HW Solutions Stat 106

HW Solutions Stat 106 - +15 Xi15 + 16 Xi16 + 17 Xi17 + 26...

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+ β 15 X i 15 + β 16 X i 16 + β 17 X i 17 + β 26 X i 26 + ± i Coef. b q b 0 8 . 028 b 1 . 127 b 2 . 003 b 3 . 021 b 4 2 . 077 Coef. b q b 5 . 724 b 6 . 467 b 7 . 766 b 12 . 354 b 13 . 066 Coef. b q b 14 . 316 b 15 . 318 b 16 . 117 b 17 . 021 b 26 . 182 e. H 0 : β 12 = ··· = β 17 = β 26 =0 , H a : not all β q =0 . F =(6 . 046 / 7) ÷ ( . 1958 / 1) = 4 . 41, F ( . 99; 7 , 1)=5 , 928. If F 5 , 928 conclude H 0 , otherwise H a . Conclude H 0 . 29.19. a. Coef. b q P -value b 0 8 . 028 b 1 . 127 . 581 b 2 . 003 . 989 b 3 . 021 . 928 Coef. b q P -value b 4 2 . 077 . 000 b 5 . 724 . 011 b 6 . 467 . 067 b 7 . 766 . 008 b. H 0 : Case i not an outlier, H a : case i an outlier ( i =3 , 14). t 3 =2 . 70, t 14 = 4 . 09, t ( . 99844; 7) = 4 . 41. If | t i |≤ 4 . 41 conclude H 0 , otherwise H a . Conclude H 0 for both cases. c. H 0 : Normal, H a : not normal. r = . 938. If r . 929 conclude H 0 , otherwise H a . Conclude H 0 . d. H 0 : β q =0 , H a : β q 6 =0 . s { b q } = . 2208. If P -value . 02 conclude H 0 , otherwise H a . Active eFects (see part a): β 4 , β 5 , β 7 e. Set X 4 = 1, X 5 =1 , X 7
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