Please use Minitab 2. (25 points) A scientist is investigating a process. She is

Question

Please use Minitab

2. (25 points) A scientist is investigating a process. She is studying the effects of three factors A,B,C on a response variable. Each factor is run at two levels. Two replicates of a 2 design are shown in the following table: C | Replicate Replicate | Totals 247 40 446 405 445 1 1 837 850 670 (1)-647 a 916 b 834 ab 880 c1687 470 429 435 -1 551 775 865 bc 1640 660 ac =1221 530 abc 1190 a. Use the Totals values to calculate the effect estimates. b. Perform the analysis of variance and find statistically significant effects. c. Develop a regression model for this process that can be used to generate predicted values at each "corner" of the design (from which residuals can be obtained).

Explanation / Answer

a) and c)
Factorial Fit: totals versus A, B, C

Estimated Effects and Coefficients for totals (coded units)

Term Effect Coef
Constant 1126.9
A -150.2 -75.1
B 18.3 9.1
C 615.3 307.6
A*B -51.8 -25.9
A*C -307.8 -153.9
B*C -57.3 -28.6
A*B*C 59.8 29.9

S = * PRESS = *

b)
Analysis of Variance for totals (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 802881 802881 267627 * *
A 1 45150 45150 45150 * *
B 1 666 666 666 * *
C 1 757065 757065 757065 * *
2-Way Interactions 3 201331 201331 67110 * *
A*B 1 5356 5356 5356 * *
A*C 1 189420 189420 189420 * *
B*C 1 6555 6555 6555 * *
3-Way Interactions 1 7140 7140 7140 * *
A*B*C 1 7140 7140 7140 * *
Residual Error 0 * * *
Total 7 1011353

data is

totals A B C

647 -1 -1 -1

916 1 -1 -1

834 -1 1 -1

880 1 1 -1

1687 -1 -1 1

1221 1 -1 1

1640 -1 1 1

1190 1 1 1

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