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### Highlights from General Least Squares Regression

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# General Least Squares Regression

### Husam Aldahiyat (view profile)

02 Feb 2009 (Updated )

Multi Dimensional Multivariable Least Squares Regression

File Information
Description

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

Required Products Symbolic Math Toolbox
MATLAB release MATLAB 7.4 (R2007a)
Other requirements A MATLAB version with the Maple Symbolic Math Toolbox, i.e. MATLAB versions EARLIER than 7.6 (R2008a).
15 Mar 2013 dav

### dav (view profile)

Hi, Is there a way to use this code with the constraint that the parameter estimates are positive?

Thanks

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03 Aug 2010 Leo Kay

### Leo Kay (view profile)

Thank you !

07 Feb 2010 Husam Aldahiyat

### Husam Aldahiyat (view profile)

I'll repeat what is stated in the requirements: You will need Maple to be able to use this code.
If this is an inconvenience, then you should check John D'Errico's
polyfitn.m function also here on the FEX.

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22 Jun 2009 Husam Aldahiyat

### Husam Aldahiyat (view profile)

You're right, this is due to the new MUPAD engine. On MATLAB versions earlier than the MuPad era the code should work fine. I will try to fix this problem as soon as possible.

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09 Jun 2009 Michal Kvasnicka

### Michal Kvasnicka (view profile)

at STRB2 function is probably infinite while loop problem

13 Mar 2009 John D'Errico

### John D'Errico (view profile)

This looks like it would be nice, though I do not have the symbolic TB to put it through its paces, so I will not offer a rating. It is an alternative to my own polyfitn, with output directly into a sym form.

A couple of comments. (Surely you would not expect me to have nothing to say.) Good help. I like to see verbose help, even when some others have been known to say my help is too verbose. I want all of the questions answered in my help, and this help made an effort. I like the examples. Error checks, and an H1 line. All good.

The code itself looks like it was carefully written, but as I said, I could not test it. I had a couple of style points though. I'd rarely recommend the use of variable names like "kkksdgsdg". When you need to debug the code, reading it will be more difficult in a year or so because of a randomly chosen string of characters. I know, sometimes it is difficult to come up with a mnemonic name, but you can try harder than that.

Finally, I'm not sure I like this style of error message:

error('MSG:ID3','lengths of martices x and y need to be the same')

If you will use a message identifier, why not provide a descriptive name instead of MSG:ID3? This reminds me of the old days writing IBM Fortran code, where each programmer learned the meaning of cryptic error messages, identified only by a few characters and a 3 digit number. We then had a manual that offered an even more cryptic explanation of that error code, if you wanted to dig for it.

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13 Mar 2009 Husam Aldahiyat

### Husam Aldahiyat (view profile)

If you liked this submission please rate it! :)

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19 Feb 2009 Mehmet Demirel