Fog computing is a promising computing paradigm for time-sensitive Internet of Things (IoT) applications. It helps to process data close to the users, in order to deliver faster processing outcomes than the Cloud; it also helps to reduce network traffic. The computation environment in the Fog computing is highly dynamic and most of the Fog devices are battery powered hence the chances of application failure is high which leads to delaying the application outcome. On the other hand, if we rerun the application in other devices after the failure it will not comply with time-sensitiveness. To solve this problem, we need to run applications in an energy-efficient manner which is a challenging task due to the dynamic nature of Fog computing environment. It is required to schedule application in such a way that the application should not fail due to the unavailability of energy. In this paper, we propose a multiple linear, regression-based resource allocation mechanism to run applications in an energy-aware manner in the Fog computing environment to minimise failures due to energy constraint. Prior works lack of energy-aware application execution considering dynamism of Fog environment. Hence, we propose A multiple linear regression-based approach which can achieve such objectives. We present a sustainable energy-aware framework and algorithm which execute applications in Fog environment in an energy-aware manner. The trade-off between energy-efficient allocation and application execution time has been investigated and shown to have a minimum negative impact on the system for energy-aware allocation. We compared our proposed method with existing approaches. Our proposed approach minimises the delay and processing by 20%, and 17% compared with the existing one. Furthermore, SLA violation decrease by 57% for the proposed energy-aware allocation.