Question: you are provided information on a RSM AND OPTIMIZATION experiment, and you are required to investigate and interpret the output which is provided below. Problem:
you are provided information on a RSM AND OPTIMIZATION experiment, and you are required to investigate and interpret the output which is provided below.
Problem:Consider the threevariable central composite design shown in the table.
| RunOrder | PtType | Blocks | Temperature | Time | Catalyst | Conversion (%) y1 | Viscosity y2 |
| 1 | 1 | 1 | -1 | -1 | -1 | 74 | 53.2 |
| 2 | 1 | 1 | 1 | -1 | -1 | 51 | 62.9 |
| 3 | 1 | 1 | -1 | 1 | -1 | 88 | 53.4 |
| 4 | 1 | 1 | 1 | 1 | -1 | 70 | 62.6 |
| 5 | 1 | 1 | -1 | -1 | 1 | 71 | 57.3 |
| 6 | 1 | 1 | 1 | -1 | 1 | 90 | 67.9 |
| 7 | 1 | 1 | -1 | 1 | 1 | 66 | 59.8 |
| 8 | 1 | 1 | 1 | 1 | 1 | 97 | 67.8 |
| 9 | -1 | 1 | -1.68179 | 0 | 0 | 76 | 59.1 |
| 10 | -1 | 1 | 1.681793 | 0 | 0 | 79 | 65.9 |
| 11 | -1 | 1 | 0 | -1.68179 | 0 | 85 | 60 |
| 12 | -1 | 1 | 0 | 1.681793 | 0 | 97 | 60.7 |
| 13 | -1 | 1 | 0 | 0 | -1.68179 | 55 | 57.4 |
| 14 | -1 | 1 | 0 | 0 | 1.681793 | 81 | 63.2 |
| 15 | 0 | 1 | 0 | 0 | 0 | 81 | 59.2 |
| 16 | 0 | 1 | 0 | 0 | 0 | 75 | 60.4 |
| 17 | 0 | 1 | 0 | 0 | 0 | 76 | 59.1 |
| 18 | 0 | 1 | 0 | 0 | 0 | 83 | 60.6 |
| 19 | 0 | 1 | 0 | 0 | 0 | 80 | 60.8 |
| 20 | 0 | 1 | 0 | 0 | 0 | 91 | 58.9 |
Part 1- Conversion percent
A partial Minitab output for the full model is shown below.
| S | R-sq | R-sq(adj) | R-sq(pred) |
| 4.71669 | 91.99% | 84.79% | 75.66% |
Model Summary
Fits and Diagnostics for Unusual Observations
| Obs | Conversion % (y1) | Fit | Resid | Std Reside | |
| 20 | 91.00 | 81.09 | 9.91 | 2.30 | R |
R Large residual
Analysis of Variance
| Source | DF | Adj SS | Adj MS | F-Value | P-Value |
| Model | 9 | 2555.73 | 283.97 | 12.76 | 0.000 |
| Linear | 3 | 763.05 | 254.35 | 11.43 | 0.001 |
| Temperature | 1 | 14.44 | 14.44 | 0.65 | 0.439 |
| Time | 1 | 222.96 | 222.96 | 10.02 | 0.010 |
| Catalyst | 1 | 525.64 | 525.64 | 23.63 | 0.001 |
| Square | 3 | 601.30 | 200.43 | 9.01 | 0.003 |
| Temperature*Temperature | 1 | 48.47 | 48.47 | 2.18 | 0.171 |
| Time*Time | 1 | 124.48 | 124.48 | 5.60 | 0.040 |
| Catalyst*Catalyst | 1 | 388.59 | 388.59 | 17.47 | 0.002 |
| 2-Way Interaction | 3 | 1191.37 | 397.12 | 17.85 | 0.000 |
| Temperature*Time | 1 | 36.12 | 36.12 | 1.62 | 0.231 |
| Temperature*Catalyst | 1 | 1035.12 | 1035.12 | 46.53 | 0.000 |
| Time*Catalyst | 1 | 120.13 | 120.13 | 5.40 | 0.043 |
| Error | 10 | 222.47 | 22.25 | ||
| Lack-of-Fit | 5 | 56.47 | 11.29 | 0.34 | 0.869 |
| Pure Error | 5 | 166.00 | 33.20 | ||
| Total | 19 | 2778.20 |
Interpret the above output. As well as discussing factor significance you are expected to discuss the unusual residual and how it may (or may not) affect the overall analysis. Is there a specific recommendation that you would make?
The partial output for the reduced model is provided.
Model Summary
| S | R-sq | R-sq(adj) | R-sq(pred) |
| 5.05856 | 88.95% | 82.50% | 69.18% |
Coded Coefficients
| Term | Coef | SE Coef | T-Value | P-Value | VIF |
| Constant | 79.59 | 1.75 | 45.45 | 0.000 | |
| Temperature | 1.03 | 1.37 | 0.75 | 0.467 | 1.00 |
| Time | 4.04 | 1.37 | 2.95 | 0.012 | 1.00 |
| Catalyst | 6.20 | 1.37 | 4.53 | 0.001 | 1.00 |
| Time*Time | 3.12 | 1.33 | 2.35 | 0.036 | 1.01 |
| Catalyst*Catalyst | -5.01 | 1.33 | -3.78 | 0.003 | 1.01 |
| Temperature*Catalyst | 11.37 | 1.79 | 6.36 | 0.000 | 1.00 |
| Time*Catalyst | -3.88 | 1.79 | -2.17 | 0.051 | 1.00 |
Analysis of Variance
| Source | DF | Adj SS | Adj MS | F-Value | P-Value |
| Model | 7 | 2471.13 | 353.02 | 13.80 | 0.000 |
| Linear | 3 | 763.05 | 254.35 | 9.94 | 0.001 |
| Temperature | 1 | 14.44 | 14.44 | 0.56 | 0.467 |
| Time | 1 | 222.96 | 222.96 | 8.71 | 0.012 |
| Catalyst | 1 | 525.64 | 525.64 | 20.54 | 0.001 |
| Square | 2 | 552.83 | 276.42 | 10.80 | 0.002 |
| Time*Time | 1 | 141.78 | 141.78 | 5.54 | 0.036 |
| Catalyst*Catalyst | 1 | 365.42 | 365.42 | 14.28 | 0.003 |
| 2-Way Interaction | 2 | 1155.25 | 577.62 | 22.57 | 0.000 |
| Temperature*Catalyst | 1 | 1035.12 | 1035.12 | 40.45 | 0.000 |
| Time*Catalyst | 1 | 120.13 | 120.13 | 4.69 | 0.051 |
| Error | 12 | 307.07 | 25.59 | ||
| Lack-of-Fit | 7 | 141.07 | 20.15 | 0.61 | 0.736 |
| Pure Error | 5 | 166.00 | 33.20 | ||
| Total | 19 | 2778.20 |
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