Generating Non Linear Equation

Hi all !

I am going to determine the value of a and b of the equation as follows :

y = 1 - ax - bx^2

where, a + b = 1

I also have a set of data to be fitted by the above equation. How can I do this with matlab?

Your guidance and help would be highly appreciated.

Answer 1

[the cyclist]

If you have the Statistics Toolbox, you can do this with nlinfit().

% Generate some pretend data to be fit
x=(0:1:10)'; % Explanatory variable
y = 1 - 0.3*x - 0.7*x.^2; % Response variable (if response were perfect)
y = y + 2*randn((size(x)));% Add some noise to response variable

% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) 1 - F.*x - (1-F).*x.^2;
F_fitted = nlinfit(x,y,f,[1]);

% Display fitted coefficients
disp(['F = ',num2str(F_fitted)])

% Plot the data and fit
figure
plot(x,y,'*',x,f(F_fitted,x),'g');
legend('data','fit')

Answer 2

[Roger Stafford]

It depends on what you want to minimize in your "fitting". To get the least squares difference between y and the above expression, do this:

 a = sum((1-y-x.^2).*(x-x.^2))/sum((x-x.*2).^2);

where x and y are vectors of the given data.

You can derive this by setting the partial derivative with respect to 'a' equal to zero and solving for 'a' for the expression

 sum((y-1+a*x+b*x^2)^2)

where b is set to 1-a.