g02dgf

Purpose

Synopsis

[rss,cov,q,b,se,res,ifail] = g02dgf(rss,irank,cov,q,svd,p,y,wk<,wt,weight,...
ifail>)

Description

 
 G02DGF uses the results given by G02DAF to fit the same set of 
 independent variables to a new dependent variable.
 
 G02DAF computes a QR decomposition of the matrix of p independent
 variables and also, if the model is not of full rank, a singular 
 value decomposition (SVD). These results can be used to compute 
 estimates of the parameters for a general linear model with a new
 dependent variable. The QR decomposition leads to the formation 
 of an upper triangular p by p matrix R and an n by n orthogonal 
                                     T       T 1/2               
 matrix Q. In addition the vector c=Q y (or Q W   y) is computed. 
 For a new dependent variable, y   , G02DGF computes a new value 
                                new                             
       T         T 1/2    
 of c=Q y    or Q W   y   .
         new           new
 
 If R is of full rank, then the least-squares parameter estimates,
 ^^^^^^                        ^^^^^^                            
 (beta), are the solution to: R(beta)=c , where c  is the first p 
                                       1         1               
 elements of c.
 
 If R is not of full rank, then G02DAF will have computed a SVD of
 R,
 
                               (D 0) T
                           R=Q (0 0)P ,
                              *       
 
 where D is a k by k diagonal matrix with non-zero diagonal 
 elements, k being the rank of R and Q  and P are p by p 
                                      *                 
 orthogonal matrices. This gives the solution
 
                         ^^^^^^    -1 T  
                         (beta)=P D  Q  c 
                                 1    *  1
                                       1 
 
 P  being the first k columns of P, i.e., P=(P P ) and Q   being 
  1                                           1 0       *       
                                                         1      
 the first k columns of Q . Details of the SVD, are made available
                         *                               
                                      *
 by G02DAF in the form of the matrix P :
 
                               ( -1 T)
                               (D  P )
                               (    1)
                             * (  T  )
                            P =( P   ).
                               (  0  )
 
 The matrix Q  is made available through the workspace of G02DAF.
             *                                                  
 
 In addition to parameter estimates, the new residuals are 
 computed and the variance-covariance matrix of the parameter 
 estimates are found by scaling the variance-covariance matrix for
 the original regression.
 

Parameters

g02dgf

Required Input Arguments:

rss                                   real
irank                                 integer
cov (:)                               real
q (:,:)                               real
svd                                   logical
p (:)                                 real
y (:)                                 real
wk (:)                                real

Optional Input Arguments:                       <Default>

wt (:)                                real     zeros(size(q,1),1)
weight (1)                            string   g02dgf01(wt)
ifail                                 integer  -1

Output Arguments:

rss                                   real
cov (:)                               real
q (:,:)                               real
b (:)                                 real
se (:)                                real
res (:)                               real
ifail                                 integer