Problem #3 (23 Factorial Design): The data collected for a 23 factorial design w

Question

Problem #3 (23 Factorial Design): The data collected for a 23 factorial design with no replication are summarized in the following table. Factor Factor Factor Response 57 41 120 11e 105 -11 1123 167 Part (a): Estimate the effect of Factor C. Part (b): Estimate the interaction between Factors A and B. Part (c): MNITAB 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) Seg ss Adi SS Adi MS 10167.4 10167.4 3389.13 597.13 55.12 0.00 DE Source Main Effects 2-Way Interactions 3 3-Way Interactions Residual Error Total 1791.4 55.1 0.0 1791.4 55.1 0.0 1 7 12013.9

Explanation / Answer

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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