Improving users' quality of experience (QoE) is crucial for sustaining the advertisement and subscription based revenue models that enable the growth of Internet video. Despite the rich literature on video and QoE measurement, our understanding of Internet video QoE is limited because of the shift from traditional methods of measuring video quality (e.g., Peak Signal-to-Noise Ratio) and user experience (e.g., opinion scores). These have been replaced by new quality metrics (e.g., rate of buffering, bitrate) and new engagement-centric measures of user experience (e.g., viewing time and number of visits). The goal of this paper is to develop a predictive model of Internet video QoE. To this end, we identify two key requirements for the QoE model: (1) it has to be tied in to observable user engagement and (2) it should be actionable to guide practical system design decisions. Achieving this goal is challenging because the quality metrics are interdependent, they have complex and counter-intuitive relationships to engagement measures, and there are many external factors that confound the relationship between quality and engagement (e.g., type of video, user connectivity). To address these challenges, we present a data-driven approach to model the metric interdependencies and their complex relationships to engagement, and propose a systematic framework to identify and account for the confounding factors. We show that a delivery infrastructure that uses our proposed model to choose CDN and bitrates can achieve more than 20% improvement in overall user engagement compared to strawman approaches.