I have a trivariate system for which component Z is highly dependent upon both the ratio between and the total values of components X and Y. When plotted on a ternary diagram (see attached) they form a very strong curvilinear relationship. Surely, there must be some way that a regression equation can be determined to calculate Z from X and Y. Can anyone help with this? None of the software I have is capable of a regression fit for a trivariate system, only bivariate fits.
In a ternary plot, the relation between A, B and C is A+B+C=100 or A+B+C=1. There are only two degrees of freedom (A,B and C can’t vary independently) in this case. So basically you can plot this (A and B) on a X-Y type graph and use a proper fitting equation. C is then calculated as 100-A-B or 1-A-B because is a dependent variable.
Unfortunately when I plot up A vs B, this is the plot I get. Not sure what kind of fit equation this would be since there are multiple B values for the same A. Suggestions?
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