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decus_20tap2_198111
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decus/20-0026/gdata.doc
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SUBROUTINE GDATA
PURPOSE
GENERATE INDEPENDENT VARIABLES UP TO THE M-TH POWER (THE
HIGHEST DEGREE POLYNOMIAL SPECIFIED) AND COMPUTE MEANS,
STANDARD DEVIATIONS, AND CORRELATION COEFFICIENTS. THIS
SUBROUTINE IS NORMALLY CALLED BEFORE SUBROUTINES ORDER,
MINV AND MULTR IN THE PERFORMANCE OF A POLYNOMIAL
REGRESSION.
USAGE
CALL GDATA (N,M,X,XBAR,STD,D,SUMSQ)
DESCRIPTION OF PARAMETERS
N - NUMBER OF OBSERVATIONS.
M - THE HIGHEST DEGREE POLYNOMIAL TO BE FITTED.
X - INPUT MATRIX (N BY M+1) . WHEN THE SUBROUTINE IS
CALLED, DATA FOR THE INDEPENDENT VARIABLE ARE
STORED IN THE FIRST COLUMN OF MATRIX X, AND DATA FOR
THE DEPENDENT VARIABLE ARE STORED IN THE LAST
COLUMN OF THE MATRIX. UPON RETURNING TO THE
CALLING ROUTINE, GENERATED POWERS OF THE INDEPENDENT
VARIABLE ARE STORED IN COLUMNS 2 THROUGH M.
XBAR - OUTPUT VECTOR OF LENGTH M+1 CONTAINING MEANS OF
INDEPENDENT AND DEPENDENT VARIABLES.
STD - OUTPUT VECTOR OF LENGTH M+1 CONTAINING STANDARD
DEVIATIONS OF INDEPENDENT AND DEPENDENT VARIABLES.
D - OUTPUT MATRIX (ONLY UPPER TRIANGULAR PORTION OF THE
SYMMETRIC MATRIX OF M+1 BY M+1) CONTAINING CORRELA-
TION COEFFICIENTS. (STORAGE MODE OF 1)
SUMSQ - OUTPUT VECTOR OF LENGTH M+1 CONTAINING SUMS OF
PRODUCTS OF DEVIATIONS FROM MEANS OF INDEPENDENT
AND DEPENDENT VARIABLES.
REMARKS
N MUST BE GREATER THAN M+1.
IF M IS EQUAL TO 5 OR GREATER, SINGLE PRECISION MAY NOT BE
SUFFICIENT TO GIVE SATISFACTORY COMPUTATIONAL RESULTS.
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
REFER TO B. OSTLE, 'STATISTICS IN RESEARCH', THE IOWA STATE
COLLEGE PRESS, 1954, CHAPTER 6.