sta108_handout6

sta108_handout6 - Handout 6 F-test for lack of fit...

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Unformatted text preview: Handout 6 F-test for lack of fit (requires replication): Growth data (reexpressed): j = 1 j = 2 j = 3 j = 4 j = 5 X 1 = 5 X 2 = 10 X 3 = 15 X 4 = 20 X 5 = 25 i = 1 Y 11 = 68 . 5 Y 12 = 79 . 4 Y 13 = 85 . 3 Y 14 = 88 . Y 15 = 90 . 4 i = 2 Y 21 = 70 . Y 22 = 77 . 6 Y 24 = 88 . 7 Y 25 = 89 . 6 i = 3 Y 34 = 86 . 3 Mean Y j Y 1 = 69 . 25 Y 2 = 78 . 5 Y 3 = 85 . 3 Y 4 = 87 . 67 Y 5 = 90 . 3 n 1 = 2 n 2 = 2 n 3 = 1 n 4 = 3 n 5 = 2 Model: Y ij = j + ij ,i = 1 ,...,n j ,j = 1 ,...,c, where { ij } are i.i.d. N (0 , 2 ). So E ( Y ij ) = j and V ar ( Y ij ) = 2 . The total number of observations is n = n 1 + + n c . Here, n = 10 and c = 5. We want to test, at a level of significance = 0 . 05 , H : j = + 1 X j for all j , against H 1 : j s do not lie on a straight line. Full model: Y ij = j + ij . Reduced model: Y ij = + 1 X j + ij ....
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This note was uploaded on 09/28/2011 for the course STA STA 108 taught by Professor Jiang during the Summer '09 term at UC Davis.

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sta108_handout6 - Handout 6 F-test for lack of fit...

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