A key challenge faced by users of public clouds today is how to request for the right amount of resources in the production datacenter that satisfies a target performance for a given cloud application. An obvious approach is to develop a performance model for a class of applications such as MapReduce. However, several recent studies have shown that even for the class of well-studied MapReduce jobs, their running times can be seriously affected by numerous external factors ranging from dozen or so configuration parameters, to the physical machine characteristics (CPU, memory, disk, and network bandwidth), to implementation deficiencies such as Java, garbage collection. These factors make direct performance modeling extremely difficult. In this paper, we propose a more practical systematic methodology to solve this problem. Our approach develops a projection model, based on insights into performance bottlenecks of MapReduce jobs and their scaling properties, and parameterized with component running times based on profiling on small clusters with sampled inputs. Evaluation results show our projection model can predict job running times with 2.7% of accuracy when scaling to 32 nodes.