```Date: Thu, 6 May 2004 19:44:34 -0700 Reply-To: Dale McLerran Sender: "SAS(r) Discussion" From: Dale McLerran Subject: Re: Parameter Estimation in the 'Orthogonal Polynomial Regression' Comments: To: Mohammad Ehsanul Karim In-Reply-To: <391aa978.0405061740.16d8b54e@posting.google.com> Content-Type: text/plain; charset=us-ascii Mohammad, You should get the Draper and Smith parameter estimates if you run the IML REGRESS routine employing design matrix X_new and response Y. Thus, the following code should return the Draper and Smith parameter estimates: 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 ; 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"}; ds_ssq = {8, 168, 168, 264, 616, 2184, 264}; x_new = fuzz(x`#sqrt(ds_ssq))`; /* Fit regression */ run regress(x_new,y,order,,,,); quit; HTH, Dale --- Mohammad Ehsanul Karim wrote: > 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 > Institute of Statistical Research and Training > University of Dhaka, Dhaka- 1000, Bangladesh > _______________________ ===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@fhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- __________________________________ Do you Yahoo!? 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