Question

Question 1: (50% CLO 2 and 50% CLO3) 36 points, a 18, b6 and d=12 The yield of a chemical process is beine studied. The two most important variables are thought to be the temperature (A) and the pressure (8). A factorial experiment with two replicates is performed. The yield data follow: Yield % Replicate 1 Replicate 2 40 42 292 43 51 60 50 65 69 150 150 * Assuming a 0.05, use ANOVA to determine the significance of the two factors and their interaction in the estimation of the process yield. Note: Show your work. b. Calculate R-squared and comment on its value. C. Draw the main effect and interaction plots. From the plots select the best pressure to be used with all temperatures and justify your selection. Note: Use suitable scale to clarify your plots

Answer 1

a.

Two-way ANOVA: Yield versus Temperature, Pressure

Source DF SS MS F P
Temperature 2 1852.75 926.375 182.24 0.000
Pressure 3 96.83 32.278 6.35 0.008
Interaction 6 473.92 78.986 15.54 0.000
Error 12 61.00 5.083
Total 23 2484.50

where means are:
Temperature Mean  
100 37.375  
150 44.375
200 58.500   
  

Pressure Mean
60 45.0000  
70 50.0000   
80 45.1667
90 46.8333

Since P-value=0.000<0.05 corresponding interaction effect so interaction effect is significantly present.

Again Temperature and Pressure are also significant since the corresponding p-values<0.05.

b. R2 for model=(1852.75 +96.83 +473.92)/2484.50= 0.9754

i.e. 97.54% of total variation in the yield is explained by this model hence the fitting is good.

c.

Interaction Plot for Yield Data Means 100 150 200 Pressure Pressure 100 150 200 Temperature 40 60 70 80 90

From this plot we see that for Temperature 200, best pressure is 90; for Temperature 150, best pressure is 80; for Temperature 100, best pressure is 70.