Date:         Thu, 8 Nov 2007 22:51:05 -0500
Reply-To:     Kwame Asom <asom77@HOTMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Kwame Asom <asom77@HOTMAIL.COM>
Subject:      Using Legendre Polynomials in SAS
Content-Type: text/plain; charset=ISO-8859-1

Hi everybody,

I have used SAS to fit a quadratic regression, regressing weight (kg) on
age in days of animals, using ORDINARY POLYNOMIALS. The summary of  the
model used is:

weight = age * age ie. age x age (quadratic regression). For cubic
regression it would be: weight = age *age * age, for quartic regression it
would be age*age*age*age. Supposing the age is 60 days and the weight is
100kg, a quadratic regression using ordinary polynomials would be:
100 kg = 60x60.

Now, I want to use SAS to fit 3rd order (ie. quadratic) LEGENDRE
POLYNOMIAL,regressing weight on age.
How do I achieve that,please? As illustrated above, using ordinary
polynomials in SAS is quite easy,but I DONT KNOW HOW TO REGRESS WEIGHT ON
AGE USING LEGENDRE POLYNOMIALS.Here is a brief discription of Legendre
polynomials.

Legendre polynomials are denoted by Pn (x) of order n. The polynomials are
either even or odd functions of x for even or odd orders n.
The first few Legendre polynomials are

     Legendre polynomials are denoted by Pn (x) of order n. The polynomials
are either even or odd functions of x for even or odd orders n.
The first few Legendre polynomials are

  Po (x) =1

  P1(x) = x

  P2(x) = ½(3x2 -1)

  P3 (x) = ½(5x3 -3x)

 PLEASE HELP ME TO USE SAS TO CODE LEGENDRE POLYNOMIALS.

Thanks in advance.

K. Asom