t2f03sol - STA 302 / 1001 H - Fall 2003 Test 2 November 10,...

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Unformatted text preview: STA 302 / 1001 H - Fall 2003 Test 2 November 10, 2003 LAST NAME:SOLUTIONS FIRST NAME: STUDENT NUMBER: ENROLLED IN: (circle one) STA 302 STA 1001 INSTRUCTIONS: Time: 50 minutes Aids allowed: calculator. A table of values from the t distribution is on the last page. A table of formulae is on the second to last page. Total points: 30 1 (a) (b) 2 (a) 2 (b) 3 (a) 3 (b) (c) 3(d) 1 1. (a) (4 points) State the simple linear regression model in matrix terms, defining all matrices and vectors. Include the Gauss-Markov assumptions. Y = X + (1 mark) where Y = Y 1 Y 2 . . . Y n , X = 1 X 1 1 X 2 . . . . . . 1 X n , = " 1 # , = 1 2 . . . n (1 mark) Gauss-Markov assumptions: (2 marks) E( ) = Cov( ) = 2 I (b) (4 points) Use matrix properties to prove e Y = where e is the vector of residuals and Y is the vector of predicted values. (Do not work with the individual elements of these matrices.) e Y = [( I- H ) Y ] HY = Y ( I- H ) HY = Y HY- Y H 2 Y = Y HY- Y HY = 2 2. The times to failure ( Y ) for 20 light bulbs were measured at 20 temperatures ( X )....
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This note was uploaded on 09/27/2009 for the course STA STA302 taught by Professor Gibbs during the Fall '04 term at University of Toronto- Toronto.

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t2f03sol - STA 302 / 1001 H - Fall 2003 Test 2 November 10,...

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