Mobile edge computing aims at improving application response time and energy efficiency by deploying data processing at the edge of the network. Due to the proliferation of Internet of Things and interactive applications, the everincreasing demand for low latency calls for novel approaches to further pushing the envelope of mobile edge computing beyond existing task offloading and distributed processing mechanisms. In this paper, we identify a new tradeoff between Quality-of-Result (QoR) and service response time in mobile edge computing. Our key idea is that a growing set of edge applications involving media processing, machine learning, and data mining can tolerate some level of quality loss in the computed result. By relaxing the need for optimal QoR, significant improvement in service response time can be achieved. Toward this end, we present a novel optimization framework, MobiQoR, which minimizes service response time and app energy consumption by jointly optimizing the QoR of all edge nodes and the offloading strategy. Analyzing the structure of the optimal solution, we show that the optimization can be efficiently solved when the tradeoff function is convex. The proposed MobiQoR is prototyped using Parse, an open source mobile back-end tool, on Android smartphones. Using representative applications including face recognition and movie recommendation, our evaluation using real-world datasets shows that MobiQoR reduces response time and energy consumption by up to 77% (in face recognition) and 189.3% (in movie recommendation) over existing strategies under the same level of QoR relaxation.