MATLAB: Standard error of regression curve

curve fittingfitregressionstandard error

Hello,
I have two vectors, named as x and y. I would like to estimate the standard error of a regressed curve of these data points. The regression model is defined as ft in the below code. Can you please let me know if there is a way to estimate the standard error of b and m coefficients of this fit type? 
x=[2;4;6;9;12;15;18]
y=[188;198;294;433;661;875;1097]
ft = fittype( 'b*x^m');
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
fitresult= fit( x, y, ft, opts );

Best Answer

Follow this answer provided by MathWorks support [here]. Since the degrees of freedom are not defined in that answer, here's a more complete answer:
% Your data and their fit
x=[2;4;6;9;12;15;18]
y=[188;198;294;433;661;875;1097]
ft = fittype( 'b*x^m');
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
[fitresult, gof] = fit( x, y, ft, opts ); % <-- also include 2nd output!
% Compute standard error of the coefficients.
alpha = 0.95; % Choose an alpha level
ci = confint(fitresult, alpha) 
df = gof.dfe; 
t = tinv((1+alpha)/2, df); 
se = (ci(2,:)-ci(1,:)) ./ (2*t) % Standard Error
% Results in same order as coefficients listed in fitresult.
% se =
%     10.0399163997427        0.0994320537151288
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