[R] Orthogonal Polynomial Regression Parameter Estimation

[WilD KID]

Dear all,

I came up with some sort of solution(!), which is :

--------------------------------------------
>  orth.fit<-lm(Y~poly(X,degree = 6))
>  co<-coef(orth.fit)
>  s<-c(sum(p0^2), sum(p1^2), sum(p2^2), sum(p3^2),
sum(p4^2), sum(p5^2), sum(p6^2)) # these pi's were
previously defined
>  nor<-co/sqrt(ss)
> 
co1<-c(alpha0,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6)
# from previous results
>  cbind(co,ss,nor,co1)
                               co   ss           nor  
        co1
(Intercept)           1.285000000    8  0.4543161069 
1.2850000000
poly(X, degree = 6)1  0.529260490  168  0.0408333333 
0.0408333333
poly(X, degree = 6)2 -0.316321867  168 -0.0244047619
-0.0244047619
poly(X, degree = 6)3 -0.221564684  264 -0.0136363636
-0.0136363636
poly(X, degree = 6)4  0.054795962  616  0.0022077922 
0.0022077922
poly(X, degree = 6)5  0.062910192 2184  0.0013461538 
0.0013461538
poly(X, degree = 6)6  0.006154575  264  0.0003787879 
0.0003787879
--------------------------------------------

Note that all values of "nor" (modified R result) and
"co1" (Draper and Smith result) matches, except the
intercept term! But i guess i can live with it:p
However, if any one has any more suggestions, please
let me know.

Thanks to all who helped me here (Douglas Bates and
Prof Brian Ripley) and elsewhere (including Dale
McLerran of comp.soft-sys.sas and Nick Cox of Stata
list).

Thank you very much for all your support.

_______________________

Mohammad Ehsanul Karim <wildscop at yahoo.com> 
Institute of Statistical Research and Training 
University of Dhaka, Dhaka- 1000, Bangladesh