420Hw05ans - STAT 420 Fall 2008 Homework #5 (due Friday,...

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Unformatted text preview: STAT 420 Fall 2008 Homework #5 (due Friday, October 3, by 3:00 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 = 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. 7 252 = = & n x x = 36. 7 455 = = & n y y = 65. 4032 1008 SXX SXY & ˆ = = = 0.25 . x y ⋅- = & ˆ ¡ ˆ = 65 – 0.25 ⋅ 36 = 56 . Least-squares regression line: y ˆ = 56 + 0.25 x . b) Give an estimate for σ , the standard deviation of the observations about the true regression line? 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 SSE OR In class we showed that since ( ) ( ) & ˆ ˆ ¡ ˆ ¡ ˆ ¡ ˆ ¡ ˆ x x y x y x y i i i i x- + = +- = + = , RSS = ( ) ( ) ( ) 2 2 2 2 2 2 ¡ ˆ ¡ ˆ ¡ ˆ ˆ =- =- =- & & & x x x x y y i i i SXX = 252....
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This note was uploaded on 05/09/2010 for the course MATH 420 taught by Professor Stepanov during the Spring '10 term at University of Illinois, Urbana Champaign.

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420Hw05ans - STAT 420 Fall 2008 Homework #5 (due Friday,...

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