12.0 QR Command                                                                 
                                                                                
     The QR option allows calculation of a high accuracy solution to            
OLS regression models, solution to principal component regressions of           
OLS models and singular value factorizations of OLS models. The general         
form of the QR command is:                                                      
                                                                                
     B34SEXEC QR options, parameters  $                                         
         MODEL Yvar = Xvar1 Xvar2   $                                           
         TITLE=('Some comment up to 80 characters')  $                          
      B34SEEND  $                                                               
                                                                                
The MODEL sentence is required.                                                 
                                                                                
QR options:                                                                     
                                                                                
     NOINT   -  Set if no intercept term is desired.                            
                                                                                
     PLOT    -  Set if a one page residual plot is desired.                     
                                                                                
QR parameters:                                                                  
                                                                                
     IBEGIN=n1  Sets beginning observation for data. Default=1.                 
                                                                                
     IEND=n2    Sets ending observation for data. Default = number of           
                  data points in current dataset.                               
                                                                                
     IFREZ=n3   If IFREZ is set, the first n3 variables listed in the           
                  MODEL sentence will be pivoted into a new position            
                  and will occur in any regression where the final              
                  number of right hand variables in less than the number        
                  on the MODEL card (if possible). Unless the NOINT             
                  option is present, n3 is assumed to include the               
                  constant.                                                     
                                                                                
     EPS=value  EPS, if present, sets a nonnegative number less than one        
                  that is used to control the stability of the solution.        
                  The QR command chooses a set of columns of X to fit           
                  whose condition number is estimated to be less that           
                  1.00 / EPS.  If EPS is not supplied, EPS defaults to V        
                  * 1.0d-16, where V is the largest sum of the absolute         
                  values of any row of X.                                       
                                                                                
     IPCC=key     If IPCC is not specified, no principal component              
                     regressions are calculated.                                
                  If key=PCREG, the PC regression is calculated.                
                  If key=PCREGLIST, a PC regression is calculated and U,        
                     V, predicted Y and the residual are listed.                
                  If key=PUNCH, U, predicted Y and the residual are             
                     placed on unit 14 in unformatted double precision.         
                  If key=LPUNCH, options PCREGLIST and PUNCH are                
                     combined.                                                  
                  If key=SPUNCH, V, predicted Y and the residual are            
                     listed and only predicted Y and the residual are           
                     placed on unit 14.                                         
                                                                                
                  NOTE:  The usual setting for IPCC is PCREG or                 
                         PCREGLIST.                                             
                                                                                
The MODEL sentence.                                                             
                                                                                
          MODEL Y = X Q P R  $                                                  
                                                                                
     The MODEL sentence sets up model with Y on the left and X Q P R on         
the right.                                                                      
                                                                                
TITLE sentence.                                                                 
                                                                                
     TITLE=('Some comment here') $                                              
                                                                                
     The TITLE sentence allows user to optionally comment output.               
                                                                                
                                                                                
Note: To save paper, the covariance matrix of regression coefficients is        
      not printed unless OUTPUT(VERBOSE) is set on the OPTIONS                  
      paragraph.                                                                
                                                                                
Sample QR setup:                                                                
                                                                                
                                                                                
     B34SEXEC QR IPCC=PCREGLIST$                                                
         MODEL Y = X1 X2  $                                                     
         TITLE=('Test of New Model')  $                                         
        B34SEEND$