HW8 Chapter 11, Section 11.1,

Description

1. 2^p factorial experiments. Read the description of the study in Exercise 40 (Chapter 11, Section 11.1, “In a study of processes used to remove impurities …”). An ANOVA table for analyzing the dataset is given below. Follow the instructions below.

Source	DF	SS	MS	F	P-Value
A	1	0.168	0.168	0.08	0.788
B	1	1.940	1.940	0.87	0.366
C	1	8.161	8.161	3.64	0.074
D	1	13.082	13.082	5.84	0.028
A*B	1	3.419	3.419	1.53	0.235
A*C	1	0.263	0.263	0.12	0.736
A*D	1	0.911	0.911	0.41	0.533
B*C	1	0.738	0.738	0.33	0.574
B*D	1	0.781	0.781	0.35	0.563
C*D	1	6.771	6.771	3.02	0.101
A*B*C	1	0.020	0.020	0.01	0.926
A*B*D	1	0.775	0.775	0.35	0.565
A*C*D	1	0.622	0.622	0.28	0.606
B*C*D	1	1.758	1.758	0.78	0.389
A*B*C*D	1	0.004	0.004	0.00	0.967
Error	16	35.851	2.241
Total	31	75.264

1. Identify the effects (main and interactions) that are significant at the =0.10 level.

2. Compute the coefficient of determination R² and give a brief interpretation. (See Formula 11K and pages L-71 to L-72) of lecture notes.)

3. Computed R²adj, the adjusted R^2, (See Formula 11K and pages L-71 to L-72) of lecture notes.)

4. Assume that only the main and interaction effects of C and D are important (two-way interaction model). Complete the ANOVA table below in this case.

Source	DF	SS	MS	F	P-Val
C	1	8.161	8.161	?	0.036
D	?	?	?	?	0.010
C*D	1	6.771	6.771	?	0.055
Error	?	?	?
Total	31	75.264

Hint: You can derive the missing values from the previous ANOVA table.

5. Compute R²adj for the ANOVA table in part (d).

5. Assume that only the main effects of C and D (two-way additive model) are important. Below is the corresponding ANOVA table. Compute R²adj

Source DF SS MS P-val

C 1 8.1608 8.1608 4.38 0.045

4. 1 13.0816 13.0816 7.02 0.013 Error 29 54.0214 1.8628

Total 31 75.2638

1. 7. Based on the R²adj values, which of the 3 fitted models do you prefer? Give a short explanation for your choice.

2. A Fractional Factorial Design. In a study of p=5 factors with two levels each, only 8 different combinations of levels of A, B, C, D, and E will be run (i.e. q=2 and the experiment is a quarter fractional). Use A, B, D as the independent factors and with generators

C = ABD and E = AD

1. List out the 8 treatments will be run.

2. Which treatments, used in the experiment, have all of B and D at their low levels?

3. What effects will be aliased with the A main effect?