This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 WorkingHotelling 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....
View
Full Document
 Summer '04
 Gibbs
 Statistics, Normal Distribution, Regression Analysis, Standard Deviation, 10%, xi −x

Click to edit the document details