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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; and and are 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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