The widespread adoption of Microservice architectures has posed many challenges regarding API design for these architectures. Several API best practices and patterns have been proposed that could help API designers ensure API quality attributes such as reliability, availability, and performance. API Request Bundling, which is in focus of this paper, is one of those patterns that aims at optimizing performance. The pattern promises substantial performance gains, but can also lead to significant drawbacks such as increased development effort and application complexity. So far, there is little to no rigorously acquired knowledge to judge whether applying Request Bundling is worth the costs in a given Microservice architecture. To improve this situation, we performed an empirical study based on a Microservice-based open source business application using realistic workload scenarios. To estimate the performance impact of Request Bundling, we derived a regression model and performed a multivariate regression analysis. These selected regression models can help distributed system engineers and architects to estimate the gain in performance or total round-trip time with or without Request Bundling. Our approach followed in the paper, can be customized to other Microservice architectures and/or to study other performance-related Microservice patterns.