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DOE: What if X's are related?


I have a general DOE question. I want to independently study the effect of 5 X's on my responses. However, one of the X's can be calculated once the 1st 4 are known. So, the 5th X is really dependent, but not a response. I made a DOE by independently varying the 1st 4, and the 5th was simply computed. I also used the 1st 4 X's only in the regression, since I would think the regression tool would "know" the 5th X is somehow related to the 1st 4, and there not needed (over-specified?). I am finding some contrary trends in some responses now, so I wonder if I've done the right thing? As one of the X's changes, that 5th one is also changing in a dependent way, so the Y trends are really trending with the variation of one independent X, and one "dependednt" X.

If I just throw in the "dependent" 5th X into the regression, will that be more accurate? Or was I right in what I did?

Thanks for you thoughts,