It comes as no surprise that $$R^2$$ (“coefficient of determination”) equals $$r^2$$ in simple regression (predictor X, criterion Y), where $$r(X,Y)$$ is Pearson’s correlation coefficient. $$R^2$$ equals the fraction of explained variance in a simple regression. However, the statistical (mathematical) background is often less clear or buried in less-intuitive formula. The goal of this post is to offer a gentle explanantion why $$R^2 = r^2$$, where $$r$$ is $$r(Y,\hat{Y})$$ and $$\hat{Y}$$ are the predicted …