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mont4e_sm_ch14_sec05

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

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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

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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 -1 50 0 -50 hardness Residual Residuals Versus hardness (response is life) 1 0 -1 50 0 -50 speed Residual Residuals Versus speed (response is life) 550 450 350 250 50 0 -50 Fitted Value Residual Residuals Versus the Fitted Values (response is life)
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

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