On-line modeling by curve-fitting

Modeling, as we use the term here, means matching a set of numbers, obtained from some theory, to a set of numbers from the laboratory. We will refer to the laboratory numbers as the observed data or curve and to the theoretical numbers as the computed data or curve. Our purpose may be to evaluate the model; or to use it to determine otherwise unobtainable values as functions of the observed curve. Thus the key problem in modeling by curve-fitting is parameter determination. The model functions contain unknown or vaguely known numbers called parameters that affect the shape of the computed curve. The problem is to find those parameter values that make the computed curve most resemble the observed curve in the least squares sense. This is why we speak of modeling by curve-fitting. Statisticians call this activity non-linear regression.