Statistical - Cubic Regression (Cubic Spline Fit) ?

[Wes Loewer]

(06-01-2022 03:20 PM)Thomas Klemm Wrote:  Use a cubic spline if you want a function that goes smoothly through the given data points.
Disadvantage: The function is defined piecewise.

This is consistent with the Prime's spline command. However, some cubic spline implementations don't limit themselves to y=f(x), but instead treat x and y parametrically, finding x(t) and y(t) where t is the parametric variable. The GeoGebra help page says:

Quote:The result of the spline command is a curve. Spline algorithm is used for x and y coordinates separately: first we determine values of t that correspond to the points (based on Euclidian distances between the points), then we find cubic splines as functions t->x and t->y.

In GeoGebra, if the first and last points are the same, forming a loop, the algorithm also smooths out where they join.