t2f03 - STA 302 / 1001 H - Fall 2003 Test 2 November 10,...

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STA 302 / 1001 H - Fall 2003 Test 2 November 10, 2003 LAST NAME: 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
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1. (a) (4 points) State the simple linear regression model in matrix terms, defning all matrices and vectors. Include the Gauss-Markov assumptions. (b) (4 points) Use matrix properties to prove e 0 ˆ Y = 0 where e is the vector oF residuals and ˆ Y is the vector oF predicted values. (Do not work with the individual elements oF these matrices.) 2
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2. The times to failure ( Y ) for 20 light bulbs were measured at 20 temperatures ( X ). A simple linear regression was carried out to explore how the failure time is related to the temperature. (a) (5 points) Here are some calculated values from the 20 data points.
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t2f03 - STA 302 / 1001 H - Fall 2003 Test 2 November 10,...

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