We studied the dissolution of microcrystalline cellulose (MCC) in binary mixtures of dimethyl sulfoxide (DMSO) and the ionic liquids: allylbenzyldimethylammonium acetate; 1-(2-methoxyethyl)-3-methylimidazolium acetate; 1,8-diazabicyclo [5.4.0]undec-7-ene-8-ium acetate; tetramethylguanidinium acetate. Using chemometrics, we determined the dependence of the mass fraction (in %) of dissolved cellulose (MCC-m%) on the temperature, T = 40, 60, and 80 °C, and the mole fraction of DMSO, χDMSO = 0.4, 0.6, and 0.8. We derived equations that quantified the dependence of MCC-m% on T and χDMSO. Cellulose dissolution increased as a function of increasing both variables; the contribution of χDMSO was larger than that of T in some cases. Solvent empirical polarity was qualitatively employed to rationalize the cellulose dissolution efficiency of the solvent. Using the solvatochromic probe 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (WB), we calculated the empirical polarity ET(WB) of cellobiose (a model for MCC) in ionic liquid (IL)–DMSO mixtures. The ET(WB) correlated perfectly with T (fixed χDMSO) and with χDMSO (fixed T). These results show that there is ground for using medium empirical polarity to assess cellulose dissolution efficiency. We calculated values of MCC-m% under conditions other than those employed to generate the statistical model and determined the corresponding MCC-m% experimentally. The excellent agreement between both values shows the robustness of the statistical model and the usefulness of our approach to predict cellulose dissolution, thus saving time, labor, and material.