where Cov(T,P) is the covariance of the target and model outputs; and s_t and s_p are the corresponding standard deviations, which are given by:

where P_(ij) is the value predicted by the individual program i for sample case j (out of n sample cases); T_j is the target value for sample case j; andandare given by the formulas:

The correlation coefficient is confined to the range [-1, 1]. When C_i = 1, there is a perfect positive linear correlation between T and P, that is, they vary by the same amount. When C_i = -1, there is a perfect negative linear correlation between T and P, that is, they vary in opposite ways (when T increases, P decreases by the same amount). When C_i = 0, there is no correlation between T and P. Intermediate values describe partial correlations and the closer to 1 or -1 the better the model.