How can I perform nonlinear regression with two input variables and one dependent variable

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Ubong Abia
Ubong Abia 2016-8-12
评论： John D'Errico 2016-8-13
I have a data set with three columns, say, Y, X1 and X2 of which Y is the dependent variable (on X1 and X2). I need to know how to use MATLAB to perform nonlinear regression with two input variables for a particular model
y=f(X1,X2)=(1+aX1+bX2)/(1+cX1+dX2).

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John D'Errico
John D'Errico 2016-8-12
编辑：John D'Errico 2016-8-12
Simpler than using nonlinear regression is to use LINEAR regression.
If you have
y=f(X1,X2)=(1+aX1+bX2)/(1+cX1+dX2)
then multiply by (1+cX1+dX2).
y*(1+cX1+dX2) = 1+aX1+aX2
or
y - 1 = a*X1 + a*X2 -c*y*x1 -d*y*x2
You can do it using no extra functions, than just some basic MATLAB.
So assume that X1, X2, and Y are all COLUMN vectors. We implement it in MATLAB as:
coefs = [X1, X2, -Y.*X1, -Y.*X2]\(Y-1);
a = coefs(1);
b = coefs(2);
c = coefs(3);
d = coefs(4);
Basically one line of code. No iterative routine needed. No starting values. Or, you can use these estimates as very good estimators of the coefficients for a nonlinear estimation.
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John D'Errico
John D'Errico 2016-8-13
(TY)
As others have said, you need to learn to use MATLAB then. I cannot teach you a complete course in basic MATLAB skills, especially when that is done so much more ably in other places. Read the getting started tutorials.

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Star Strider
Star Strider 2016-8-12
This will work:
X1 = randi(9, 1, 10); % Create Data
X2 = randi(9, 1, 10); % Create Data
Y = randi(99, 10, 1); % Create Data
XY = [X1(:) X2(:)]; % Create Independent Variable Matrix
Y = Y(:); % Dependent Variable
% % % MAPPING: p(1) = a, p(2) = b, p(3) = c, p(4) = d,
f = @(p,x) (1+p(1).*x(:,1)+p(2).*x(:,2))./(1+p(3).*x(:,1)+p(4)*x(:,2));
SSECF = @(p) sum((Y-f(p,XY)).^2); % Sum-Squared-Error Cost Function
P = fminsearch(SSECF, [1; 1; 1; 1]); % Estimate Parameters
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Ubong Abia
Ubong Abia 2016-8-12
You have been most helpful Star Strider. Quick one, how different are the codes from the curve fitting tool as I believe there is a platform for one to type a custom equation and obtain parameters. Is there a difference between the regression codes and the curve fitting tool in terms of getting accurate coefficients?
Star Strider
Star Strider 2016-8-13
I do not have the Curve Fitting Toolbox. (I have the Optimization and Statistics Toolboxes, so don’t need it for what I do.) I prefer to use fminsearch in my Answers because everyone has it.
My code will give you accurate coefficients for your model. It may be more robust that code using the gradient-descent algorithms.

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Amos
Amos 2016-8-12
You could use lsqcurvefit for that, where prbably X1 and X2 need to be put together into a single array, and a,b,c,d also need to be put together into a parameter array p.

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