5. Process Improvement 5.5. Advanced topics 5.5.9. An EDA approach to experimental design 5.5.9.9. Cumulative residual standard deviation plot 5.5.9.9.5. Motivation: What is the Form of the Model? 

Models for various values of k 
From the above discussion, we thus note and recommend a form
of the model that consists of an additive constant plus a linear
combination of main effects and interactions. What then is the
specific form for the linear combination?
The following are the full models for various values of k. The selected final model will be a subset of the full model.

Ordered linear combination 
The listing above has the terms ordered with the main effects, then
the 2factor interactions, then the 3factor interactions, etc. In
practice, it is recommended that the terms be ordered by importance
(whether they be main effects or interactions). Aside from providing a
functional representation of the response, models should help
reinforce what is driving the response, which such a reordering does.
Thus for k = 2, if factor 2 is most important, the 2factor
interaction is next in importance, and factor 1 is least important,
then it is recommended that the above ordering of
\( \begin{array}{lcl} Y & = & f(X_{1},X_{2}) + \epsilon \\ & = & c + B_{1}X_{1} + B_{2}X_{2} + B_{12}X_{1}X_{2} + \epsilon \end{array} \) \( \begin{array}{lcl} Y & = & f(X_{1},X_{2}) + \epsilon \\ & = & c + B_{2}X_{2} + B_{12}X_{1}X_{2} + B_{1}X_{1} + \epsilon \end{array} \) 