With rapid growth in smart phones and mobile data, effectively managing cellular data networks is important in meeting user performance expectations. However, the scale, complexity and dynamics of a large 3G cellular network make it a challenging task to understand the diverse factors that affect its performance. In this paper we study the RNC (Radio Network Controller)-level performance in one of the largest cellular network carriers in US. Using large amount of datasets collected from various sources across the network and over time, we investigate the key factors that influence the network performance in terms of the round-trip times and loss rates (averaged over an hourly time scale). We start by performing the 'first-order' property analysis to analyze the correlation and impact of each factor on the network performance. We then apply RuleFit - a powerful supervised machine learning tool that combines linear regression and decision trees - to develop models and analyze the relative importance of various factors in estimating and predicting the network performance. Our analysis culminates with the detection and diagnosis of both 'transient' and 'persistent' performance anomalies, with discussion on the complex interactions and differing effects of the various factors that may influence the 3G UMTS (Universal Mobile Telecommunications System) network performance.