Linear trajectory models provide mathematical advantages to autonomous driving applications such as motion prediction. However, linear models' expressive power and bias for real-world trajectories have not been thoroughly analyzed. We present an in-depth empirical analysis of the trade-off between model complexity and fit error in modelling object trajectories. We analyze vehicle, cyclist, and pedestrian trajectories. Our methodology estimates observation noise and prior distributions over model parameters from several large-scale datasets. Incorporating these priors can then regularize prediction models. Our results show that linear models do represent real-world trajectories with high fidelity at very moderate model complexity. This suggests the feasibility of using linear trajectory models in future motion prediction systems with inherent mathematical advantages.