quiz8Sp2011_key

# quiz8Sp2011_key - ) / ( n-2) = p 21 , 026 . 1 / (7-2) = 64...

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NAME: Stat 205 Quiz 8 To investigate the dependence of energy expenditure on body build, researchers used under- water weight techniques to determine the fat-free body mass for each of seven men. The also measured the total 24-hour energy expenditure for each man during conditions of quiet sedentary activity. Let Y be the energy expenditure (kcal) and X be the fat-free mass (kg). The data are plotted here: 50 55 60 65 70 75 2000 2200 2400 fat_free_mass energy_expenditure Here are the statistics needed to answer the questions below: ¯ x = 62 . 40 , ¯ y = 2 , 168 , ( x i - ¯ x ) 2 = 877 . 74 , ( x i - ¯ x )( y i - ¯ y ) = 21 , 953 . 7 , SS ( resid ) = 21 , 026 . 1 . (a) Compute b 0 and b 1 from regressing Y on X . What is the ﬁtted regression line? Answer: b 1 = ( x i - ¯ x )( y i - ¯ y ) ( x i - ¯ x ) 2 = 21 , 953 . 7 877 . 74 = 25.01 b 0 = 2 , 168 - 25 . 012(62 . 40) = 607.3 The ﬁtted line is Y = 607.3 + 25.01 x (b) Find a 95% conﬁdence interval for β 1 . Answer: First, s y | x = p SS ( resid

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Unformatted text preview: ) / ( n-2) = p 21 , 026 . 1 / (7-2) = 64 . 85 . Then SE b 1 = s y | x / p ∑ ( x i-¯ x ) 2 = 64 . 85 / √ 877 . 74 = 2 . 19 . From the back of the book, t . 975 = 2 . 571 on df = 7-2 = 5 . So a 95% conﬁdence interval is 25 . 01 ± 2 . 571(2 . 19) giving (19.4,30.6) (c) Test H : β 1 = 0 at the 5% signiﬁcance level. What does this test imply about the relation-ship between fat-free mass and energy expenditure? Answer: Since the 95% conﬁdence interval does not include zero, we reject H : β 1 = 0 at the 5% signiﬁcance level. There is a signiﬁcant (positive) linear relationship between energy expenditure and fat-free mass. (d) Answer: At X = 65 kg, we have ˆ Y = 607 . 3 + 25 . 01 × 65 ≈ 2233 kcal...
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## This note was uploaded on 12/14/2011 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.

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quiz8Sp2011_key - ) / ( n-2) = p 21 , 026 . 1 / (7-2) = 64...

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