How do i obtain a function from multiple variables?

I have a set of data that is consisted of 5 arrays. There is no relation between them two by two. Is there a way that i can obtain a function of four variables to give the other one?

[Yagmur Gencoglu]

For example i have five arrays full of random variables like;

A = [1 5 9 6 3 5] B = [5 6 9 3 5 8] C = [7 4 1 2 5 4] D = [5 4 2 3 6 8] E = [7 8 5 9 6 2]

is there a way that i can obtain a function like

E = f(A,B,C,D) ?

[Walter Roberson]

Perhaps a scattered interpolant?

It depends: do you need to find some formula given the data, or do you just need to be able to interpolate given those particular data points?

[Yagmur Gencoglu]

i need a formula

[Birdman]

Check my answer. You will obtain a formula.

[Walter Roberson]

Do you have a model that you are fitting the parameters to? There are an infinite number of relationships that can be computed between any finite set of points, and there is no inherent reason to consider one of the possible relationships to be "better" than the others.

Answer 1

[Birdman]

Firstly, download the function from the following link(when you open the file, take MultiPolyRegress.m to your directory):

https://www.mathworks.com/matlabcentral/fileexchange/34918-multivariate-polynomial-regression

Then, in command line, write the following line:

X=[A' B' C' D'];%should be columnwise(6x4)
Y=E';
reg=MultiPolyRegress(X,Y,2);
func=reg.PolynomialExpression

and you will have an expression of four variables. Let me know the results.

[Yagmur Gencoglu]

works perfectly, thank you so much