Here's my little discussion example for a quadratic regression:

http://pj.freefaculty.org/R/WorkingExamples/regression-quadratic-1.R

Students press me to know the benefits of poly() over the more obvious
regression formulas.

I think I understand the theory on why poly() should be more numerically
stable, but I'm having trouble writing down an example that proves the
benefit of this.

I am beginning to suspect that because R's lm uses a QR decomposition under
the hood, the instability that we used to see when we inverted (X'X) is no
longer so serious as it used to be. When the columns in X are

x1 x2 x3 x3squared

then the QR decomposition is doing about the same thing as we would do if
we replaced x3 and x3squared by the poly(x3, 2) results.

Or not. I'm not arguing that, I'm thinking out loud, hoping you'll correct
me.

pj


-- 
Paul E. Johnson
Professor, Political Science      Assoc. Director
1541 Lilac Lane, Room 504      Center for Research Methods
University of Kansas                 University of Kansas
http://pj.freefaculty.org               http://quant.ku.edu

	[[alternative HTML version deleted]]

