I have a relationship $y=f(x)$ for which I can obtain data through simulation.
I have good reason to suspect that this relationship is quadratic (rather than, say, exponential), and would like to provide evidence for this.
I was thinking of the following method, and I would like to ask if there is anything wrong with it:
a) Obtain $y$ data for a limited interval of $x$, say $x\in (0, x_a)$.
b) Fit a quadratic function to this data using least squares regression.
c) Obtain data for a larger value of $x$ (say $10x_a$) and check the percentage error that the model leads to when extrapolated to this value.
Does this prove anything?