Solution to Tutorial 9

# Solution to Tutorial 9 - . 5470 X with s ( b ) = 0 . 8370...

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Solutions to Tutorial 9 1. (a) (145) (b) (0)–0.9596; (4)–0.7338; (45)–(-0.1927); (145)–(-4.6600) The model calculated: (0), (1), (2), (3), (4), (5), (14), (24), (34), (45), (145), (245), (345), (1245), (1345). (c) (12345)–(-4.5600), (1345)–(-4.6157), (145)–(-4.6600) The model calculated: (12345), (2345), (1345), (1245), (1235), (1234), (345), (145), (135), (134), (45), (15), (14). (d) SSE ( F )=0 . 2406 df =34 , SSE ( R )=0 . 2618 df =46 , F = (0 . 2618 0 . 2406) / 2 0 . 2406 / 34 =1 . 4979 <F (0 . 95 , 2 , 34) = 3 . 3158 Thus, they can be removed. 2. see R-code 3. (a) s ( b 0 )=0 . 8229 and s ( b 1 )=0 . 2634 (b) DW =0 . 9737425 <D U =1 . 15 and >d L =0 . 95 no conclusion (d) H 0 : ρ =0 ,H a : ρ> 0 .DW =1 . 76 ,d L =0 . 93 ,d U =1 . 13 . If DW > 1 . 13 conclude H 0 ,i f DW < 0 . 93 conclude H a , otherwise the test is inconclusive. Conclude H 0 (e) ˆ Y =94 .
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Unformatted text preview: . 5470 X with s ( b ) = 0 . 8370 and s ( b 1 ) = 0 . 2622 (c) r = 0 . 3319 , b = 63 . 3840 , b 1 = 50 . 5470 and ˆ Y = 63 . 3840 + 50 . 5470 X with s ( b ) = 0 . 5592 , s ( b 1 ) = 0 . 2622 (f) t (0 . 995; 17) = 2 . 898 , 50 . 5470 ± 2 : 898 ∗ (0 . 2622) , i.e. 49 . 787 ≤ β 1 ≤ 51 . 307 (g) ˆ Y = 94 . 8720 + 50 . 5470 ∗ 4 . 625 4. Let ˜ Y t = Y t − ρ 1 Y t − 1 − ρ 2 Y t − 2 and ˜ X t = X t − ρ 1 X t − 1 − ρ 2 X t − 2 . Then ˜ Y t = β (1 − ρ 1 − ρ 2 ) + β 1 ˜ X t + { ε t − ρ 1 ε t − 1 − ρ 2 ε t − 2 } i.e. ˜ Y t = β + β 1 ˜ X t + u i 1...
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## This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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