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Fit Analyses |
A standard measure of goodness of fit is the mean residual sum of squares
A single criterion that combines the two criteria is then given by
The estimator that results from minimizing S()is called the smoothing spline estimator.
This estimator fits a cubic polynomial
in each interval between points.
At each point xi, the curve and its
first two derivatives are continuous (Reinsch 1967).
The smoothing parameter
controls the amount of
smoothing; that is, it controls the trade-off between the
goodness of fit to the data and the smoothness of the fit.
You select a smoothing parameter
by
specifying a constant c in the formula
After choosing Curves:Spline, you specify a smoothing parameter selection method in the Spline Fit dialog.
The default Method:GCV uses a c value that
minimizes the generalized cross validation mean
squared error .Figure 39.41 displays smoothing spline estimates
with c values of 0.0017 (the GCV value) and 15.2219 (DF=3).
Use the slider in the table to change
the c value of the spline fit.
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