st: Re: spline regression (Kit Baum)

[Kit Baum <baum@bc.edu>]

Mohammed,

If you graph x vs y, and break the line at the knot points, a linear  
spline allows the line to have kinks, like a dot-to-dot drawing. A  
quadratic spline has constant first derivatives == slopes at the knot  
points, so that it will not have any kinks. I don't know how to  
explain a second derivative in this context except to say that a  
curved line may have more or less curvature (such as a railroad track  
on a curve may be a broad curve or a sharp curve) and holding the  
second derivative constant causes the degree of curvature to be equal  
before and after the knot point (so that the locomotive will not  
derail at the knot point).


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


On Mar 24, 2008, at 02:33 , Mohammed wrote:


> 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
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