# The objective function

Sections, surfaces and contours of the objective function

It is valuable to be able to explore the contours of the surface defined by the objective function as a function of the parameters i.e.

         WSSQ/NDOF = f(p(1), p(2), ..., p(n))

at the solution point, in order to assess the local geometry. After any regression you can plot this objective function as a function of any 1 or 2 chosen parameters, the others being fixed at their best fit values. Note that these plots are in unscaled external, i.e. user coordinates. Information about curvature and elliptic eccentricity in internal coordinates is available as the eigenvalues and condition number of the scaled internal Hessian matrix.

Visualising the best fit of a surface to data

When a best fit function of two variables, say

         z = f(x,y)

has been fitted, you can view a 3D representation of the best fit surface. You can also create a succession of sections through the best fit surface by fixing y then varying x, or fixing x then varying y. Such slices have ranges set by the data, and will only be created if there is at least one data point in the slice. ASCII files of successive sections should then be imported into SIMPLOT to display the fit to data as a series of built up sections.

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