MATLAB: Least square value of x and y values of a fitted model

curve fittingerrorregressionstatistics

I'm attempting to determine the R-squared value of a fitted model compared to experimental data using the vertical and horizontal error values. I can only find methods for the vertical value, ANY help would be greatly appreciated. The horizontal value is proving especially difficult.

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These are known as errors-in-variables models, http://en.wikipedia.org/wiki/Errors-in-variables_models. I am not personally familiar with the techniques here. You might find some information in this old thread:

http://www.mathworks.com/matlabcentral/newsreader/view_thread/137563

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Have you seen this?

http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/xform2lineardemo.html

MATLAB: R-squared value for fitted line

Using the Wikipedia article on Coefficient of Determination, it’s easiest (and likely correct) to compute the R-squared value on your data using the nonlinear regression and not the log-log linear fit:

dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
x1dry = linspace(min(x1), max(x1));
pwrfit = @(b,x) b(2) .* x.^b(1);
OLSCF = @(b) sum((dry-pwrfit(b,x1)).^2);
B = fminsearch(OLSCF, [-2; 50]);
SStot = sum((dry - mean(dry)).^2);      % Compute R-squared
SSres = OLSCF(B);
Rsq   = 1 - (SSres/SStot);

When I did this calculation, I got R-squared to be 0.998. Do the same with your ‘wet’ value, with the appropriate changes in the code.

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