A number characterising the model prediction quality ( goodness of fit ):

R^2 = 1 - \frac{MSE(x, \hat x)}{MSE(x, \bar x)}

where

	observed variable represented by a discrete data set of numerical samples
	predictor of variable , represented by another discrete data set of numerical samples, with the same number of samples predicted at the same conditions as the original samples
	mean value of the variable , which can be considered as some sort of extreme predictor with zero variability
	mean square error between a variable and its predictor
	mean square error between a variable and its mean value

It is similar to Mean Square Error (MSE) but quantifies the model prediction efficiency in normalized way which sometimes is more suitable for computations.

The coefficient of determination normally ranges between :

0, indicating that prediction error is within the variance of the observed variable around its mean value

and

1, indicating a fine fit, fairly reproducing the variability of the

The values falling outside the above range indicate a substantial mismatch between variable and model prediction and have a meaning that gap between predicted and actual values is higher than the variance of the actual data.

See also