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From |
"Sergiy Radyakin" <serjradyakin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Re: spline regression (Kit Baum) |

Date |
Sun, 23 Mar 2008 11:52:36 -0400 |

This page has a nice applet illustrating the concept of one-sided derivatives: http://www.ies.co.jp/math/java/calc/limrl/limrl.html On 3/23/08, Mohammed El Faramawi <melfaram@yahoo.com> wrote: > Hi Kit, > Thank you very much. Pardon me, I am not good in MAth. > i will be very grateful if you explain more what you > mean by "the derivative (slope) of the function is > equal on either side of each knot point, but the > curvature on either side may differ" and "The first > and second derivatives of the function are equal on > either side of each knot point." Thanks again Kit > > > --- Kit Baum <baum@bc.edu> wrote: > > > Mohammed said > > > > 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. > > > > Kit > > > > Kit Baum, Boston College Economics and DIW Berlin > > http://ideas.repec.org/e/pba1.html > > An Introduction to Modern Econometrics Using Stata: > > http://www.stata-press.com/books/imeus.html > > > > > > * > > * For searches and help try: > > * > > http://www.stata.com/support/faqs/res/findit.html > > * http://www.stata.com/support/statalist/faq > > * http://www.ats.ucla.edu/stat/stata/ > > > > > > ____________________________________________________________________________________ > Never miss a thing. Make Yahoo your home page. > http://www.yahoo.com/r/hs > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: re: linear and cubic spline regression***From:*Kit Baum <baum@bc.edu>

**st: Re: spline regression (Kit Baum)***From:*Mohammed El Faramawi <melfaram@yahoo.com>

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