Non linear Least square fitting

I have a data set with three columns of X, Y and Y_error coordinates... I have to fit a equation

y = a[x^(-1/k) - 37^(-1/k)]

and find a and k along with the error associated with them. Also while fitting we have to consider the 3rd column also i.e the errors with Y coordinate.

So basically I have to do weighted non linear LS fitting and all this without using CFTOOL

Answer 1

[Star Strider]

This is how I would do it:

% % b(1) = a,   b(2) = k
y = @(b,x) b(1).*[x.^(-1./b(2)) - 37.^(-1./b(2))];
XYE = rand(10,3);                       % X, Y, Error Vectors Matrix — Create Data
X = XYE(:,1);                           % X Data
Y = XYE(:,2);                           % Y Data
W = XYE(:,3);                           % Weight Data
WLSCF = @(b) sum(W.*(Y - y(b,X)).^2);   % Weighted Least Squares Cost Function
B = fminsearch(WLSCF, rand(2,1));

The error vector is apparently the weighting vector. My ‘XYE’ matrix has as its first column X, second column Y and third column E.

See 4.4.3.2. Weighted Least Squares for more information.