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Many modern networked applications require specific levels of service quality from the underlying network. Moreover, next-generation networked applications are expected to adapt to changes in the underlying network, services, and user interactions. While some applications have built-in adaptivity, the adaptation itself requires specification of a system model. This paper presents Sapphire, an experimental approach for systematic model generation for application adaptation within a target network. It employs a nearly-automated, statistical design of experiments to characterize the relationships of both application and network-level parameters. First, it applies the Analysis of Variance (ANOVA) method to identify the most significant parameters and their interactions that affect performance. Next, it generates a model of application performance with respect to these parameters within the ranges of measurements. The key benefit of the framework is the integration of several well-established concepts of statistical modeling and distributed systems in the form of simple APIs so that existing applications can take advantage of it. We demonstrate the usefulness and flexibility of Sapphire by generating a performance model of an audio streaming application. We show that many existing multimedia and QoS-sensitive applications can exploit a statistical modeling approach such as Sapphire to incorporate application adaptivity. The approach can also be used for feedback control of distributed applications, tuning network and application parameters to achieve service levels in a target network.