The progressive deployment of cell sites in wireless networks to deal with the massive demand of wireless services experienced in the last years has led to a huge increase in energy consumption and associated operational expenditures for wireless network operators. As a result, significant research efforts are being recently devoted towards energy efficient wireless communications. The use of relay nodes that enhance coverage/capacity in wireless systems has been identified as a means to improve energy efficiency thanks to the associated reduction in transmit power. In this context, this paper presents the assessment of the energy savings that can be achieved by means of relaying in a wireless system. As a difference from prior works where the impact of relaying on energy efficiency is obtained as a result of multiple aggregated effects, the analysis performed in this paper will highlight, separately, the role played by each of the key elements influencing on the performance, such as the propagation and shadowing effects, the energy consumption model parameters and the influence of the bit rate and spectral efficiency. ; Peer Reviewed ; Postprint (published version)