I have a question about cubic spline regression and
linear spline regressionv. I would like to know what
are the differences between them?
From a mathematical standpoint a linear spline, defined over a
number of 'knot points' (or join points) is continuous but not
differentiable. It is the equivalent of a dot-to-dot drawing from
kindergarten.
A quadratic spline is continuous and once differentiable. That is,
the derivative (slope) of the function is equal on either side of
each knot point, but the curvature on either side may differ.
A cubic spline is continuous and twice differentiable. The first and
second derivatives of the function are equal on either side of each
knot point.
A polynomial spline of order k is differentiable (k-1) times.
There are different kinds of splines; e.g. b-splines that have
similar properties, but are defined using different mathematics than
polynomial splines.
Linear splines are discussed in my book, referenced below.
