The model and a design

In two-factors, the full second-order polynomial (FSOP) model is 

At least six distinctly different factor combinations (/ = 6) are required to fit the six parameters of this model (p = 6). To provide three degrees of freedom for lack of fit, /must be increased to 9. To provide three degrees of freedom for purely experimental uncertainty, n must be increased to 12. 

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The choice of design will depend on how detailed the desired infonnation is to be. If it is strongly suspected that certain variables will interact, it is recommended that terms for these interaction should be included in the model, and a design be selected which can estimate these parameters. Use a Resolution V design by which each two-variable interaction can be estimated, or use a Resolution TV design which will confound the interaction effect. These can then be isolated by complementary runs. 

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