p-values out of cftool fitting result

Question

Alberto Salinaro 2015-2-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/179579-p-values-out-of-cftool-fitting-result

回答： Greig 2015-2-22

Is it possible to extract/calculate the p-values from the output of a curve fitting session? I used the cftool to fit a surface (matrix of measured data) to find a model of two variables (e.g. time and temperature), to explain the dependency of the data on them. I get a nice fit as I expected. Now I would like to estimate which coefficient has more influence on the measured data, namely if time or temperature. The result is the following:

Linear model Poly22:
     ditfit(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
       where x is normalized by mean 200 and std 122.2
       and where y is normalized by mean 1213 and std 45.83
     Coefficients (with 95% confidence bounds):
       p00 =  2.725e+010  (2.466e+010, 2.983e+010)
       p10 = -1.337e+010  (-1.487e+010, -1.186e+010)
       p01 = -1.437e+010  (-1.588e+010, -1.287e+010)
       p20 =   3.03e+009  (1.341e+009, 4.72e+009)
       p11 =  5.453e+009  (4.083e+009, 6.822e+009)
       p02 =   5.91e+009  (4.22e+009, 7.599e+009)

How can I do that?

Thanks, Alberto S.

P.S. I have MATLAB Version 7.13.0.564 (R2011b)

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Answer 1

Greig 2015-2-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/179579-p-values-out-of-cftool-fitting-result#answer_168826

在 MATLAB Online 中打开

To extract the coefficients use the "fit" function....

[fitobject,gof,output]=fit([x, y], z, 'poly22');

fitobject.p00, fitobject.p10, etc contain all of the coefficients. For more info type

doc fit

In terms of which coefficient influences the model most, it is better to ask which term influence the model most (e.g., p00, or p10*x, or p01*y, or p20*x^2, etc). Not sure if MATLAB has a specific tool to do this, but a simple approach would be to remove each term one by one and assess the fit. So something like...

coeffs = fieldnames(fitobject);
n=length(coeffs);
for ii=1:n
dummy_fit = fitobject; % copy to dummy variable
dummy_fit.(coeffs{ii}) = 0; % set desired coefficient to zero
zhat = dummy_fit(x, y); % get the model estimate
residual(ii) = norm(z-zhat) % get the residual
end

This loops through all the coefficients and gets the residual when each one is set to zero. Note, that overriding a coefficient value in the fit object spits out a warning, for your purposes this is not important. There may be a smarter way of doing this, but this should work OK.