The recent proliferation of Data Grids and the increasingly common practice of using resources as distributed data stores provide a convenient environment for communities of researchers to share, replicate, and manage access to copies of large datasets. This has led to the question of which replica can be accessed most efficiently. In such environments, fetching data from one of the several replica locations requires accurate predictions of end-to-end transfer times. The answer to this question can depend on many factors, including physical characteristics of the resources and the load behavior on the CPUs, networks, and storage devices that are part of the end-to-end data path linking possible sources and sinks. Our approach combines end-to-end application throughput observations with network and disk load variations and captures whole-system performance and variations in load patterns. Our predictions characterize the effect of load variations of several shared devices (network and disk) on file transfer times. We develop a suite of univariate and multivariate predictors that can use multiple data sources to improve the accuracy of the predictions as well as address Data Grid variations (availability of data and sporadic nature of transfers). We ran a large set of data transfer experiments using GridFTP and observed performance predictions within 15% error for our testbed sites, which is quite promising for a pragmatic system.