where #$ %&$ is the predicted dipole moment from the linear regression model and erf(;) is the error function. [We note that the #̂$ %&$ inside the error function is assumed to be multiplied by a constant of 1 D -1 to make the argument of the function dimensionless.] As the dipole moment of a molecule tends toward zero, our weighting function approaches 1. In other words, the weighted residual tends toward being an exact residual. As the dipole moment of a molecule becomes large, our weighting function approaches 1/#̂$ %&$ , and therefore the weighted residual tends toward being a fractional residual. For example, by 2.0 D, the weighting function has a value that is 98.8% of 1/#̂$ %&$ . In addition, this weighting function is continuous, smoothly varying, and does not require choosing any particular transition value for the "switch" between exact and fractional residuals. The weighted residuals for each of the method/basis set combinations are shown in Figure .