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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