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In wireless sensor networks, clustering allows the aggregation of sensor data. It is well known that leveraging the correlation between different samples of the observed data will lead to better utilization of energy reserve. However, no previous work has analyzed the effect of non-ideal data aggregation in multi-hop sensor networks. In this paper, we propose a novel analytical framework to study how partially correlated data affect the performance of clustering algorithms. We analyze the behavior of multi-hop routing and, by combining random geometry techniques and rate distortion theory, predict the total energy consumption and network lifetime. We show that when a moderate amount of correlation is available, the optimal probabilities that lead to minimum energy consumption are far from optimality in terms of network lifetime. In addition, we study the sensitivity of the total energy consumption and network lifetime to the amount of correlation and compression distortion constraint.