In this paper, we attempt to predict users' quality of experience (QoE) with the log data collected from the web sites of Internet video service providers. To this end, we first collect service log data in the wild from one of the Top 5 most popular providers in China. Then we do a series of data preprocessing to format the original semi-structured log data to structured. We calculate several key video quality metrics, such as join time and frame rate, and explore the distributions of each quality metric, as well as the relationship between individual quality metric and user engagement. Considering that user engagement may be a result of comprehensive effect of several metrics, we apply fuzzy decision tree (FDT), a kind of classification algorithms in the area of machine learning, to develop the predictive model of user QoE for Internet video. Finally, we compare the prediction accuracy of our model with the model developed using decision tree on several different datasets. Our model separately achieves about 20% and 10% improvement in prediction accuracy on the dataset of sessions with the same content type and the dataset of sessions with mobile access devices.