Get equation of the surface from curve fitting

Hello,

I have a variable A that is depedent on two other variables N and phi.

I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A.

From here there's any way to get the surface function?

If not, which other method can I use to get a function that describes the surface (can be without the toolboox)?

Thanks.

[Star Strider]

Does the process that created it have a mathematical expression (mathematical model)?

[Gonçalo]

@Star Strider Kinda yes. This process was was to study the perfomance of thr auto.arima algorithm perfomance in ARMA models, this one is AR(1) where N represents the sample size, phi represents phi_1 in the AR(1) equation. The variable A represents the P(algorithm returns AR(1) | correct model is AR(1) ), so the probability of the algorithm correctly finds the model order, knowing the model order.

[Cris LaPierre]

In curve fitting, you need to supply the equation. The fitting is accomplished by adjusting the coefficients of the equation to minimize error. Without the equation, you can't curve fit.

This looks like a response surface model. If there is not already an equation used by others in this space, you might consider looking into adapting the greco, minto, or hierarchy model for your use case.

[Dyuman Joshi]

How did you get the surface you showed?

"I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A."

"If not, which other method can I use to get a function that describes the surface (can be without the toolboox)?"

I can only think of interpolation for this. See scatteredInterpolant.

Other contributers might have a better idea.

Answer 1

[Catalytic]

I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A.

Just use interp2 -

A=interp2(NData,phiData, N,phi)

[Gonçalo]

I would like the equation in is mathematical form so that I'm no depended on MatLab

[Sam Chak]

Hi @Gonçalo

Please address the previous inquiries in the comments. It will assist others in providing you with the necessary help.

If your objective is to have a surface equation that predicts the points within the given intervals, you can consider fitting the following equation:

[Matt J]

I would like the equation in is mathematical form so that I'm no depended on MatLab

How will you do the mathematical operations needed to evaluate the equation at different (N,phi)? If you'll be doing that with alternative software, the software can probably do interpolation as well. There's no need to go through Matlab at all.

Answer 2

[Joe Vinciguerra]

To my knowledge you can't extract fit parameters from nonparametric fitting methods such as Lowess ( https://www.mathworks.com/help/curvefit/nonparametric-fitting.html )

If you want to extract the equation, you need to define an equation; instead of using Lowess, try Polynomial or Custom Equation ( https://www.mathworks.com/help/curvefit/fit.html )