Controlling charge transport through molecules is challenging because it requires engineering of the energy of molecular orbitals involved in the transport process. While side groups are central to maintaining solubility in many molecular materials, their role in modulating charge transport through single-molecule junctions has received less attention. Here, using two break-junction techniques and computational modeling, we investigate systematically the effect of electron-donating and -withdrawing side groups on the charge transport through single molecules. By characterizing the conductance and thermopower, we demonstrate that side groups can be used to manipulate energy levels of the transport orbitals. Furthermore, we develop a novel statistical approach to model quantum transport through molecular junctions. The proposed method does not treat the electrodes' chemical potential as a free parameter and leads to more robust prediction of electrical conductance as confirmed by our experiment. The new method is generic and can be used to predict the conductance of molecules.