Squared Pearson correlation is the square of correlation().
Details
$$r^2= \frac{\left[\sum_{i=1}^{n}(obs_i-\bar{obs})(pred_i-\bar{pred})\right]^2} {\sum_{i=1}^{n}(obs_i-\bar{obs})^2\sum_{i=1}^{n}(pred_i-\bar{pred})^2}.$$
It ranges from zero to one and summarizes the strength, but not the sign, of
linear association. It describes the dispersion of predictions and
observations around their fitted linear relationship rather than their
departure from the 1:1 line. Consequently, r2() is insensitive to additive
bias and proportional scaling: a value of one can occur even when predictions
are systematically biased or have a different scale from the observations.
It should therefore not be interpreted as a general measure of predictive
agreement or accuracy.
Do not confuse lowercase r2() with nse(), mec(), or uppercase R2(),
which are model-efficiency statistics and are sensitive to departures from
the line of equality. It returns NA with a warning when fewer than two
valid pairs remain or either vector has zero variance.
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
r2(1:3, c(1, 3, 2))
#> [1] 0.25