420Hw03ans - STAT 420 Homework#3(due Friday February 8 by...

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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 Beer Consumption, x Time, y ( ) 2 x x - ( ) ( ) y y x x - - ( ) 2 y y - 0 62 1296 108 9 12 50 576 360 225 24 59 144 72 36 36 74 0 0 81 48 59 144 –72 36 60 83 576 432 324 72 68 1296 108 9 Sum: 252 455 4032 1008 720 SXX SXY SYY 7 252 = = n x x = 36. 7 455 = = n y y = 65. 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 ).

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a) Find the equation of the least-squares regression line. 4032 1008 SXX SXY 1 ˆ = = = 0.25 . x y - = 1 0 ˆ ˆ = 65 – 0.25 36 = 56 . Least-squares regression line: y ˆ = 56 + 0.25 x . x y y ˆ e e 2 0 62 56 6 36 12 50 59 9 81 24 59 62 3 9 36 74 65 9 81 48 59 68 9 81 60 83 71 12 144 72 68 74 6 36 Sum: 0 468 RSS b) Give an estimate for σ , the standard deviation of the observations about the true
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420Hw03ans - STAT 420 Homework#3(due Friday February 8 by...

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