# t1f05 - STA 302 1001 H Fall 2005 Test 1 LAST NAME FIRST...

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Unformatted text preview: STA 302 / 1001 H - Fall 2005 Test 1 October 19, 2005 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 ) = 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 r = ∑ ( X i- X )( Y i- Y ) p ∑ ( X i- X ) 2 ∑ ( Y i- Y ) 2 Working-Hotelling coefficient: W = p 2 F 2 ,n- 2;1- α 1 2 3 4abc 4def 4ghi 1 1. (10 points) A simple linear regression model is fit on n observed data points. (a) What is the difference between β 1 and b 1 ? (b) What does it mean if R 2 = 1? (c) In lecture we showed ∑ n i =1 e i = 0 and ∑ n i =1 e i X i = 0. Show that ∑ n i =1 e i ˆ Y i = 0. (You may use the results shown in class if they are helpful.) (d) Explain why the result in (c) implies that the residuals and predicted values are uncor- related and why this is useful....
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t1f05 - STA 302 1001 H Fall 2005 Test 1 LAST NAME FIRST...

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