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As Web services and the semantic Web become more important, enabling technologies such as Web service ontologies will grow larger. The ability of mobile devices, such as cell phones and PDAs, to download and reason across them will be severely limited. Given that an agent on a mobile device only needs a subset of what is described in a Web service ontology, an ontology sub-graph can be created. In this paper, we develop a empirical software engineering approach to build a prediction model to measure the quality in terms of correct query handling of ontology sub-graphs relative to the original ontology - mean average recall of the sub-graph compared to the original ontology is used as the quality standard. Our metrics allow speedy selection of a sub-graph for use by a mobile device.