t2sols04 - STA 302 / 1001 H - Summer 2004 Test 2 June 16,...

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Unformatted text preview: STA 302 / 1001 H - Summer 2004 Test 2 June 16, 2004 LAST NAME:SOLUTIONS 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 second to last page (page 8). A table of formulae is on the last page (page 9). Total points: 30 1 2 3 ab 3 cdef 1 1. Suppose the following four pairs of observations have been made Y i 1 2 1 3 X i 1 2 3 and a simple linear regression is to be fit to the data. ( X X )- 1 = 7 / 10- 3 / 10- 3 / 10 1 / 5 ! and e e = 1 . 5 (a) (1 point) State the X matrix. 1 1 1 1 2 1 3 (b) (3 marks) Find the least squares estimates of the slope and intercept of the regression line. b = ( X X )- 1 X Y = 7 / 10- 3 / 10- 3 / 10 1 / 5 ! 1 1 1 1 1 2 3 ! 1 2 1 3 = 7 / 10- 3 / 10- 3 / 10 1 / 5 ! 7 13 ! = 1 . 5 ! (c) (2 marks) Estimate the covariance between the estimators of the slope and intercept. s 2 = 1 . 5 / 2 = . 75 Cov( b , b 1 ) = . 75(- 3 / 10) =- . 225 2 2. For the multiple linear regression model Y = X + , the least squares estimates are b = ( X X )-...
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t2sols04 - STA 302 / 1001 H - Summer 2004 Test 2 June 16,...

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