Question

Question #2 (30 points) The yield of a chemical process is being studied. The two most important variables a thought to be the pressure and the temperature. Three levels of each factor are selected, and a factorial experiment with two replicates is performed. The yield data are as follows: Pressure (psig) Temperature (C) 150 200 90.4 90.2 90.1 90.3 90.5 90.7 215 90.7 90.6 90.5 90.6 90.8 90.9 230 90.2 90.4 89.9 90.1 90.4 90.1 160 170 a. Write the statistical model for this experiment b. From the contour plot and interaction plots below, do you think including the interaction effect is nee Interaction Graph 91.00 0.712 904 90.13 07 50 215 30 230 A Pressure The following is an incomplete ANOVA table, complete it! of Variance nalysis DF Adi S$ Adi MS F-Value p-value 0.009 0.000 0.470 0.30111 Temperature Pressure Temperature Pressure Error Total 0.76778 0.06889 1.29778 d. Comment on the significance of the treatment factors on the yield and the interaction between the two factors.

Answer 1

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General Linear Model: res versus Temperature, Pressure Method Factor coding(1, 0, +1) Factor Information Factor Temperature Fixed Pressure Type Levels Values 3 150, 160, 170 3 200, 215, 230 Fixed Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value 8.47 0.009 2 0.76778 0.38389 21.59 0.000 0.97 0.470 Temperature Pressure 2 0.30111 0.15056 Temperature* Pressure 4 0.06889 0.01722 9 0.16000 0.01778 Error Total 17 1.29778 Model Summary S R-Sq R-Sq(adj) R-sq(pred) 50.68% 76.71% 0.133333 87.67%

Coefficients Term Constant Temperature Coef SE Coef T-Value P-Value VI 90.411l 0.0314 2876.86 0.000 150 160 0.13 0.903 1.33 -0.1611 0.0444 -3.63 0.006 1.33 0.0056 0.0444 Pressure -0.0444 0.0444 -1.00 0.343 1.33 6.12 0.000 1.3;3 215 0.2722 0.0444 Temperature*Pressure 150 200 150 215 160 200 160 215 -0.0722 0.0629 -1.15 0.280 1.78 -0.0389 0.0629 -0.62 0.551 1.78 -0.0056 0.0629 -0.09 0.932 1.78 0.44 0.669 1.78 0.0278 0.0629 Regression Equation res 90.4111 + 0.0056 Temperature 150-0.1611 Temperature 160 + 0.1556 Temperature 170 - 0.0444 Pressure_200 + 0.2722 Pressure_215 - 0.2278 Pressure_230 - 0.0722 Temperature*Pressure 150 200 - 0.0389 Temperature* Pressure_150 215 + 0.1111 Temperature*Pressure_150 230 - 0.0056 Temperature* Pressure_160 200 + 0.0278 Temperature*Pressure_160 215 - 0.0222 Temperature* Pressure_160 230 + 0.0778 Temperature*Pressure_170 200 + 0.0111 Temperature* Pressure_170 215 - 0.0889 Temperature*Pressure_170 230