Problem #3 (23 Factorial Design; 20 Points): The data collected for a 23 factori

Question

Problem #3 (23 Factorial Design; 20 Points): The data collected for a 23 factorial design with no replication are summarized in the following table Factor Factor Factor Response 57 120 110 105 123 167 Part (a): Estimate the effect of Factor C. Part (b): Estimate the interaction between Factors A and B Part (c): MINITAB produced the following results. Explain in up to two sentences why no F tests can be performed (and no p-values can be produced) for any hypothesis testing. Analysis of Variance for C8 (coded units) DF Source Main Effects 2-Way Interactions 3-Way Interactions Residual Error Total seq SS 10167.4 1791.4 55.1 0.0 12013.9 Adj ss 10167.4 1791.4 55.1 0.0 Adj MS 3389.13 597.13 55.12 0.00

Explanation / Answer

Solution:

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Model 7 12013.9 1716.27 * *
Linear 3 10167.4 3389.12 * *
A 1 741.1 741.13 * *
B 1 3321.1 3321.13 * *
C 1 6105.1 6105.12 * *
2-Way Interactions 3 1791.4 597.13 * *
A*B 1 1770.1 1770.12 * *
A*C 1 0.1 0.13 * *
B*C 1 21.1 21.13 * *
3-Way Interactions 1 55.1 55.12 * *
A*B*C 1 55.1 55.12 * *
Error 0 * *
Total 7 12013.9

Model Summary

S R-sq R-sq(adj) R-sq(pred)
* 100.00% * *

Coded Coefficients

SE
Term Effect Coef Coef T-Value P-Value VIF
Constant 98.63 * * *
A 19.250 9.625 * * * 1.00
B 40.75 20.37 * * * 1.00
C 55.25 27.63 * * * 1.00
A*B 29.75 14.87 * * * 1.00
A*C 0.2500 0.1250 * * * 1.00
B*C -3.250 -1.625 * * * 1.00
A*B*C -5.250 -2.625 * * * 1.00

The F-test of overall significance is a specific form of the F test it compares a model with no predictors thats why F test performed no F value also from F value p-value can be determined therefore there is no F-value and p-value.

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