# t1sol - STA 302 1001 H Summer 2004 Test 1 – June 2 2004...

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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 ) = σ 2 ∑ ( X i- X ) 2 Var( b ) = σ 2 1 n + X 2 ∑ ( X i- X ) 2 Cov( b , b 1 ) =- σ 2 X ∑ ( X i- X ) 2 SSTO = ∑ ( Y i- Y ) 2 SSE = ∑ ( Y i- ˆ Y i ) 2 SSR = b 2 1 ∑ ( X i- X ) 2 = ∑ ( ˆ Y i- Y ) 2 σ 2 { ˆ Y h } = Var( ˆ Y h ) = σ 2 1 n + ( X h- X ) 2 ∑ ( X i- X ) 2 σ 2 { pred } = Var( Y h- ˆ Y h ) = σ 2 1 + 1 n + ( X h- X ) 2 ∑ ( X i- X ) 2 Working-Hotelling coefficient: W = p 2 F 2 ,n- 2;1- α 1 2 3 abcd 3 efg 1 1. (a) (2 points) Consider the simple linear regression model Y i = β + β 1 X i + ² i where the ² i ’s are independent and identically distributed with the N (0 , σ 2 ) distribution. Assume the X i ’s are fixed. What is the distribution of Y i when X i is 10? Y i ∼ N ( β + 10 β 1 , σ 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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t1sol - STA 302 1001 H Summer 2004 Test 1 – June 2 2004...

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