Updated Version
Let's say, $y$ is my target value. And $p,q,r,s,t$ are the variables that change $y$ (basic 2D curves found from interpolation). My goal is to find an equation for solving $y$ when all the variables are present. I have the following source:
One scenario: $y$ changes with change of $p$ while other variables are constant. Basic 2D curve found from interpolation.
Similar scenarios for $q,r,s,t$.
- How do I find an equation for each scenario? (including the effects of the constant variables)
- Is it possible to find a master equation for $y$ when all the variables are variable?
I hope I'm interpreting your question correctly.
If so, in general, the answer is no. Consider a function of two variables, $a$ and $b$. Suppose that $x$, as a function of $a$, is $a + 1$ when $b = 0$. $$ x(a, 0) = a + 1 $$ And suppose that $x$, as a function of $b$, is $b+2$ when $a = 0$: $$ x(0, b) = b + 2 $$ Let $$ f(a, b) = a + b + 3 $$
Then $f$ is a function that matches the two known properties of $x$.
But now also consider $$ g(a, b) = a + b + 3 + ab $$
The function $g$ also matches the two known properties of $x$. Since there are two possible solutions, in general it's impossible to find "the" function that matches your given data.