Pearson product-moment correlation between observations and predictions.
Details
$$r = \frac{\sum_{i = 1}^{n}(obs_i - \bar{obs})(pred_i - \bar{pred})} {\sqrt{\sum_{i = 1}^{n}(obs_i - \bar{obs})^2\sum_{i = 1}^{n}(pred_i - \bar{pred})^2}}$$
Correlation ranges from -1 to 1: one indicates a perfect increasing linear
association, minus one a perfect decreasing linear association, and zero no
linear association. It returns NA with a warning when fewer than two valid
pairs remain or either vector has zero variance. Correlation is
unaffected by additive bias and proportional scaling, so it measures pattern
association rather than agreement or prediction accuracy. Interpret it with
bias(), rmse(), and an agreement measure such as ccc().
References
Willmott, C. J. (1984). On the evaluation of model performance in physical geography. In G. L. Gaile and C. J. Willmott (Eds.), Spatial Statistics and Models (pp. 443-460). D. Reidel.
Legates, D. R. and McCabe, G. J. (1999). Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation. Water Resources Research, 35(1), 233-241. doi:10.1029/1998WR900018
Examples
correlation(1:3, c(1, 3, 2))
#> [1] 0.5