Context. The process that heats the solar chromosphere is a difficult target for observational studies because the assumption of local thermal equilibrium (LTE) is not valid in the upper solar atmosphere, which complicates the analysis of spectra. Aims: We investigate the linear correlation coefficient between the intensities at different wavelengths in photospheric and chromospheric spectral lines because the correlation can be determined directly for any spectra from observations or modeling. Waves which propagate vertically through the stratified solar atmosphere affect different wavelengths at different times when the contribution functions for each wavelength peak in different layers. This leads to a characteristic pattern of (non-)coherence of the intensity at various wavelengths with respect to each other which carries information on the physical processes. Methods: We derived the correlation matrices for several photospheric and chromospheric spectral lines from observations. We separated locations with a significant photospheric polarization signal and thus magnetic fields from those without a polarization signal. For comparison with the observations, we calculated correlation matrices for spectra from simplified LTE modeling approaches, 1-D NLTE simulations, and a 3-D MHD simulation run. We applied the correlation method also to temperature maps at different optical depth layers derived from a LTE inversion of Ca II H spectra. Results: We find that all photospheric spectral lines show a similar pattern: a pronounced asymmetry of the correlation between line core and red or blue wing. The pattern cannot be reproduced with a simulation of the granulation pattern, but with waves that travel upwards through the formation heights of the lines. The correct asymmetry between red and blue wing only appears when a temperature enhancement occurs simultaneously with a downflow velocity in the wave simulation. All chromospheric spectral lines show a more complex pattern. The 1-D NLTE simulations of monochromatic waves produce a correlation matrix that qualitatively matches the observations near the very core of the Ca II H line. The photospheric signature is well reproduced in the correlation matrix derived from the 3-D MHD simulation. Conclusions: The correlation matrices of observed photospheric and chromospheric spectral lines are highly structured with characteristic and different patterns in every spectral line. The comparison with matrices derived from simulations and simple modeling suggests that the main driver of the detected patterns are upwards propagating waves. Application of the correlation method to 3-D temperature cubes seems to be a promising tool for a detailed comparison of simulation results and observations in future studies.