Obtaining uncertainty in parameters fitting discrete data points with component data, using "\" or "mldivide"
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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.
采纳的回答
Star Strider
2017-7-9
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.
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Walter Roberson
2017-7-9
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curvefit() is the only related call that returns r-squared directly. https://www.mathworks.com/help/curvefit/fit.html#outputarg_gof
2 个评论
Jonas Yeung
2017-7-9
编辑：Jonas Yeung
2017-7-9
Walter Roberson
2017-7-9
%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
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