Date: Thu, 6 May 2004 18:40:58 -0700 Mohammad Ehsanul Karim "SAS(r) Discussion" Mohammad Ehsanul Karim http://groups.google.com Re: Parameter Estimation in the 'Orthogonal Polynomial Regression' text/plain; charset=ISO-8859-1

dmclerra@fhcrc.org

Dear Dale McLerran,

First of all, thank you very much for your nice illustrative e-mail which was very helpful for a SAS newbie like me.

However, i had a little problem: i could not get Draper and Smith's parameter estimates (1.2850000000, 0.0408333300, -0.024404760, -0.013636360, 0.0022077920, 0.0013461540, 0.0003787879) directly from SAS out put. [but i calculated and found that SAS estimates / SS(respective column from the design matrix) gives the correct result - well, except for the intercept term]. Can you please tell me how to obtain the Draper and Smith's parameter estimates directly from SAS output? _____________________________

i used the following code: _____________________________ title 'PROC ORTHOREG used with drsm data'; data drsm; input Y X; Year=X-1956; datalines; 0.93 1957 0.99 1958 1.11 1959 1.33 1960 1.52 1961 1.60 1962 1.47 1963 1.33 1964 ; run;

proc iml; use drsm; read all var {X} into year; read all var {y} into y; /* return orthogonal polynomial design matrix of order 6 */ x = orpol(year-1956,6); /* Labels to use for design matrix */ order = {"Intercept", "1st order", "2nd order", "3rd order", "4th order", "5th order", "6th order"}; /* Fit regression */ run regress(x,y,order,,,,);

ds_ssq = {8, 168, 168, 264, 616, 2184, 264}; x_new = fuzz(x`#sqrt(ds_ssq))`; print x_new; _____________________________

and the out put was: _____________________________ PROC ORTHOREG used with drsm data 1

07:23

NAME B STDB T PROBT Intercept 3.6345289 0.0116074 313.12147 0.0020331 1st order 0.5292605 0.0116074 45.596783 0.0139597 2nd order -0.316322 0.0116074 -27.25172 0.0233502 3rd order -0.221565 0.0116074 -19.08821 0.033321 4th order 0.054796 0.0116074 4.7207748 0.1328905 5th order 0.0629102 0.0116074 5.4198309 0.1161549 6th order 0.0061546 0.0116074 0.5302281 0.6896245

Covariance of Estimates

COVB Intercept 1st order 2nd order 3rd order 4th order 5th order 6th order

Intercept 0.0001 36E-21 -6E-20 12E-20 -3E-19 52E-20 -2E-18 1st order 36E-21 0.0001 14E-20 -2E-19 46E-20 -1E-18 29E-19 2nd order -6E-20 14E-20 0.0001 39E-20 -8E-19 17E-19 -5E-18 3rd order 12E-20 -2E-19 39E-20 0.0001 13E-19 -3E-18 86E-19 4th order -3E-19 46E-20 -8E-19 13E-19 0.0001 59E-19 -2E-17 5th order 52E-20 -1E-18 17E-19 -3E-18 59E-19 0.0001 39E-18 6th order -2E-18 29E-19 -5E-18 86E-19 -2E-17 39E-18 0.0001

Correlation of Estimates

CORRB Intercept 1st order 2nd order 3rd order 4th order 5th order 6th order

Intercept 1 27E-17 -4E-16 91E-17 -2E-15 39E-16 -1E-14 1st order 27E-17 1 1E-15 -2E-15 34E-16 -8E-15 22E-15 2nd order -4E-16 1E-15 1 29E-16 -6E-15 13E-15 -4E-14 3rd order 91E-17 -2E-15 29E-16 1 97E-16 -2E-14 64E-15 4th order -2E-15 34E-16 -6E-15 97E-16 1 43E-15 -1E-13 5th order 39E-16 -8E-15 13E-15 -2E-14 43E-15 1 29E-14 6th order -1E-14 22E-15 -4E-14 64E-15 -1E-13 29E-14 1

X_NEW 1 -7 7 -7 7 -7 1 1 -5 1 5 -13 23 -5 1 -3 -3 7 -3 -17 9 1 -1 -5 3 9 -15 -5 1 1 -5 -3 9 15 -5 1 3 -3 -7 -3 17 9 1 5 1 -5 -13 -23 -5 1 7 7 7 7 7 1

Thank you very much for your kind support.

_______________________

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

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