What type of modeling, analysis, and methodology would you use for the following example:
Let's say you have factors A, B, and C in a DOE. You capture responses Y and Z. A combination of B+C increases both Y and Z using a specific regression model, and theoretically (from your discipline and experience), you know that response Y is dependent on Z. How would I best represent the relationship between Y and Z? Only suggestions on what type of analysis would best describe my relationship? Can I use Z as a factor in my model to try to explain Y?
For a more concrete example, let's say I'm a metallurgist exploring the effects of heating media, heat-treatment temperatures, and cooling rates on metals. (Not my exact discipline, but very visual) The responses I'm capturing are the metal's ultimate tensile strength and crystallinity percentage. I know that my maximum tensile strength increases with crystallinity, and that both my responses increase as my cooling rate decreases and my heat-treatment temperatures increase. For this example, let's say the crystallinity rises by 1.5% every 10 degrees, and UTS increases by 8% with each additional 10 degrees of crystallinity, while UTS increases by 3% with each additional 10 degrees of crystallinity. Is this a mathematical algebra problem? Can I drop crystallinity as a factor when it is a captured response?
Thank you very much for your time and expertise!!
