# t2s04 - STA 302 1001 H Summer 2004 Test 2 LAST NAME STUDENT...

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

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1. Suppose the following four pairs of observations have been made Y i 1 2 1 3 X i 0 1 2 3 and a simple linear regression is to be Ft to the data. ( X 0 X ) - 1 = 7 / 10 - 3 / 10 - 3 / 10 1 / 5 ! and e 0 e = 1 . 5 (a) (1 point) State the X matrix. (b) (3 marks) ±ind the least squares estimates of the slope and intercept of the regression line. (c) (2 marks) Estimate the covariance between the estimators of the slope and intercept. 2
2. For the multiple linear regression model Y = X β + ² , the least squares estimates are b = ( X 0 X ) - 1 X 0 Y and the residuals are e = Y - Xb . Assume the Gauss- Markov conditions hold. (a) (3 marks) Show that

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t2s04 - STA 302 1001 H Summer 2004 Test 2 LAST NAME STUDENT...

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