A 23 factorial experiment was conducted to estimate the effects of three factors
ID: 3312438 • Letter: A
Question
A 23 factorial experiment was conducted to estimate the effects of three factors on the vield of a chemical reaction. The factors were A: catalyst concentration (low or high), B: reagent (standard formulation or new formulation), and C: stirring rate (slow or fast). Three replicates were obtained for each treatment. The yields, presented in the following table, are measured as a percent of a theoretical maximum Replicates Label (1)71.6770.5567.4 78.4675.4281.77 77.1478.25 78.33 79.7276.17 78.41 72.6571.0373.54 80.1 73.9174.81 80.273.4974.86 abc 75.5880.2871.64 ac Estimate all main effects and interactions. Find the standard errors on all effects and test the hypothesis if any of them can be neglected. Use 95% confidence interval for hypothesis testing Create a regression model for the experiment. Test if any of the regression coefficients can be neglected using 95% confidence interval. Rewrite the regression equation with only significant coefficients. a. b. c. d.Explanation / Answer
A,B] Coded Coefficients
Term Effect Coef SE Coef T-Value P-Value VIF
Constant 75.641 0.572 132.33 0.000
A 3.097 1.548 0.572 2.71 0.015 1.00
B 2.730 1.365 0.572 2.39 0.030 1.00
C -0.933 -0.467 0.572 -0.82 0.426 1.00
A*B -3.175 -1.587 0.572 -2.78 0.013 1.00
A*C -1.338 -0.669 0.572 -1.17 0.259 1.00
B*C -1.062 -0.531 0.572 -0.93 0.367 1.00
A*B*C 1.067 0.533 0.572 0.93 0.365 1.00
C] Regression Equation in Uncoded Units
response = 75.641 + 1.548 A + 1.365 B - 0.467 C - 1.587 A*B - 0.669 A*C - 0.531 B*C
+ 0.533 A*B*C
D] Pvalue (c) = 0.426 > alpha = 0.05 therefore we neglect that factor.
Regression Equation in Uncoded Units
response = 75.641 + 1.548 A + 1.365 B - 1.587 A*B
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