The data exploration up to now has revealed several relationships between Xs, which may be Hot Xs, and the two Ys of interest, MFI and CI. At this point, Carl and the team embark on the task of modeling the relationships in a multivariate framework.
Carl formulates a plan and explains it to his teammates. First, they will develop two models, one that relates the Xs to MFI and one that relates the Xs to CI. By examining the results, they will determine Hot Xs for each response and reformulate the models in terms of these Hot Xs. Then, they will use the profiler to simultaneously optimize both models, finding the best settings for the entire collection of Hot Xs. Once this is accomplished, they will find optimal operating ranges for these Xs. They will then investigate how variation in the Hot Xs propagates to variation in the Ys.
Carl struggles with the issue of what to do with the four MFI outliers. He realizes that he could include these four rows in the model development process and, once a model is selected, check to see if they are influential (using visual techniques and statistical measures such as Cook's D). Or, he could just develop models without them.
Looking back at the histograms and control charts for MFI, Carl sees that they are very much beyond the range of most of the MFI measurements. More to the point, they are far beyond the specification limits for MFI. The fact that they are associated with ...