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420Hw03 - STAT 420 Homework#3(due Friday February 8 by 4:00...

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STAT 420 Spring 2008 Homework #3 (due Friday, February 8, by 4:00 p.m.) 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 = β 0 + β 1 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? d) How much time would you expect the employee to need to perform the task after consuming 144 ounces of beer.
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1. (continued) e) The company statistician said that the prediction obtained in part (d) should be
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