ch12 - CHAPTER 12 Sections 12-1 223 553 10 a) X X = 223...

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CHAPTER 12 Sections 12-1 12-1. a) = XX 10 223 553 223 5200 9 12352 553 12352 31729 . = Xy 1916 0 43550 8 104736 8 . . . b) so = 126 . 1 713 . 3 055 . 171 ˆ β 2 1 126 . 1 714 . 3 055 . 171 ˆ x x y + = c) 49 . 189 ) 43 ( 126 . 1 ) 18 ( 714 . 3 055 . 171 ˆ = + = y 12-2. a) y X X X = 1 ) ( ˆ ⎡− = 2532 . 0 0931 . 0 9122 . 1 ˆ b) 2 1 2532 . 0 0931 . 0 9122 . 1 ˆ x x y + + = 3678 . 29 ) 50 ( 2532 . 0 ) 200 ( 0931 . 0 9122 . 1 ˆ = + + = y 12-3. a) Model 1 Model 2 ± yx = + + 100 2 8 1 ± .( ) yx x x 2 2 = = + + + 95 15 3 2 4 11 x ± y = + 108 2 1 ± . = + 101 55 1 x 2 8 = ± () = + + 100 2 4 8 1 ± ) x = + + + 95 3 8 16 ± y = x + 132 2 1 ± . = + 119 17 5 1 MODEL 1 0 20 40 60 80 100 120 140 160 024681 0 x y y = 132 + 2 x y = 108 + 2 x 12-1
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M O D E L 2 0 50 100 150 200 250 300 350 0 5 10 15 x y y = 101 + 5.5 x y = 119 + 17.5 x The interaction term in model 2 affects the slope of the regression equation. That is, it modifies the amount of change per unit of on . x 1 ± y b) x 2 5 = ± () yx =++ 100 2 4 5 1 ± =+ 120 2 1 Then, 2 is the expected change on per unit of . ± y x 1 NO, it does not depend on the value of x 2 , because there is no relationship or interaction between these two variables in model 1. c) x 2 5 = x 2 2 = x 2 8 = ± .( )( yx x ) + + 95 15 3 5 2 5 11 ± . = + 110 115 1 ± . = + 101 55 1 ± . = + 119 17 5 1 Change per unit of x 1 11.5 5.5 17.5 Yes, result does depend on the value of x 2 , because x 2 interacts with x 1 . 12-4 The regression equation is y = - 2.75 + 0.00362 x2 + 0.204 x7 - 0.00467 x8 Predictor Coef SE Coef T P Constant -2.747 7.823 -0.35 0.729 x2 0.0036229 0.0006868 5.28 0.000 x7 0.20355 0.08677 2.35 0.028 x8 -0.004673 0.001272 -3.67 0.001 S = 1.687 R-Sq = 79.1% R-Sq(adj) = 76.5% Analysis of Variance Source DF SS MS F P Regression 3 258.683 86.228 30.31 0.000 Residual Error 24 68.281 2.845 Total 27 326.964 a) 8 7 2 0047 . 0 2035 . 0 0036 . 0 747 . 2 ˆ x x x y + + = b) 845 . 2 ˆ 2 = σ c) , , , and 823 . 7 ) ˆ ( 0 = β se 0006868 . ) ˆ ( 2 = se 08677 . ) ˆ ( 7 = se 001272 . ) ˆ ( 8 = se d) ) 1800 ( 004673 . 0 ) 60 ( 20355 . 0 ) 2000 ( 0036229 . 0 747 . 2 ˆ + + = y games. 8 3 . 8 ˆ = y 12-2
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12-5. Predictor Coef StDev T P Constant 33.449 1.576 21.22 0.000 xl -0.054349 0.006329 -8.59 0.000 x6 1.0782 0.6997 1.54 0.138 S = 2.834 R-Sq = 82.9% R-Sq(adj) = 81.3% Analysis of Variance Source DF SS MS F P Regression 2 856.24 428.12 53.32 0.000 Error 22 176.66 8.03 Total 24 1032.90 a) 6 1 07822 . 1 05435 . 0 4491 . 33 ˆ x x y + = b) 03 . 8 ˆ 2 = σ c) mpg. 30 . 19 ) 2 ( 07822 . 1 ) 300 ( 05435 . 0 4491 . 33 ˆ = + = y 12-6 Predictor Coef SE Coef T P Constant -123.1 157.3 -0.78 0.459 X1 0.7573 0.2791 2.71 0.030 X2 7.519 4.010 1.87 0.103 X3 2.483 1.809 1.37 0.212 X4 -0.4811 0.5552 -0.87 0.415 S = 11.79 R-Sq = 85.2% R-Sq(adj) = 76.8% Analysis of Variance Source DF SS MS F P Regression 4 5600.5 1400.1 10.08 0.005 Residual Error 7 972.5 138.9 Total 11 6572.9 a) 4 3 2 1 4811 . 0 483 . 2 519 . 7 7573 . 0 1 . 123 ˆ x x x x y + + + = b) 00 . 139 ˆ 2 = c) , , , , and 3 . 157 ) ˆ ( 0 = β se 2791 . 0 ) ˆ ( 1 = se 010 . 4 ) ˆ ( 2 = se 809 . 1 ) ˆ ( 3 = se 5552 . 0 ) ˆ ( 4 = se d) 476 . 290 ) 98 ( 4811 . 0 ) 90 ( 483 . 2 ) 24 ( 519 . 7 ) 75 ( 7573 . 0 1 . 123 ˆ = + + + = y 12-7. Predictor Coef SE Coef T P Constant 383.80 36.22 10.60 0.002 Xl -3.6381 0.5665 -6.42 0.008 X2 -0.11168 0.04338 -2.57 0.082 S = 12.35 R-Sq = 98.5% R-Sq(adj) = 97.5% Analysis of Variance Source DF SS MS F P Regression 2 29787 14894 97.59 0.002 Residual Error 3 458 153 Total 5 30245 a) 2 1 1119 . 0 6381 . 3 80 . 383 ˆ x x y = b) , , , and 0 . 153 ˆ 2 = 22 . 36 ) ˆ ( 0 = se 5665 . 0 ) ˆ ( 1 = se 04338 . ) ˆ ( 2 = se c) 95 . 180 ) 1000 ( 1119 . 0 ) 25 ( 6381 . 3 80 . 383 ˆ = = y d) Predictor Coef SE Coef T P Constant 484.0 101.3 4.78 0.041 Xl -7.656 3.846 -1.99 0.185 X2 -0.2221 0.1129 -1.97 0.188 X1*X2 0.004087 0.003871 1.06 0.402 S = 12.12 R-Sq = 99.0% R-Sq(adj) = 97.6% Analysis of Variance Source DF SS MS F P Regression 3 29951.4 9983.8 67.92 0.015 Residual Error 2 294.0 147.0 Total 5 30245.3 12 2 1 0041 . 0 222 . 0 656 . 7 0 . 484 ˆ x x x y = 12-3
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e) , , , and 0 . 147 ˆ 2 = σ 3 . 101 ) ˆ ( 0 = β se 846 . 3 ) ˆ ( 1 = se 113 . 0 ) ˆ ( 2 = se 0039 . 0 ) ˆ ( 12 = se f) 1 . 173 ) 1000 )( 25 ( 0041 . 0 ) 1000 ( 222 . 0 ) 25 ( 656 . 7 0 . 484 ˆ = = y The predicted value is smaller 12-8.
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue University.

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ch12 - CHAPTER 12 Sections 12-1 223 553 10 a) X X = 223...

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