Let’s say there are 6 or more independent input variables you suspect influence the dependent output variable. A fractional factorial using 7 or 8 input variables can become expensive and very difficult to control. You must really start making tradeoffs between efficiency and effectiveness of the experiment.
What if you could get your hands on some passive data (without turning knobs) to screen variables before performing active experimentation (turning knobs)? This is where I see the most value of tools such as multiple regression, ANOVA, and t-tests. By the time you go into the active DOE you are working with only 4 or 5 pink and red X’s. It makes for an experiment that has fewer tradeoff’s between efficiency and effectiveness. It’s sort of like Shainin’s “Talk to the parts.”, except what you are really doing is listening to the process… not the intuition of engineers to set up the experiment.
The DOE then becomes less exploratory and more of a way to develop and refine the process model using the 4 or 5 significant variables. The results of the DOE are used to increase your ability to predict the process output based on where the inputs are set. Hypothesis testing using passive data alone can seldom do that.
Anyway, I see multiple regression as one of several good screening tools for DOE. The DOE is used to “set” the process model. It seems to be the most effective and efficient way I’ve found. With all that said, I have seen such a strong signal analyzing passive data with multiple regression that a DOE isn’t even needed, but that is rare.