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mont4e_sm_ch12_sec01

# mont4e_sm_ch12_sec01 - CHAPTER 12 Sections 12-1 12-1 223...

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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 x 2 2 = ± yx =++ 100 2 8 1 ± .( ) x =+ + + 95 15 3 2 4 11 x x x ± y 108 2 1 ± . 101 55 1 x 2 8 = ± () 100 2 4 8 1 ± ) 95 15 3 8 16 ± y 132 2 1 ± . 119 17 5 1 MODEL 1 0 20 40 60 80 100 120 140 160 02468 1 0 x y y = 132 + 2 y = 108 + 2 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 ± y per unit of . 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 = ± .( ) ( 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. 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 = σ 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 12-2
12-5. The regression equation is mpg = 49.9 - 0.0104 cid - 0.0012 rhp - 0.00324 etw + 0.29 cmp - 3.86 axle + 0.190 n/v Predictor Coef SE Coef T P Constant 49.90 19.67 2.54 0.024 cid -0.01045 0.02338 -0.45 0.662 rhp -0.00120 0.01631 -0.07 0.942 etw -0.0032364 0.0009459 -3.42 0.004 cmp 0.292 1.765 0.17 0.871 axle -3.855 1.329 -2.90 0.012 n/v 0.1897 0.2730 0.69 0.498 S = 2.22830 R-Sq = 89.3% R-Sq(adj) = 84.8% Analysis of Variance Source DF SS MS F P Regression 6 581.898 96.983 19.53 0.000 Residual Error 14 69.514 4.965 Total 20 651.412 a) 6 5 4 3 2 1 1897 . 0 855 . 3 292 . 0 00324 . 0 0012 . 0 01045 . 0 90 . 49 ˆ x x x x x x y + + = where v n x axle x cmp x etw x rhp x cid x / 6 5 4 3 2 1 = = = = = = b) 965 . 4 ˆ 2 = σ , , , , 67 . 19 ) ˆ ( 0 = β se 02338 . 0 ) ˆ ( 1 = se 01631 . 0 ) ˆ ( 2 = se 0009459 . 0 ) ˆ ( 3 = se , and 765 . 1 ) ˆ ( 4 = se 329 . 1 ) ˆ ( 5 = se 273 . 0 ) ˆ ( 6 = se c) ) 9 . 30 ( 1897 . 0 ) 07 . 3 ( 855 . 3 ) 9 . 9 ( 292 . 0 ) 4500 ( 0032 . 0 ) 253 ( 0012 . 0 ) 215 ( 01045 . 0 90 . 49 ˆ + + = y = 29.867 12-6.

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mont4e_sm_ch12_sec01 - CHAPTER 12 Sections 12-1 12-1 223...

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