420Hw02ans - STAT 420 Homework #2 (due Friday, February 3,...

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STAT 420 Homework #2 Spring 2012 (due Friday, February 3, by 4:00 p.m.) 1. Do NOT use a computer. The upper management at Initech wants to examine the relationship between the number of years on the job ( x ) and the number of TPS reports produced ( y ) for the middle-management employees. The data are as follows: x y 1 7 2 4 3 13 3 10 4 10 5 16 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. Σ x = 18, 6 18 = = n x x = 3. Σ y = 60, 6 60 = = n y y = 10. SXX = Σ ( x x ) 2 = 10, SXY = Σ ( x x ) ( y y ) = Σ ( x x ) y = 24. ( ) ( ) ( ) 10 24 2 1 β ˆ = = - - - x x y y x x = 2.4 . x y 1 0 β ˆ β ˆ - = = 10 – 2.4 3 = 2.8 . The least-squares regression line: y ˆ = 2.8 + 2.4 x .
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b) Calculate the fitted values i Y ˆ . c) Calculate the residuals e i . Does the sum of the residuals equal zero? b) c) x y y ˆ e 1 7 5.2 1.8 2 4 7.6 – 3.6 3 13 10 3 3 10 10 0 4 10 12.4 – 2.4 5 16 14.8 1.2 Total: 0
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2. The upper management at Initech wants to examine the relationship between the number of years on the job ( x ) and the number of TPS reports produced ( y ) for the middle-management employees. The data are as follows: x 1 2 3 3 4 5 Y 7 4 13 10 10 16 Consider the model Y i
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420Hw02ans - STAT 420 Homework #2 (due Friday, February 3,...

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