General Least Squares Regression

Multi Dimensional Multivariable Least Squares Regression

The code manually derives the expression fm(x1,x2,x3,...,xk) for
the equally spaced points in (k+1) dimensions, where m is the order of the approximation f.

Example:

x1=[6 7 8 5 3 2 1 2 5 8];
x2=[9 7 0 8 5 6 4 3 2 10];
y=[9 7 6 4 3 2 5 6 8 1];

mreg([x1;x2],y,1)
ans =
5.542073-.2829251*x2+.2310048*x1

mreg([x1;x2],y,2)
ans =
3.797949-.6754073*x2-.2393447e-1*x2^2
+2.256645*x1+.8248780e-1*x1*x2
-.2478672*x1^2

mreg([x1;x2],y,3)
ans =
-24.62814+33.15517*x2-9.837215*x2^2+.8316257*x2^3
-17.31119*x1+7.450905*x1*x2-.6438069*x1*x2^2
+.3614982*x1^2-.4148167*x1^2*x2+.2851207*x1^3

Example:

x1=[6 7 8 5 3 2 1 2 5 8 5 4];
x2=[9 7 0 8 5 6 4 3 2 10 5 7];
x3=[8 9 7 6 5 4 3 5 6 7 5 3];
y=[9 7 6 4 3 2 5 6 8 1 8 0];

mreg([x1;x2;x3],y,2)
ans =
32.48905-7.049319*x3+.1384845*x3^2-6.246954*x2
+1.259510*x2*x3-.4498889e-1*x2^2+5.668323*x1
-.4038119*x1*x3-.3257156*x1*x2-.1031725*x1^2