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Various Wireless Sensor Network (WSN) applications require the common task of collecting the data from the sensor nodes using the sink. Since the procedure of collecting data is iterative, an effective technique is necessary to obtain the data efficiently by reducing the consumption of nodal energy. Hence, a technique for data reduction in WSN is presented in this paper by proposing a prediction algorithm, called Hierarchical Fractional Bidirectional Least-Mean Square (HFBLMS) algorithm. The novel algorithm is designed by modifying Hierarchical Least-Mean Square (HLMS) algorithm with the inclusion of BLMS for bidirectional-based data prediction and Fractional Calculus (FC) in the weight update process. Data redundancy is achieved by transmitting only those data required based on the data predicted at the sensor node and the sink. Moreover, the proposed HFBLMS algorithm reduces the energy consumption in the network by the effective prediction attained by BLMS. Two metrics, such as energy consumption and prediction error, are used for the evaluation of performance of the HFBLMS prediction algorithm, where it can attain energy values of 0.3587 and 0.1953 at the maximum number of rounds and prediction errors of just 0.0213 and 0.0095, using air quality and localization datasets, respectively.