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Unformatted text preview: Stat/ME 424, Spring 2008 First Midterm Examination (Total : 100 points) • This is a closed book exam, except for three pages of notes. • You are allowed to use calculators. • There are four problems in this exam. In order to get full credit, please answer all problems. • Please put your answers in a blue book with your name on the blue book cover. Problem 1 (40 pts) A simple linear regression model y = β + β 1 x + ε with ε ∼ N ( , σ 2 ) is fitted to the accom panying data on x = % refusederived fuel (RDF) heat input and y = % efficiency for a certain boiler. x 37 30 48 29 27 16 20 y 78.0 77.2 74.4 77.7 76.9 79.0 82.1 76.5 with ¯ y = 77 . 725, ¯ x = 25 . 875, ˆ β = 81 . 173, ∑ ( x i ¯ x ) 2 = 1442 . 875 and RSS = 8 . 7328 (a) Compute a 95% confidence interval for β 1 . You may find the following information useful. Upper percentiles of t distributions: t 6 , . 025 = 2 . 45 , t 6 , . 05 = 1 . 94 , t 7 , . 05 = 1 . 89 , t 7 , . 025 = 2 . 36 , t 8 , . 025 = 2 . 31 , t 8 , . 05 = 1 . 86 ....
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 Spring '08
 peter
 Regression Analysis, linear regression model, heat input

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