mont4e_sm_ch12_sec06 - Residuals V er sus P P GF (response...

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Sections 12-6 12-66. a) 2 33 . 0 205 . 189 15 . 26219 ˆ x x y + = b) H j 0 0 : β = for all j H j 1 0 : β for at least one j α = 0.05 5 , 2 , 05 . 0 5 , 2 , 05 . 0 79 . 5 2045 . 17 f f f f > = = Reject H and conclude that model is significant at α = 0.05 0 c) H 01 1 0 : β= H 11 1 0 : β≠ α = 0.05 571 . 2 | | 571 . 2 45 . 2 0 5 , 025 . 3 8 , 025 . , 0 > / = = = = t t t t t p n α Do not reject H and conclude insufficient evidence to support value of quadratic term in model at α = 0.05 0 d) One residual is an outlier 12-47
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Normality assumption appears acceptable Residuals against fitted values are somewhat unusual, but the impact of the outlier should be considered. -50 -40 -30 -20 -10 0 10 20 30 40 50 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Normal Score Residual Normal Probability Plot of the Residuals (response is y) 500 600 700 800 -50 -40 -30 -20 -10 0 10 20 30 40 50 Fitted Value Residual Residuals Versus the Fitted Values (response is y) 12-67. a) 2 495 . 1 232 . 1 633 . 1 ˆ x x y + = b) f 0 = 1858613, reject H 0 c) t 0 = 601.64, reject H 0 d) Model is acceptable. Observation number 10 has large leverage. 12-48
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-0.004 -0.002 0.000 0.002 0.004 0.006 -1 0 1 Normal Score Residual Normal Probability Plot of the Residuals (response is y) 0.0 0.5 1.0 1.5 2.0 2.5 -0.004 -0.002 0.000 0.002 0.004 0.006 x Residual Residuals Versus x (response is y) -8 -7 -6 -5 -4 -3 -2 -0.004 -0.002 0.000 0.002 0.004 0.006 Fitted Value Residuals Versus the Fitted Values (response is y) 12-68. a) 2 47 . 1 38 . 1 46 . 4 ˆ x x y + + = b) 0 : 0 = j H β for all j 12-49
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0 : 1 j H β for at least one j α = 0.05 9 , 2 , 05 . 0 0 9 , 2 , 05 . 0 26 . 4 99 . 1044 f f f f > = = Reject H 0 and conclude regression model is significant at α = 0.05 c) 0 : 11 0 = H 0 : 11 1 H α = 0.05 9 , 025 . 0 0 9 , 025 . 0 | | 262 . 2 97 . 2 t t t t > = = Reject H 0 and conclude that β is significant at α = 0.05 11 d) Observation number 9 is an extreme outlier. -5 -4 -3 -2 -1 0 1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is y) 25 35 45 55 65 75 85 0 1 Fitted Value Residual Residuals Versus the Fitted Values (response is y) 12-50
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e) 3 2 51 . 0 04 . 7 01 . 48 36 . 87 ˆ x x x y + + = 0 : 33 0 = β H 0 : 33 1 H α = 0.05 8 , 025 . 0 0 8 , 025 . 0 | | 306 . 2 91 . 0 t t t t > / = = Do not reject H 0 and conclude that cubic term is not significant at α = 0.05 12-69. a) Predictor Coef SE Coef T P Constant -1.769 1.287 -1.37 0.188 xl 0.4208 0.2942 1.43 0.172 x2 0.2225 0.1307 1.70 0.108 x3 -0.12800 0.07025 -1.82 0.087 x1x2 -0.01988 0.01204 -1.65 0.118 x1x3 0.009151 0.007621 1.20 0.247 x2x3 0.002576 0.007039 0.37 0.719 x1^2 -0.01932 0.01680 -1.15 0.267 x2^2 -0.00745 0.01205 -0.62 0.545 x3^3 0.000824 0.001441 0.57 0.575 S = 0.06092 R-Sq = 91.7% R-Sq(adj) = 87.0% Analysis of Variance Source DF SS MS F P Regression 9 0.655671 0.072852 19.63 0.000 Residual Error 16 0.059386 0.003712 Total 25 0.715057 13 12 3 2 1 009 . 0 02 . 0 128 . 0 222 . 0 421 . 0 769 . 1 ˆ x x x x x y + + + = 2 3 2 2 2 1 23 001 . 0 007 . 0 019 . 0 003 . 0 x x x x + + b) H 0 all 0 23 3 2 1 = = = = " H 1 at least one 0 j 16 , 9 , 05 . 0 0 16 , 9 , 05 . 0 54 . 2 628 . 19 f f f f > = = Reject H 0 and conclude that the model is significant at α = 0.05 c) Model is acceptable. 12-51
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-0.05 0.00 0.05 0.10 -2 -1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is y) 0.0 0.1 0.2 0.3 0.4 0.5 -0.05 0.00 0.05 0.10 Fitted Value Residual Residuals Versus the Fitted Values (response is y) d) 0 : 23 13 12 33 22 11 0 = = = = = = β H H 1 at least one 0 16 , 6 , 05 . 0 16 , 6 , 05 . 6 0359 . 0 0 3 2 1 23 13 12 33 22 11 0 74 . 2 612 . 1 003712 . 0 / ) , , , | , , , , , ( f f f MS r SS f E R > / = = = = ββ Do not reject H 0 0359 . 0 619763 . 0 65567068 . 0 ) | ( ) | ( ) | ( 0 3 2 1 0 3 2 1 23 13 12 33 22 11 0 3 2 1 23 13 12 33 22 11 = = = βββ R R R SS SS SS Reduced Model: 3 3 2 2 1 1 0 x x x y + + + = 12-70.
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch12_sec06 - Residuals V er sus P P GF (response...

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