ABSTRACT
It is frequently required to fit the parameters of a simplemathematical model describing a physical input-output relation to measured or computed sample data. The general concept of regression is to minimize the error in the sense of an expected value. Assume that the output quantity z is related to the n input quantities x1 . . .xn that are assembled into a vector x by a functional relation f (.) with the formal representation
z = f (p,x) (3.1) in which the function f depends on a parameter vector p= [p1,p2, . . . ,pν]T whose values have yet to be determined. We assume that the available samples contain pairs (x(k), z(k)),k=1 . . .m of corresponding inputs and outputs. It is important to realize that these samples may contain random variability which is not described by the functional relation given in Eq. 3.1. Regression is carried out by minimizing the mean square difference (residual) S between the observed values z(k) and the predicted values f (p;x(k)) by choosing an appropriate parameter vector p∗.
