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420Hw05 - STAT 420(due Friday October 3 by 3:00 p.m...

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STAT 420 Fall 2008 Homework #5 (due Friday, October 3, by 3:00 p.m.) Do NOT use a computer for this homework assignment. Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. An employee claims that drinking beer has no effect on the amount of time it takes for him to perform a particular task. The following data show how many seconds he took to perform the task after consuming various quantities of beer, measured in ounces: Beer Consumption, x Time, y 0 62 12 50 24 59 36 74 48 59 60 83 72 68 Σ x = 252, Σ y = 455, Σ x 2 = 13,104, Σ y 2 = 30,295, Σ x y = 17,388, Σ ( x x ) 2 = 4032, Σ ( y y ) 2 = 720, Σ ( x x ) ( y y ) = Σ ( x x ) y = 1,008. Consider the model Y i = α + β x i + ε i ., where ε i ’s are i.i.d. N ( 0, σ 2 ) . a) Find the equation of the least-squares regression line. b) Give an estimate for σ , the standard deviation of the observations about the true regression line? c) What proportion of observed variation in time needed to perform the task is explained by a straight-line relationship with the amount of beer consumed?
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