Sensor-rich Context Management Frameworks (CMF) for Ubiquitous Systems should be able to continuosly gather raw data from observed entities (e.g., people, surround enviroment) in order to characterize the current situation (i.e., context). However, the energy of sensors can end up, which reduce the ability of CMF for detecting the current situation, directly affecting the availability of context-aware applications/services. This paper propose a data reduction approach to lower the amount of data sent to CMF over the network, minimising the energy consumption and the network traffic of sensor-rich CMF. The proposed data reduction approach rebuilds data that are not intentionally sent from sensors by prediction based on simple linear regression. The gathered raw data is modeled by linear equations and its parameters are sent to the CMF, instead of a set of readings. Thus, it reduces the communication overhead between sensors and CMF, enhancing the lifetime of sensors. Experimental results show that is possible to reduce the amount of packets sent over the network to 3% in ECG monitoring service, and 12.15% in beehive monitoring service with mean square error of 0.0009 and 0.0981, respectively.