## General Least Squares Regression

version 1.1.0.0 (3.43 KB) by
Multi Dimensional Multivariable Least Squares Regression

Updated 09 Sep 2009

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

### Cite As

Husam Aldahiyat (2021). General Least Squares Regression (https://www.mathworks.com/matlabcentral/fileexchange/22865-general-least-squares-regression), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2007a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux