Experimental Design Interpretation A single replicate 2 4 experiment is designed

Question

Experimental Design Interpretation

A single replicate 24 experiment is designed. The experimenthas factors A, B, C, and D, each of which can be set to +1 or -1. We conduct asingle replicate of this experiment, collecting the response for each possiblecombination of factor settings. This data is below:

We compute the factorial and interaction effects from this data, and determine thatthe following effects are significant:

Factorial Effect A = -17.909

Factorial Effect C = 15.171

Interaction Effect AC = -13.666

Compute the residuals for this model; which of the following normalprobability plots represent these residuals?

*** Below are the screenshots of the potential answers. Please list A, B, C, or D based on the order of the graphs in the screenshots. Thank you!

Treatment Combination Factor A Factor B Factor C Factor D Response -1 -1 -1 -1 -1 2.45 d -1 -1 -1 1 3.94 c -1 -1 1 -1 32 cd -1 -1 1 1 31.44 b -1 1 -1 -1 4.92 bd -1 1 -1 1 2.81 bc -1 1 1 -1 34.34 bcd -1 1 1 1 31.69 a 1 -1 -1 -1 -1.06 ad 1 -1 -1 1 -1.51 ac 1 -1 1 -1 0.32 acd 1 -1 1 1 0.13 ab 1 1 -1 -1 -0.15 abd 1 1 -1 1 -0.13 abc 1 1 1 -1 0.7 abcd 1 1 1 1 2.02 O Lecrae-I'll Find You (Lyr × / Take Test Final Exam-2 x e Chegg Study | Guided S) C Secure https://myasucourses asu.edu/webapps/assessment take/launch.Jsp?course assessment id:82494418 course id:3553901&content; id- 15682677 18stepznu Arizona State ASU Home My ASU Colleges & Schools Map & Locations Contact Us Austin Wallin 8 Blackboard Home Courses Organizations Help -Factorial Effect A-17.909 Factorial Effect C = 15.171 . Interaction Effect AC--13.666 Compute the residuals for this model: which of the following normalprobability plots represent these residuals? -2.5 -2 1.5.1.0 -as 005 1.0 1.5 2.0 Residualbs Rasiduas Click Save and submit to save and submit. Click Save All Answers to save all nswers. Save All Answers Save and Submit 1:32 PM /25/2017 Type here to search 9 49) ^

Explanation / Answer

figure 3 is right plor of residuals.

SE
Term Effect Coef Coef T-Value P-Value VIF
Constant 8.994 * * *
A -17.909 -8.954 * * * 1.00
B 1.0612 0.5306 * * * 1.00
C 15.171 7.586 * * * 1.00
D -0.3913 -0.1956 * * * 1.00
A*B 0.07875 0.03937 * * * 1.00
A*C -13.666 -6.833 * * * 1.00
A*D 0.5663 0.2831 * * * 1.00
B*C 0.15375 0.07687 * * * 1.00
B*D -0.4638 -0.2319 * * * 1.00
C*D -0.12875 -0.06438 * * * 1.00
A*B*C -0.15875 -0.07937 * * * 1.00
A*B*D 0.9587 0.4794 * * * 1.00
A*C*D 0.5188 0.2594 * * * 1.00
B*C*D 0.3188 0.1594 * * * 1.00
A*B*C*D -0.05875 -0.02937 * * * 1.00

Regression Equation in Uncoded Units

response = 2.450 - 3.510 A + 2.470 B + 29.55 C + 1.490 D - 1.560 A*B - 28.17 A*C - 1.940 A*D
- 0.1300 B*C - 3.600 B*D - 2.050 C*D - 0.4000 A*B*C + 4.070 A*B*D + 2.310 A*C*D
+ 1.510 B*C*D - 0.4700 A*B*C*D

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