R has become a cornerstone of scientific and statistical computing due to its extensive package ecosystem, expressive syntax, and strong support for reproducible analysis. However, as data sizes and computational demands grow, native R parallelism support remains limited. This paper presents RCOMPSs, a scalable runtime system that enables efficient parallel execution of R applications on multicore and manycore systems. RCOMPSs adopts a dynamic, task-based programming model, allowing users to write code in a sequential style, while the runtime automatically handles asynchronous task execution, dependency tracking, and scheduling across available resources. We present RCOMPSs using three representative data analysis algorithms, i.e., K-nearest neighbors (KNN) classification, K-means clustering, and linear regression and evaluate their performance on two modern HPC systems: KAUST Shaheen-III and Barcelona Supercomputing Center (BSC) MareNostrum 5. Experimental results reveal that RCOMPSs demonstrates both strong and weak scalability on up to 128 cores per node and across 32 nodes. For KNN and K-means, parallel efficiency remains above 70% in most settings, while linear regression maintains acceptable performance under shared and distributed memory configurations despite its deeper task dependencies. Overall, RCOMPSs significantly enhances the parallel capabilities of R with minimal, automated, and runtime-aware user intervention, making it a practical solution for large-scale data analytics in high-performance environments.