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Unformatted text preview: STA 302 / 1001 H  Summer 2004 Test 1 June 2, 2004 LAST NAME: FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: Time: 60 minutes Aids allowed: calculator. A table of values from the t distribution is on the last page (page 7). Total points: 40 Some formulae: b 1 = ( X i X )( Y i Y ) ( X i 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 WorkingHotelling coefficient: W = p 2 F 2 ,n 2;1 1 2 3 abcd 3 efg 1 1. (a) (2 points) Consider the simple linear regression model Y i = + 1 X i + i where the i s are independent and identically distributed with the N (0 , 2 ) distribution. Assume the X i s are fixed. What is the distribution of Y i when X i is 10? Y i N ( + 10 1 , 2 ) (b) (3 points) The least squares estimate of the Y intercept for the model in (a) is b as given on the first page. Show that b is an unbiased estimate of the intercept in the model. You may take as known any results that were proved in lecture....
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 Summer '04
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