3.3 Smoothing

In this section, we will assume that we have a data set that we would like to fit with a function having a known form. The function may be a straight line, a parabola, an exponential curve, or have some other shape; we will just assume that we know how to write the general form of the function (the so-called parametric form), even though we don't yet know the value of its coefficients (the parameters). We will not expect the function to pass exactly through the data points, but we want the curve to pass close to them. Before we can design a method that gives us a good fit to the data, we need to decide what we mean by “a good fit.”