# Cubic splines better than quadratic splines?

I have read in a number of places that cubic splines are of more practical use than quadratic splines in general (there are exceptions of course). Anyone know specifically why they are more applicable/better?

• Cubic spline has continuous second derivative, while quadratic spline only has continuous first derivative. So cubic spline is smoother. Apr 5, 2015 at 17:33
• Yeah, but would a fourth order spline be even smoother or does it get worse if you go even higher order? If not, and it also gets better, i.e. it is always just a tradeoff between complexity and accuracy, why does cubic seem to be enough for most applications? Apr 5, 2015 at 18:01
• I believe you can get higher smoothness but as you said there has to be a point to stop. People stop at cubic spline because it has smoothness at second derivative, which means it minimizes the curvature of the function. And that is enough for most of the applications. Apr 5, 2015 at 18:40
• Also, in the regression spline/least squares sense, it has some (statistical) optimality properties, probably connected to the fact of minimizing curvature. See the book Hastie, Tibshirani, et.al "Elements of Statistical Learning" for this viewpoint. Dec 7, 2017 at 9:59