How to get correlation coefficient exponential decay?

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Fabian Moreno 2022-4-26

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https://ww2.mathworks.cn/matlabcentral/answers/1705825-how-to-get-correlation-coefficient-exponential-decay

评论： Mathieu NOE 2022-4-28

Hello, I would like to get the correlation coefficient from the exponential decay model. I used the following code:

ft = fittype( 'a*exp(-b*x)+c', 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';

and got from the R2 the correlation coefficient

Rsqr=sqrt(gof.rsquare)

but the (r) is positive, is there a form to get the correlation coefficient negative. Obviously my data shows a decreasing exponentail decay.

And I don't use the corrcoef because it suppose to be use with a linear data, but what about exponentail decay?

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Fabian Moreno 2022-4-27

Hello, @Mathieu NOE! Thanks for your answer. I am going to share my figure to show you my result. Also, could you please explain me why I have to multiply the Rsqr value by sigh (b)? I didn't understand.

Mathieu NOE 2022-4-28

hello

you have decaying exponentials here so sign(b) is negative (obviously) which is how I create the negative R

If you had a positive b , then R shoud be positive too

That may sound like a "trick" but there is probably no other matlab way to do it as all fit function returns R squared , which , of course reamins positive in all circumstances.

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