Energy efficiency is a primary concern for wireless sensor networks (WSNs). One of its most energy-intensive processes is the radio communication. This work uses a predictor combined with a Kalman filter (KF) to reduce the communication energy cost for cluster-based WSNs. The technique, called PKF, is suitable for typical WSN applications with adjustable data quality and tens of picojoule computation cost. However, it is challenging to precisely quantify its underlying process from a mathematical point of view. Through an in-depth mathematical analysis, we formulate the tradeoff between energy efficiency and reconstruction quality of PKF. One of our prominent results for that is the explicit expression for the covariance of the doubly truncated multivariate normal distribution; it improves the previous methods and has generality. The validity and accuracy of the analysis are verified with both artificial and real signals. The simulation results, using real temperature values, demonstrate the efficiency of PKF: without additional data degradation, it reduces the communication cost by more than 88%. Compared to previous works based on KF, PKF requires less computational effort while improving the reconstruction quality; compared with the techniques without KF, the advantages of PKF are even more significant. It reduces the transmission rate of them by at least 29%. Besides, it can be integrated into network level techniques to further extend the whole network lifetime.