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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online