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Last update: February 19, 2014


Pearson Correlation Coefficient

The correlation coefficient Ci of an individual model i is evaluated by the equation:

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

where P(ij) is the value predicted by the individual model i for record j (out of n records); Tj is the target value for record j; andandare given by the formulas:

The correlation coefficient is confined to the range [-1, 1]. When Ci = 1, there is a perfect positive linear correlation between T and P, that is, they vary by the same amount. When Ci = -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 Ci = 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.

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