page 358. (b) See pages 360-361 of the textbook. 3. Answer: Let z 0 = (1 , 15 , 60) 0 . Use the results on pages 374-375 of the textbook. (a) prediction = z 0 0 ˆ β = 73.18. (a) 95% prediction interval = 73 . 18 ± 2 . 11 *
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Unformatted text preview: q s 2 [1 + z ( Z Z )-1 z ], which is approx-imately 73 . 18 ± 6 . 98. [The calculation shows that ( Z Z )-1 matrix might have some rounding errors.] 4. You may use Section 6.2 to solve this problem. E±ectively, we are concerned with μ 1-μ 2 = (1 ,-1) μ . The result of page 279 applies with C = (1 ,-1) and q = 2. Alternatively, let ¯ d = ¯ x 1-¯ x 2 . Then, Var( ¯ d ) = 1 n [Var( x 1 ) + Var( x 2 ) + 2Cov( x 1 , x 2 )], where x i denotes the i-th index. You can apply the usual t-test for the ¯ d . Here ¯ d =-4 . 3 and Var( ¯ d ) = 1.42. The t-ratio is-3 . 61, which is signi²cant at the 5% level....
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This note was uploaded on 12/16/2011 for the course STAT 5705 taught by Professor Staff during the Fall '09 term at FSU.

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