Ratios of ${\left(\frac{{\mathrm{N}\mathrm{H}}_2\mathrm{C}\mathrm{H}\mathrm{O}}{{\mathrm{C}\mathrm{H}}_3\mathrm{O}\mathrm{H}}\right)}_{\text{low }{\kappa }_{\mathrm{m}\mathrm{m}}}/{\left(\frac{{\mathrm{N}\mathrm{H}}_2\mathrm{C}\mathrm{H}\mathrm{O}}{{\mathrm{C}\mathrm{H}}_3\mathrm{O}\mathrm{H}}\right)}_{\text{high }{\kappa }_{\mathrm{m}\mathrm{m}}}$. The numerator and denominator correspond to the same models but with the only difference being low-millimeter opacity versus high-millimeter opacity dust in the models. Pink indicates the high-mass models, and blue shows the low-mass ones. Filled circles are the envelope-only models, and the empty circles are those with a disk. In most of the low-mass envelope-plus-disk models with optically thick dust, methanol was not detected, and thus there is only one blue empty circle. The effect of dust alone on the scatter observed in Fig. 5 is less than a factor of three; thus, most of the scatter in Fig. 5 is driven by the difference in source structure.