The multi-tier implementation has become the industry standard for developing scalable client-server enterprise applications. Since these applications are performance sensitive, effective models for dynamic resource provisioning and for delivering quality of service to these applications become critical. Workloads in such environments are characterized by client sessions of interdependent requests with changing transaction mix and load over time, making model adaptivity to the observed workload changes a critical requirement for model effectiveness. In this work, we apply a regression-based approximation of the CPU demand of client transactions on a given hardware. Then we use this approximation in an analytic model of a simple network of queues, each queue representing a tier, and show the approximation?s effectiveness for modeling diverse workloads with a changing transaction mix over time. Using the TPCW benchmark and its three different transaction mixes we investigate factors that impact the efficiency and accuracy of the proposed performance prediction models. Experimental results show that this regression-based approach provides a simple and powerful solution for efficient capacity planning and resource provisioning of multi-tier applications under changing workload conditions.