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I saw the below equation given for "Coefficient of determination" in a paper and thought it must be a typo, then I saw it in another paper too. Would anyone know what this is and how it is different than the coefficient of determination formula I know? Thank you in advance.

The equation of interest is $R^2=1-\frac{\sum(X_m-X_p)^2}{\sum(X_m)^2}$ where $X_m$ and $X_p$ are the measured and predicted values, respectively.

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Would anyone know what this is and how it is different than the coefficient of determination formula I know?

It is the same if you know that $X$ (unconditionally) has mean zero. I gather you rarely know that the true (unconditionally) mean is zero though.

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  • $\begingroup$ correct. Their X doesnt have mean zero! after reading your answer I tried to see the difference by using an example in EXCEL and found that yeah whenever mean(X) == 0; this equation is the same. Then I thought maybe they had normalized their inputs so that they got mean 0. but its not the case... anyway. thank you. $\endgroup$ – Massoud Hosseinali Aug 13 '18 at 22:50

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