Analyzing the residuals from these linear model fits requires some care. In particular, one of the core assumptions of ordinary least squares (OLS) linear regression is that the residuals (# $%&$ -#$ %&$ ) should have a constant variance. In other words, the size of the residual should not depend on the magnitude of the fitted predicted dipole moment (#$ %&$ ), which in this case is just # '()* multiplied by the slope of the linear model fit. Such behavior is readily violated in electronic structure calculations because, for example, nonpolar molecular species that have experimental dipole moments of exactly zero are reliably predicted to have dipole moments of exactly zero as well (i.e., zero variance in the prediction). [As described in the Methods, this is another reason why we have not employed OLS linear regression in this work and have instead used nonparametric Theil-Sen linear regression for our statistical inference.] A more reasonable assumption might be that electronic structure calculations yield predictions that have some inherent percent or fractional error. If this were the case, then the residuals should be divided by the fitted dipole moments to yield a fractional residual (i.e., (# $%&$ -#$ %&$ )/#$ %&$ ) before comparing different electronic structure methods. This approach, however, can lead to molecules with small dipole moments erroneously dominating the residual analysis.