Finding the optimal model when analyzing multi-factor experimental data with the same number of repetitions is possible by simply pooling factors with large p-values in the analysis of variance table into error terms, because all factors, including interactions, are mutually orthogonal. However, when there are covariates that must be taken into consideration, it is not possible to create an analysis of variance table by decomposing the sum of squares. Miyagawa (2008) in "The Science of Problem Discovery and Solution - The Basics of SQC" includes an example of an analysis of three-factor experimental data that includes covariates, and presents results that are primarily based on a graph with a regression line overlaid on a stratified scatter plot, as well as the results of a regression analysis using dummy variables. Miyagawa emphasizes that inference from estimated values of regression parameters is not easy, and that nothing beats painstaking stratification in a scatter plot. Here, we will demonstrate a multifaceted and comprehensive problem-solving method that involves selecting variables, including interactions, using the "stepwise method" in JMP's "fit model," then utilizing the "prediction profile" and "interaction profile" using the "standard least squares method," and then connecting this to a lattice-type stratified scatter plot using "Graph Builder." Furthermore, in addition to drawing in JMP, we will also show how to create the scatter plots required for problem solving using Excel.
