The decision about which terms to include and exclude from a response surface model is important. Several considerations affect the decision.
- Usually, the first step in excluding a term is to observe its p-value: if the p-value is less than the alpha level (α), the term should remain in the model.
- Even if the p-value is less than α, you may want to exclude the term. But, you should first consider:
- How adjusted R-squared and S change when the term is excluded. The higher the adjusted R-squared the better the model. The lower the S the better the model. Therefore, if excluding the term decreases the adjusted R and increases the S, the term should remain in the model.
- How lack-of-fit is affected by excluding a term. You can determine the lack-of-fit by assessing the residual plots.
- How excluding a lower-order term affects the model hierarchy. In a hierarchical model, all lower-order terms that comprise the higher-order terms also appear in the model. For example, a model that includes the interaction term A*B*C is hierarchical if it includes these terms: A, B, C, A*B, A*C, and B*C. Response surface models must be hierarchical if you want to produce an equation in uncoded (or natural) units.
All the previous are statistical considerations. Sometimes you might want, for sound technical or scientific reasons, to include a term in the model even if it does not seem significant. A combination of technical and statistical knowledge, therefore, must guide your decisions.