Fig 1. Illustrating the generalised R².

Panel A: Data is normally distributed about the alternative model—the white regression line Y = sin(X). The null model is the blue Y = 0. Marginal distributions of X and Y are represented above and to the right. The classical R² is calculated using deviations of the samples from the blue and white lines. Panel B depicts the probability distribution over x_i, y_i for the alternative (red) and null (blue) models. Panel C shows the height of the observations on the alternative distribution, relative to the null distribution. The generalised R² is calculated from the ratio of these heights, and does not require an explicit regression line (white), which is included only as a guide for the eye. See section 2 of S1 File for numerical examples of varying noise levels.