mont4e_sm_ch14_sec05 - Section 14-5 14-12 a) Analysis of...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
14-14 Section 14-5 14-12 a) Analysis of Variance for life (coded units) Source DF SS MS F P A 1 1332 1332 0.54 0.483
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
14-15 B 1 28392 28392 11.53 0.009 C 1 20592 20592 8.36 0.020 A*B 1 506 506 0.21 0.662 A*C 1 56882 56882 23.10 0.001 B*C 1 2352 2352 0.96 0.357 A*B*C 1 4830 4830 1.96 0.199 Error 8 19700 2463 Total 15 134588 S = 49.6236 R-Sq = 85.36% R-Sq(adj) = 72.56% Hardness, angle and the speed-angle interaction are significant. b) Estimated Effects and Coefficients for life (coded units) Term Effect Coef SE Coef T P Constant 413.13 12.41 33.30 0.000 speed 18.25 9.12 12.41 0.74 0.483 hardness 84.25 42.12 12.41 3.40 0.009 angle 71.75 35.87 12.41 2.89 0.020 speed*hardness -11.25 -5.63 12.41 -0.45 0.662 speed*angle -119.25 -59.62 12.41 -4.81 0.001 hardness*angle -24.25 -12.12 12.41 -0.98 0.357 speed*hardness*angle -34.75 -17.37 12.41 -1.40 0.199 y ˆ = 413.125 + 9.125 x 1 + 45.12 x 2 + 35.87 x 3 59.62 x 1 x 3 c) Analysis of the residuals shows that all assumptions are reasonable. 1 0 -1 50 0 -50 angle Residual Residuals Versus angle (response is life) 1 0 50 0 hardness Residuals Versus hardness (response is life) 1 0 50 0 speed Resi dual s Versus speed (response is life) 550 450 350 250 50 0 Fit ed Value Residuals Versus the Fitted Values (response is life)
Background image of page 2
14-16 -50 0 50 -2 -1 0 1 2 Normal Score Residual Normal Probability Plot of the Residuals (response is resp) 14-13 Term Effect Coef SE Coef T P Constant 175.250 0.5467 320.59 0.000 A 17.000 8.500 0.5467 15.55 0.000 B -1.625 -0.812 0.5467 -1.49 0.157 C 10.875 5.438 0.5467 9.95 0.000 D 8.375 4.187 0.5467 7.66 0.000 A*B -0.125 -0.063 0.5467 -0.11 0.910 A*C -0.625 -0.313 0.5467 -0.57 0.575 A*D 9.125 4.562 0.5467 8.35 0.000 B*C -0.250 -0.125 0.5467 -0.23 0.822 B*D 1.250 0.625 0.5467 1.14 0.270 C*D -1.250 -0.625 0.5467 -1.14 0.270 A*B*C 0.750 0.375 0.5467 0.69 0.503 A*B*D -0.500 -0.250 0.5467 -0.46 0.654 A*C*D -0.000 -0.000 0.5467 -0.00 1.000 B*C*D 0.125 0.063 0.5467 0.11 0.910 A*B*C*D -1.625 -0.812 0.5467 -1.49 0.157 Factors A, C, and D are significant as well as the interaction AD. 14-14 a) Estimated Effects and Coefficients for strength Term Effect A 1462.13 B 3537.87 C -137.12 D 474.62 E 425.38 A*B 1199.62 A*C 124.62 A*D 62.87 A*E 62.12 B*C -99.63 B*D -12.88 B*E -12.12 C*D 112.13 C*E -62.13 D*E 224.62 A*B*C -62.88 A*B*D 200.38 A*B*E 49.63 A*C*D 75.38 A*C*E 99.63 A*D*E -87.12 B*C*D 99.62 B*C*E -74.63 B*D*E -62.88 C*D*E 37.13
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
14-17 A*B*C*D -12.12 A*B*C*E 12.13 A*B*D*E 0.37 A*C*D*E 150.37 B*C*D*E -25.38 A*B*C*D*E 62.88 b) 3000 2000 100 0 2 1 0 - -2 Effect Normal Score ABD DE E D AB A B Normal Probability Plot of the Effects (response is strength, Alpha = .10) The effects that appear to be important are A, B, D, E, and the interactions AB, DE, and ABD. c) To maximize strength, the variables A, B, D, and E should be increased. Variable C is not significant thus any level of C would be acceptable. The regression equation is 4 2 1 5 4 2 1 5 4 2 1 2 . 100 3 . 112 8 . 599 7 . 212 3 . 237 9 . 1768 1 . 731 7 . 2888 ˆ x x x x x x x x x x x y + + + + + + + = Predictor Coef StDev T P Constant 2887.69 39.10 73.86 0.000 A 731.06 39.10 18.70 0.000 B 1768.94 39.10 45.24 0.000 D 237.31 39.10 6.07 0.000 E 212.69 39.10 5.44 0.000 AB 599.81 39.10 15.34 0.000 DE 112.31 39.10 2.87 0.008 ABD 100.19 39.10 2.56 0.017 S = 221.2 R-Sq = 99.1% R-Sq(adj) = 98.9% Analysis of Variance Source DF SS MS F P Regression 7 132722308 18960330 387.58 0.000 Error 24 1174077 48920 Total 31 133896385 Source DF Seq SS A 1 17102476 B 1 100132476 D 1 1802151 E 1 1447551 AB 1 11512801 DE 1 403651 ABD 1 321201
Background image of page 4
14-18 d) P-Value: 0.905 A-Squared: 0.182 Anderson-Darling Normality Test N: 32 StDev: 194.611 Average: 0.0000000 400 300 200 100 0 -100 -200 -300 -400 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability RESI1 Normal Probability Plot 1 0 -1 500 400 300 200 100 0 -100 -200 -300 -400 DE Residual Residuals Versus DE (response is streng) 1 0 -1 500 400 300 200 100 0 -100 -200 -300 -400 ABD Residuals Versus ABD (response is strengt) The normal probability plot of the residuals indicates the assumption of normality is reasonable.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 19

mont4e_sm_ch14_sec05 - Section 14-5 14-12 a) Analysis of...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online