Companies have been increasing the amount of data that they collect from their systems and processes, considering the decrease in the cost of memory and storage technologies in recent years. The emergence of technologies such as Big Data, Cloud Computing, E-Science, and the growing complexity of information systems made evident that traceability and provenance are promising approaches. Provenance has been successfully used in complex domains, like health sciences, chemical industries, and scientific computing, considering that these areas require a comprehensive semantic traceability mechanism. Based on these, we investigate the use of provenance in the context of Software Process (SP) and introduce a novel approach based on provenance concepts to model and represent SP data. It addresses SP provenance data capturing, storing, new information inferencing and visualization. The main contribution of our approach is PROV-SwProcess, a provenance model to deal with the specificities of SP and its ability in supporting process managers to deal with vast amounts of execution data during the process analysis and data-driven decision-making. A set of analysis possibilities were derived from this model, using SP goals and questions. A case study was conducted in collaboration with a software development company to instantiate the PROV-SwProcess model (using the proposed approach) with real-word process data. This study showed that 87.5% of the analysis possibilities using real data was correct and can assist in decision-making, while 62.5% of them are not possible to be performed by the process manager using his currently dashboard or process management tool.