# Practice Problem on 2K Design

A factorial design of five variables with three replications is provided in MS Excel File 3. Practice Problem 2 on 2K Factorial Design of Experiment TOE.xlsx

MS Excel File 3. Practice Problem on 2K Factorial Design of Experiment

### 2.6.2. Questions

1. Using MS Excel, calculate contrast, effect, estimate, sum of squares for all main and all interaction effects

a. Interpret one significant main effect and one significant two-way interaction in the context of the problem.

2. Write down the estimate regression equation

a. Explain one linear coefficient (effect estimate) in the context of the problem

3. Develop the ANOVA Table

4. How the contrast, effect, estimate, and the sum of square are related? How, they are connected to the statistical significance? Which effects are larger? How likely are they contributing to the sum of square?

### 2.6.2. Solution

The complete solution is provided in MS Excel File 4. Practice Problem 2 on 2K Factorial Design of Experiment TOE Solution.xlsx

MS Excel File 4. Solution to the Practice Problem on 2K Factorial Design of Experiment

1. Check the MS Excel File 4 for the detail Solution. Table 7 shows the solution summary. The process of finding the numbers in Table 7 is shown in MS Excel File 4.

Table 7. Solution Summary 2. Regression Equation

Y = 14.917 + 1.000 A + 1.271 B + 1.521 C + 1.042 D + 1.333 E - 0.271 A*B - 0.063 A*C - 0.583 A*D - 0.625 A*E + 0.375 B*C + 0.021 B*D - 0.438 B*E - 0.313 C*D + 0.188 C*E + 0.792 D*E + 0.250 A*B*C - 0.396 A*B*D - 0.604 A*B*E - 0.271 A*C*D - 0.438 A*C*E + 0.375 A*D*E - 0.167 B*C*D + 0.917 B*C*E - 0.104 B*D*E + 0.188 C*D*E + 0.667 A*B*C*D + 0.667 A*B*C*E - 0.062 A*B*D*E + 0.104 A*C*D*E - 0.375 B*C*D*E - 0.250 A*B*C*D*E

3. ANOVA table 4. All main effects and a few interactions are significant shown in the ANOVA table with bold texts.