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From: "Tom Lane" <tlane@mathworks.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: multiple variable exponential regression
Date: Wed, 6 Nov 2013 12:30:21 -0500
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> I was using other nonlinear regression methods but was getting an 
> imaginary solution (a+ib) form
...
> modelfun = @(b, x)((100 - 15*(x(2, :).^b(1)))) - (40*((x(3, :).^b(2)))) - 
> (15*((x(4, :).^b(3)))) x = TestData;
> y = x(1, :);
>
> [beta, R, J, CovB, MSE] = nlinfit(x, y, modelfun, beta0, opts);

One thing I see here is that you have not removed the y column from x, so 
x(1,:) will refer to the same thing as y. In general, if you have any 
negative x values this could yield imaginary results as the nlinfit function 
manipulates the b values. You could use abs() in your modelfun to avoid 
that, but I don't know if that makes sense in your application.

-- Tom