A regression-based residual echo suppression (RES) system and process for suppressing the portion of the microphone signal corresponding to a playback of a speaker audio signal that was not suppressed by an acoustic echo canceller (AEC). In general, a prescribed regression technique is used between a prescribed spectral attribute of multiple past and present, fixed-length, periods (e.g., frames) of the speaker signal and the same spectral attribute of a current period (e.g., frame) of the echo residual in the output of the AEC. This automatically takes into consideration the correlation between the time periods of the speaker signal. The parameters of the regression can be easily tracked using adaptive methods. Multiple applications of RES can be used to produce better results and this system and process can be applied to stereo-RES as well.