( ) 4 1 1 1 145 1 110 1
(baking powder) 1 ( ) ( ) 1 10g 1 1 2.5g 1 1 1 1 60 10 (two level design, D-optimal) 32 1/2 fraction Two Level Fractional Factorial Design D-Optimal Design
1. 60 120 2. 3. 40 10 ( 20 ) 20
5 30 4. 5. 6. 60 40 7. ( ) 8. 60 9. 15 Std run Block (cm) 4 1 Block 1 4 145-1 7.5 16 2 Block 1 4 145 1 7.85 8 3 Block 1 4 145-1 6.9 3 4 Block 1 1 145-1 5.2 7 5 Block 1 1 145-1 4.3 10 6 Block 1 4 110 1 8.4 12 7 Block 1 4 145 1 8.7 2 8 Block 1 4 110-1 6.25 5 9 Block 1 1 110-1 5.6 1 10 Block 1 1 110-1 4.15 15 11 Block 1 1 145 1 6.15 11 12 Block 1 1 145 1 6.25 6 13 Block 1 4 110-1 6.4 9 14 Block 1 1 110 1 5.7 14 15 Block 1 4 110 1 8.05 13 16 Block 1 1 110 1 4.6
ANOVA DESIGN-EXPERT Plot Outlier T 3.50 1.75 Outlier T -1.75-3.50 1 4 7 10 13 16 Run Num ber DESIGN-EXPERT Plot Cook's Distance 1.00 0.75 Cook's Distance 0.50 0.25 1 4 7 10 13 16 Run Num ber
ANOVA Response: ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 27.785 5 5.557 17.52997 01 significant A 20.47563 1 20.47563 64.59188 < 01 B 0.855625 1 0.855625 2.699132 0.1314 C 0.330625 1 0.330625 1.042981 0.3312 D 5.5225 1 5.5225 17.42114 19 E 0.600625 1 0.600625 1.894716 0.1987 Residual 3.17 10 0.317 Cor Total 30.955 15 The Model F-value of 17.53 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are significant. In this case A, D are significant model terms. A ( ) D ( ) A D ANOVA ANOVA Use your mouse to right click on individual cells for definitions. Response: ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 25.998125 2 12.9990625 34.09160257 < 01 significant A 20.475625 1 20.475625 53.69978565 < 01 D 5.5225 1 5.5225 14.48341949 22 Residual 4.956875 13 0.381298077 Cor Total 30.955 15
The Model F-value of 34.09 implies the model is significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are significant. In this case A, D are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve your model. Std. Dev. 0.617493382 R-Squared 0.839868357 Mean 6.375 Adj R-Squared 0.81523272 C.V. 9.686170699 Pred R-Squared 0.757433725 PRESS 7.508639053 Adeq Precision 12.85611544 The "Pred R-Squared" of 0.7574 is in reasonable agreement with the "Adj R-Squared" of 0.8152. "Adeq Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 12.856 indicates an adequate signal. This model can be used to navigate the design space. Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF Intercept 6.375 1 0.154373346 6.041496663 6.708503337 A- 1.13125 1 0.154373346 0.797746663 1.464753337 1 D- 0.5875 1 0.154373346 0.253996663 0.921003337 1 pattern transformation
DESIGN-EXPERT Plot Norm al Plot of Residuals 99 95 Normal % Probability 90 80 70 50 30 20 10 5 1-2.21-1.24-0.26 0.72 1.70 Studentized Residuals DESIGN-EXPERT Plot Residuals vs. Predicted 3.00 Studentized Residuals 1.50-1.50-3.00 4.66 5.52 6.38 7.23 8.09 Predicted
DESIGN-EXPERT Plot Residuals vs. Run 3.00 Studentized Residuals 1.50-1.50-3.00 1 4 7 10 13 16 Run Num ber DESIGN-EXPERT Plot Residuals vs. 3.00 Studentized Residuals 1.50-1.50-3.00 1 2 3 4
DESIGN-EXPERT Plot Residuals vs. 3.00 Studentized Residuals 1.50-1.50-3.00-1 0 1 DESIGN-EXPERT Plot Lam bda Current = 1 Best = 1.26 L o w C.I. = -0.4 3 High C.I. = 2.98 Recom m end transform : None (Lam bda = 1) Ln(ResidualSS) Box-Cox Plot for Power Transforms 3.01 2.66 2.30 1.95 1.59-3 -2-1 0 1 2 3 Lam bda model Final Equation in Terms of Actual Factors: = 4.48958333 0.75416667 * 0.5875 *
A D transform best model A D output?? 145 145 ( 130 145 110 ) D-optimal 2 level 2 replicate 12 3 level-1 4 0 5 level +1 10:1 level -1 15:1 level 0 20:1 level +1 ANOVA( )
Std Run Block 7 1 Block 1-1 0 7.5 10 2 Block 1-1 -1 7.7 6 3 Block 1-1 -1 7.8 2 4 Block 1 1 1 7.6 9 5 Block 1 0 1 8.2 1 6 Block 1 1-1 7.8 4 7 Block 1 0 0 8.3 5 8 Block 1-1 1 7.3 8 9 Block 1 0-1 8.1 12 10 Block 1 1 1 7.8 11 11 Block 1 1-1 7.4 3 12 Block 1 1 0 7.5 DESIGN-EXPERT Plot C ook's D istance 1.00 0.75 Cook's Distance 0.50 0.25 1 3 5 7 9 11 Run Num ber ANOVA Use your mouse to right click on individual cells for definitions. Response: ANOVA for Response Surface Quadratic Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 0.943172 5 0.1886343 6.78425 0.0186 significant
A 0.017422 1 0.01742206 0.62659 0.4588 B 0.025957 1 0.02595674 0.93354 0.3713 A2 0.867143 1 0.86714252 31.1868 14 B2 1041 1 104107 0.03744 0.8530 AB 0.113275 1 0.11327495 4.07394 0.0901 Residual 0.166828 6 0.02780475 Lack of Fit 0.061828 3 0.0206095 0.58884 0.6629 not significant Pure Error 0.105 3 0.035 Cor Total 1.11 11 The Model F-value of 6.78 implies the model is significant. There is only a 1.86% chance that a "Model F-Value" this large could occur due to noise. Values of "Prob > F" less than 0.0500 indicate model terms are significant. In this case A ++2 - + are significant model terms. Values greater than 0.1000 indicate the model terms are not significant. If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may improve your model. The "Lack of Fit F-value" of 0.59 implies the Lack of Fit is not significant relative to the pure error. There is a 66.29% chance that a "Lack of Fit F-value" this large could occur due to noise. Non-significant lack of fit is good -- we want the model to fit. Std. Dev. 0.166748 R-Squared 0.8497 Mean 8.35 Adj R-Squared 0.72446 C.V. 1.996977 Pred R-Squared 0.43275 PRESS 0.629652 Adeq Precision 7.76776 The "Pred R-Squared" of 0.4327 is not as close to the "Adj R-Squared" of 0.7245 as one might normally expect. This may indicate a large block effect or a possible problem with your model and/or data. Things to consider are model reduction, response tranformation, outliers, etc. "Adeq Precision" measures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 7.768 indicates an adequate signal. This model can be used to navigate the design space. Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF
Intercept 8.785488 1 0.12203598 8.48688 9.0841 A- 0.04533 1 0.05726558-0.0948 0.18545 1.051649077 B- -0.05533 1 0.05726558-0.1955 0.08479 1.051649077 A2-0.628232 1 0.11249532-0.9035-0.35297 1.024076517 B2 0.021768 1 0.11249532-0.2535 0.29703 1.024076517 AB 0.131662 1 0.06523098-0.028 0.29128 1.058487247 ANOVA A 2 model model pattern transformation DESIGN-EXPERT Plot Normal Plot of Residuals 99 95 Normal % Probability 90 80 70 50 30 20 10 5 1-1.37-0.52 0.33 1.18 2.03 Studentized Residuals
DESIGN-EXPERT Plot Residuals vs. Predicted 3.00 Studentized Residuals 1.50-1.50-3.00 7.35 7.58 7.80 8.03 8.26 Predicted DESIGN-EXPERT Plot Residuals vs. Run 3.00 Studentized Residuals 1.50-1.50-3.00 1 3 5 7 9 11 Run Num ber
DESIGN-EXPERT Plot Residuals vs. 3.00 Studentized Residuals 1.50-1.50-3.00-1 0 1 DESIGN-EXPERT Plot Residuals vs. 3.00 Studentized Residuals 1.50-1.50-3.00-1 0 1
DESIGN-EXPERT Plot Lam bda Current = 1 Best = 3 L o w C.I. = H ig h C.I. = Recom m end transform : None (Lam bda = 1) Ln(ResidualSS) Box-Cox Plot for Power Transforms -1.16-1.32-1.48-1.64-1.80-3 -2-1 0 1 2 3 Lam bda
A D 3D plot 4 4 10:1 1.
2. 50 10 1 3. 60 4.
28 Design-expert