The integration of cellular communication with Unmanned Aerial Vehicles (UAVs) extends the range of command and control and payload communications of autonomous UAV applications. Accurate modeling of this air-to-ground wireless environment aids UAV mission planning. Models built on and insights obtained from real-life experiments intricately capture the variations in air-to-ground link quality with UAV position, offering more fidelity for simulations and system design than those that rely on generic theoretical models designed for ground scenarios or ray-tracing simulations. In this work, we conduct aerial flights at the Aerial Experimentation and Research Platform for Advanced Wireless (AERPAW) Lake Wheeler testbed to study the variation in key performance indicators (KPIs) of a private 4G/5G cellular base station (BS) with the UAV's altitude, distance from the BS, elevation, and azimuth relative to the BS. Variations in 4G and 5G physical layer KPIs and application layer throughput are logged and analyzed, using two Android smartphones: a Keysight Nemo device, with enhanced KPI access, through a rooted operating system, and a standard smartphone running a custom application that utilizes open-source Android APIs. The observed signal strength measurements are compared to theoretical predictions from free space path loss models that incorporate the BS antenna radiation patterns. Mathematical model parameters for polynomial curve approximations are derived to fit the observed data. Light machine learning approaches, namely random forests, gradient boosting regressors and neural networks, are used to model KPI behaviour as a function of UAV position relative to the BS. The insights and models generated from real-life experiments in this study can serve as valuable tools in the design, simulation and deployment of cellular communication-based UAV systems.