Overview

In the context of system identification applied to aircraft, regression refers to a statistical technique for modeling and investigating relationships among measured variables. An example of a regression is the following model relating the nondimensional pitching moment coefficient C _m, to angle of attack ? and Mach number M, for data collected during a wind-tunnel test:

In this example, ? and M are variables that are set to selected values for each experimental test point, and measurements of ?, M, and C _m are made. The pitching moment coefficient C _m is assumed to depend on ? and M in the manner postulated by the form of the model shown in Eq. (5.1), where , , , and are constant model parameters to be determined. Accordingly, ? and M are called the independent variables, and C _m is called the dependent variable or the response variable. There may be other variables that could affect C _m, but these are held fixed during the test, insofar as it is known what the influential variables might be.

Since the independent variables ? and M are set by the experimenter for each data point, it is assumed that they can be measured without error. The dependent variable C _m is subject to random measurement errors, and is therefore a random variable. The random error term v _m includes random effects of unknown...