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Unformatted text preview: STA 302 H1F / 1001 HF Fall 2007 Test 1 October 24, 2007 LAST NAME: FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: Time: 90 minutes Aids allowed: calculator. A table of values from the t distribution is on the last page (page 8). Total points: 50 Some formulae: b 1 = ( X i X )( Y i Y ) ( X i X ) 2 = X i Y i n X Y X 2 i n X 2 b = Y b 1 X Var( b 1 ) = 2 ( X i X ) 2 Var( b ) = 2 1 n + X 2 ( X i X ) 2 Cov( b , b 1 ) = 2 X ( X i X ) 2 SSTO = ( Y i Y ) 2 SSE = ( Y i Y i ) 2 SSR = b 2 1 ( X i X ) 2 = ( Y i Y ) 2 2 { Y h } = Var( Y h ) = 2 1 n + ( X h X ) 2 ( X i X ) 2 2 { pred } = Var( Y h Y h ) = 2 1 + 1 n + ( X h X ) 2 ( X i X ) 2 r = ( X i X )( Y i Y ) p ( X i X ) 2 ( Y i Y ) 2 WorkingHotelling coefficient: W = p 2 F 2 ,n 2; 1 2a 2bcdef 2ghi 2j 3 1 1. The following questions require derivations of results for the simple linear regression model. (a) (2 marks) In lecture we showed that n i =1 e i = 0 and n i =1 e i X i = 0. Given these results, what is n i =1 e i Y i ? Justify your answer. (b) (5 marks) Show that the total Sum of Squares in a regression can be decomposed as n X i =1 Y i Y 2 + n X i =1 Y i Y i 2 You may use any results that were derived in lecture....
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 Fall '09

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