Fig. 2: Deviation from scaling laws explained by environmental and economic factors.

a, The residuals of the wastewater scaling relationship can be explained by the combination of annual precipitation (Precip) and per capita GDP (perGDP) using a planar function (Residual = 0.35log₁₀(perGDP) + 0.0001Precip − 1.6; r² = 0.24, n = 282). b, The residual of the MSW scaling law can be explained by per capita GDP in a nonlinear relationship (Residual = 0.28log₁₀(perGDP) − 1.14; r² = 0.26, n = 165). c, The residual of the GHG scaling law can be explained by per capita GDP in a nonlinear relationship (Residual = 0.6log₁₀(perGDP) − 2.56; r² = 0.36, n = 148). Note that we removed three outliers from this regression. Keeping the three outliers would not alter the slope of the regression (slope = 0.6) but would shift downwards the intercept (intercept = −2.65). See Extended Data Fig. 3 for a version of the regression in which we retained the outliers. The error bands (gray shading) in b and c represent the CIs of each regression fit around the mean. Note that in b and c, the x axes are logarithmic scales, while the residual values on the y axes are in log₁₀ units.