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A B Extraction (%) 13 11 62.9 13 11 65.4 15 11 76.1 15 11 72.3 2.009.0016.0023.0030.00100.00105.00110.00115.00120.00125.00130.00135.00140.00145.00150.00SurfaceAreaA:AmmoniumB: Stir Rate0.450.50.550.60.652.009.0016.0023.0030.00100.00105.00110.00115.00120.00125.00130.00135.00140.00145.00150.00Overlay PlotA:AmmoniumB: Stir RateDensity: 14.000SurfaceArea: 0.600
Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments, Wiley, NY 5-64 13 13 87.5 13 13 84.2 15 13 102.3 15 13 105.6 (a)Analyze the extraction response. Draw appropriate conclusions about the effects of the significant factors on the response. Factors A and B are significant. The AB interaction is moderately significant. Response1ExtractionANOVA for selected factorial modelAnalysis of variance table [Partial sum of squares - Type III]Sum ofMeanFp-valueSourceSquaresdfSquareValueProb > FModel 1752.16 3 584.05 110.02 0.0003 significant A-PEG396.211396.2174.630.0010B-Na2SO41323.5511323.55249.32< 0.0001AB32.40132.406.100.0689Pure Error 21.24 4 5.31 Cor Total 1773.40 7 The Model F-value of 110.02 implies the model is significant. There is only a 0.03% 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, B are significant model terms. CoefficientStandard95% CI95% CIFactorEstimateDFErrorLowHighVIFIntercept 82.04 1 0.81 79.78 84.30 A-PEG 7.04 1 0.81 4.78 9.30 1.00 B-Na2SO4 12.86 1 0.81 10.60 15.12 1.00 AB 2.01 1 0.81 -0.25 4.27 1.00 (b)Prepare appropriate residual plots and comment on model adequacy. ResidualsNormal % ProbabilityNormal Plot ofResiduals-2-101215102030507080909599
Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments, Wiley, NY 5-65 PredictedResidualsResiduals vs. Predicted-2-101260.0070.0080.0090.00100.00110.00PEGResidualsResiduals vs. PEG-2-10121.001.201.401.601.802.00
Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments, Wiley, NY 5-66 (c)Construct contour plots to aid in practical interpretation of the density response. 5.34.Reconsider the experiment in Problem 5.4. Suppose that this experiment had been conducted in three blocks, with each replicate a block. Assume that the observations in the data table are given in order, that is, the first observation in each cell comes from the first replicate, and so on. Reanalyze the data as a factorial experiment in blocks and estimate the variance component for blocks. Does it appear that blocking was useful in this experiment? Feed Rate Block Depth of Cut (in) (in/min) 0.15 0.18 0.20 0.25 1 74 79 82 99 22B:Na2SO4ResidualsResiduals vs. Na2SO4-2-10121.001.201.401.601.802.0013.0013.5014.0014.5015.0011.0011.5012.0012.5013.00ExtractionA:PEGB: Na2SO47080901002222
Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments, Wiley, NY
0.20 2 64 68 88 104 3 60 73 92 96 1 92 98 99 104 0.25 2 86 104 108 110 3 88 88 95 99 1 99 104 108 114 0.30 2 98 99 110 111 3 102 95 99 107 The MSEwas reduced from 28.72 to 23.12. This had very little effect on the results. The variance component estimate for the blocks is: [][]( )( )Blocks290.3323.12ˆ5.6034EMSMSabβσ===Design Expert OutputResponse:Surface FinishANOVA for selected factorial modelAnalysis of variance table [Classical sum of squares - Type II]Sum ofMeanFSourceSquaresDFSquareValueProb > FBlock 180.67 2 90.33 Model 5842.67 11 531.15 22.97 < 0.0001 significant A-Feed Rate3160.5021580.2568.35< 0.0001B-Depth of Cut2125.113708.3730.64< 0.0001AB

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