Obtaining uncertainty in parameters fitting discrete data points with component data, using "\" or "mldivide"

I'm not too familiar with the statistics behind least-square fitting, but please bear with me.

I would like to fit a data set ("Result") with linear combinations of component data sets ("a", "b"). I'm currently using the "\" command, which is equivalent to mldivide:

x =[a;b]'\Result'

A linear combination of the red and yellow curve creates the blue curve that fits the blue curve.

For example, a result would be:

    x = 

    0.9796 

    0.2119

However, is there any way I can obtain uncertainty/error from doing this? Thanks.

Answer 1

[Star Strider]

The statistics and Machine Learning Toolbox regress (link) function can also do this.

For your problem, it would be:

[b,bint] = regress(Result', [a;b]');

with ‘b’ the estimated parameters, and ‘bint’ their confidence intervals.

The documentation says that the F-statistic and p-value (in the stats output if you ask for it) may not be accurate without an intercept term, so ignore them.

Answer 2

[Walter Roberson]

curvefit() is the only related call that returns r-squared directly. https://www.mathworks.com/help/curvefit/fit.html#outputarg_gof

[Jonas Yeung]

To clarify, I'm asking if I can obtain uncertainties for the calculatd values. From my understanding, the curve-fitting toolbox fits analytical functions and not user-obtained discrete values.

[Walter Roberson]

%create some input data.
%replace this section with reading in your a, b, and c
t = linspace(0,1,50);
a = exp(-(t-1/2).^2);
b = tan(t);
x1 = randn(); x2 = randn();
c = a*x1 + b*x2;    %x1 and x2 will need to be recovered

%create the fitting type
ft = fittype('a*x1+b*x2', 'coeff', {'x1','x2'}, 'indep', {'a','b'});

%guess an initial solution to keep it quiet
x0 = [.5 .5]

%do the fitting
[x, gof] = fit( [a(:), b(:)], c(:), ft, 'StartPoint', x0 )

%how good was it?
gof.rsquare