quantifing goodness of fit between two data sets

Hi everyone,

I have two data sets, one is empirical data gathered from an experiment and the other is data from a model that is suppose to simulate the experiment. Eventually it's just two vectors. I want to quantify the goodness of fit between the model and empirical data to a single number. how can I do this?

Thanks!!

Answer 1

[Star Strider]

If ‘Q’ are your data and ‘Qest’ are the model values, one option is to compute the Coefficient of determination () value:

RMSE = sqrt(mean((Q -  Qest).^2));              % Compute RMSE

OLSCF = @(b) sum((Q-Qfcn(b,yez)).^2);
SStot = sum((Q - mean(Q)).^2);
SSres = OLSCF(B);
Rsq   = 1 - (SSres/SStot);                      % Compute R-squared

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[yuval steinberg]

first of all thank you very much!

but one question, what is the variable "B" that is in OLSCF?

[Star Strider]

My pleasure!

The ‘b’ is an argument to the ‘OLSCF’ (ordinary least squares cost function) anonymous function. That function computes the sum-of-squares for a funciton that did not make it to my Answer.

A different, better and more understandable bit of code to do the same thing is:

yfit = @(b,x) exp(b(1)) .* x.^b(2);                         % Power Function
SSECF = @(b) sum((yfit(b,x) - y).^2);                       % Sum-Squared-Error Cost Function
B = fminsearch(SSECF, [1; 1]);

ypred = yfit(B,x);
SSE=sum((y-ypred).^2);
SST=sum((y-mean(y)).^2);
Rsq   = 1 - (SSE/SST);

Here, the idea is to compute the value for the fit of this particular power function given by ‘yfit’ (where ‘x’ and ‘y’ are the data vectors) and the data, using the fminsearch function to do the nonlinear regression. Here ‘B’ is the coefficients vector comkputed by fminsearch.

Following that, the code calculates ‘ypred’ (the predicted value, corresponding to your model vector) and the actual data. The ‘SSE’ value is explained sum-of-squares, and ‘SST’ is the total sum-of-squares, as described in the Wikipedia article. .

So here, ‘ypred’ is your model, ‘y’ your data vector, and ‘Rsq’ the desired result.

My apologies for the confusion, since I should have chosen this example instead in the beginning.

[yuval steinberg]

exellent, thanks again!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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[yuval steinberg]

sure, this is my first time on the forum:)

[Star Strider]

Thank you!