Two-dimensional electronic-vibrational (2DEV) spectroscopy is an experimental technique that shows great promise in its ability to provide detailed information concerning the interactions between the electronic and vibrational degrees of freedom in molecular systems. The physical quantities 2DEV is particularly suited for measuring have not yet been fully determined, nor how these effects manifest in the spectra. In this work, we investigate the use of the center line slope of a peak in a 2DEV spectrum as a measure of both the dynamic and static correlations between the electronic and vibrational states of a dye molecule in solution. We show how this center line slope is directly related to the solvation correlation function for the vibrational degrees of freedom. We also demonstrate how the strength with which the vibration on the electronic excited state couples to its bath can be extracted from a set of 2DEV spectra. These analytical techniques are then applied to experimental data from the laser dye 3,3'-diethylthiatricarbocyanine iodide in deuterated chloroform, where we determine the lifetime of the correlation between the electronic transition frequency and the transition frequency for the backbone C = C stretch mode to be ∼1.7 ps. Furthermore, we find that on the electronic excited state, this mode couples to the bath ∼1.5 times more strongly than on the electronic ground state.