Acoustic room compensation techniques, which allow a sound reproduction system to counteract undesired alteration to the sound scene due to excessive room resonances, have been widely studied. Extensive efforts have been reported to enlarge the region over which room equalization is effective and to contrast variations of room transfer functions in space. A speaker-tuning technology "Trueplay" allows users to compensate for undesired room effects over an extended listening area based on a spatially averaged power response of the room, which is conventionally measured using microphones on portable devices when users move around the room. In this work, we propose a novel system that leverages measured speaker echo path self-responses to predict the room average power responses using a local PCA based approach. Experimental results confirm the effectiveness of the proposed estimation method, which further leads to a room compensation filter design that achieves a good sound similarity compared to the reference system with the ground-truth room average power response while outperforming other systems that do not leverage the proposed estimator.