How cubic splines is different from the natural cubic splines?

model

#1

I am currently studying the methods which are used to fit nonlinear models while studying them I found one great method is splined . I found two types of splines one is cubic splines and is natural cubic splines .

cubic splines- A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of control points. The second derivative of each polynomial is commonly set to zero at the endpoints since this provides a boundary condition that completes the system of equations.

natural cubic splines - A natural cubic spline extrapolates linearly beyond the boundary knots.

I want to know which one of them is the better one and why


#2

@sid100158- Natural cubic splines is better one cubic spline because it has less number of degree of freedom and also it does not extrapolate at the ends which are usually a case of cubic splines.

As we can see that it extrapolates at the end.But natural cubic splines fit perfectly.

Hope this helps!

Regards,
Hinduja