LOG TO ILLUSTRATE "REMOVING PROJECTIONS" USING DATA-STEP 
CALCULATIONS IN SAS.
================================================= 10/10/08

data meatmat;
   set home.meat (keep=pbe cbe dinc cfo rdinc);
proc means data=meatmat mean;
   output out = meatavg mean= pbem cbem dincm cfom rdincm; 
  run;
proc print data=meatavg; run;

Obs  _TYPE_  _FREQ_    pbem     cbem    dincm     cfom    rdincm

 1      0      17    69.0588  53.0882  44.6235  91.0059  68.6529


meatmat1 = 17 x 5 matrix with columns pbe, cbe, dinc, cfo, rdinc
           obtained by substracting mean from each column

data auxm (drop=i);
   set meatavg (drop=_TYPE_ _FREQ_);
   do i=1 to 17; output; end; run;
data meatmat1;
   merge meatmat auxm;
   pbe1=pbe-pbem; 
   cbe1=cbe-cbem;
   dinc1=dinc-dincm;
   cfo1=cfo-cfom;
   rdinc1=rdinc-rdincm; 
   prod12= pbe1*cbe1; prod32=dinc1*cbe1;
   prod42= cfo1*cbe1; prod52=rdinc1*cbe1; 
   cbe1sq=cbe1**2; run;

/* Now we remove projection on cbe */

proc means data=meatmat1 mean;
  var prod12 prod32 prod42 prod52 
      cbe1sq;
 output out=coeffs mean= 
     m12 m32 m42 m52 m22;

data auxm2 (keep=b1 b3 b4 b5);
   set coeffs (drop=_TYPE_ _FREQ_);
   b1=m12/m22; b3=m32/m22; b4=m42/m22; b5=m52/m22;
   do i=1 to 17; output; end; run;

data meatmat2;
   merge meatmat1 (keep=pbe1 cbe1 dinc1 cfo1 rdinc1)
         auxm2 (keep=b1 b3 b4 b5);
   pbe2 = pbe1-b1*cbe1;   dinc2= dinc1-b3*cbe1;
   cfo2 = cfo1-b4*cbe1;   rdinc2=rdinc1-b5*cbe1;

proc corr data=meatmat2;
  var pbe2; with dinc2 cfo2 rdinc2; run;

Pearson Correlation Coefficients, N = 17
       Prob > |r| under H0: Rho=0

                pbe2

dinc2       -0.65996
              0.0039

cfo2        -0.69039
              0.0022

rdinc2      -0.49545
              0.0431
COMPARE WITH

proc corr data=meatmat;
   var pbe; with dinc cfo rdinc;
     partial cbe; run;
Pearson Partial Correlation Coefficients, N = 17
       Prob > |r| under H0: Partial Rho=0

                pbe

dinc       -0.65996
             0.0054

cfo        -0.69039
             0.0031

rdinc      -0.49545
             0.0510


OK!!