Good evening fellows,
I have 4 performance indicators (efficiency, effectiveness, etc.) that evaluate a system, and a heat trend function which provides a physical interpretation of what's happening as I tweak some physical properties - variables (eg., the wall thickness increases).
I developed a new composite function which incorporates these 4 different performance indicators using the weighted sum method (G = αF1 +βF2 + γF3 + δF4) to investigate if this surrogate tracks the changes in the system more accurately.
My question is the following:
Both the 4 performance indicators as well as the composite function have different polynomial and exponential relationships with the heat trend function I want to associate them with. What would be the optimal way to approach my statistical analysis?
Would the coefficient of determination R^2 for different polynomial/exponential relationships hold as a comparison metric? Both Kendal's tau and Spearman's rho come back as perfect positive correlation (1) for most cases most of the functions are monotonically related so I can't use them to compare how accurate they are.
Thank you in advance!