Question

please solve the problem

this with the path found in part (a). 11.8. The data shown in the Table P11.2 were collected in an experiment to optimize crystal growth as a function of three variables x, x2, and x3. Large values of y (yield in grams) are desirable. Fit a second-order model and analyze the fitted surface. Under what set of conditions is maximum growth achieved? 9:57 P ^階脈目d) ENG 429201 ■TABLE p11.2 The Crystal Growth Experiment, Problem 118 TO 80 70 100 75 100 1.682 162 1S2 1682 1.682 65 82 113 100 1632 糕 100 avul'da İn Table pu 3 were collecid by a demi-

Answer 1

Growth ANOVA for Response Surface Quadratic Model Analysis of variance table [Partial sum of squares - Type IIII Sum of p-value Prob >F 0.1179 0.7929 0.6582 0.7474 0.6272 0.5246 0.4046 Value 2.20 0.073 0.21 0.11 025 0.43 0.76 1.08 12.18 7.23 df 3556.22 13.07 37.36 19.7 45.13 78.13 136.13 193.38 2189.02 1299.63 1797.53 938.20 859.33 5353.75 Model A-A B-B C-C AB AC 395.14 13.07 37.36 19.7 45.13 78.13 136.13 193.38 2189.02 1299.63 79.75 187.64 171.87 not significant 0.3241 0.0058 0.0227 10 Lack of Fit Pure Error Cor Total 1.09 0.4628 not significant 19 The "Model F-value" of 2.20 implies the model is not significant relative to the noise. 11.79 % chance that a "Model F-value" this large could occur due to noise. There is a R-Squared Adj R-Squared 0.3621 Pred Adeq Precision3.971 0.6642 Std. Dev Mean С.V.% PRESS 13.41 83.25 16.10 8365.77 R-Squared 0.5626

95% CI High VIF 112.83 Coefficient Estimatedf 95% CI Low 88.47 Standard Error 5.47 3.63 3.63 3.63 4.74 4.74 4.74 Factor Intercept 1.00 1.00 1.00 1.00 1.00 1.00 1.65 1.20 2.37 3.13 4.12 3.66 12.32 9.49 -6.43 9.28 8.19 13.69 14.6 9.74 6.88 2.94 7.44 S.44 4.21 B-B C-C AB AC BC 3.53 11.53 -20.19 10 1.02 1.02 B2 C2 3.53 3.53 4.45 Final Equation in Terms of Actual Factors Growth +100.65022 +0.97816 +1.65395 -1.20118 +2.37500 3.12500 -4.12500 3.66244 -12.32236 9.49463 o sl x2 x1x2 x1x3 x2 x3 x12 reasonable reduced model is shown below.

Design Ex ANOVA for Response Surface Reduced Quadratic Model Analysis of variance table [Partial sum of squares - Type IIII Sum of p-value Prob F 0.0084 0.6260 0.7228 0.0021 0.0125 Value 5.12 025 0.13 13.80 8.04 3090.40 37.36 19.71 2082.16 1213.87 2263.35 1404.02 859.33 5353.75 772.60 37.36 19.71 2082.16 1213.87 150.89 140.40 171.87 B-B C-C 15 10 Lack of Fit Pure Error Cor Total 0.82 0.6339 not significant 19 The Model F-value of 5.12 implies the model is significant. There is only a 0.84% chance that a "Model F-Value" this large could occur due to noise. R-Squared Std. Dev 12.28 83.25 14.76 4479.20 0.5772 Adj R-Squared .4645 Pred R С.V.% PRESS -Squared0.1634 Adeq Precision5.961 95% CI Coefficient Estimate 97.65 1.65 Standard 95% CI High 106.72 8.74 5.88 5.10 Factor VIF 88.59 5.43 -8.29 18.82 1.00 1.00 1.01 1.01 B-B C-C 3.32 3.32 3.22 1.20 11.96 -9.13 B2 2.27 Final Equation in Terms of Coded Factors: +97.65 +1.65 -11.96 9.13 Final Equation in Terms of Actual Factors: +97.65184 +1.65395 1.20118 11.95829 -9.13056 x2 x22

The contour plot identifies a maximum near the center of the design space. Growth 1.00 81.7192 81.7192 85.7249 Prediction 97.7485 95% CI Low 88.6941 95% CI High 106.803 SE Mean 4.248 SE Pred X1 X2 0.50 12.9975 0.07 0.07 0.00 0.50 85.7249 81.7192 1.00 1.00 0.00 0.50 1.00 -0.50 B: B