A model is a simplified version of some aspect of the real world. We build models to try to gain understanding, and we can increase the complexity as we learn more about the underlying system.
A mathematical model is a mathematical representation of a real-work process, often taking the form of an equation (or set of equations) to describe the relationships amongst several variables.
A simple example is the equation that relates distance moved, m, of a free-falling object to time, sec, with gravity m/sec is:
Mathematical models such as these are deterministic and do not allow for any uncertainty.
A statistical model incorporates random variation in at least one of the quantities. Random variation may be intrinsic to the real-world process, as in many biological contexts, or arising from our inability to make direct measurements with sufficient precision.
Exercise 1.1
Define the free-falling model with measurement error in both distance and time.