Trailing-Edge
-
PDP-10 Archives
-
decuslib20-02
-
decus/20-0026/multr.doc
There are 2 other files named multr.doc in the archive. Click here to see a list.
SUBROUTINE MULTR
PURPOSE
PERFORM A MULTIPLE LINEAR REGRESSION ANALYSIS FOR A
DEPENDENT VARIABLE AND A SET OF INDEPENDENT VARIABLES. THIS
SUBROUTINE IS NORMALLY USED IN THE PERFORMANCE OF MULTIPLE
AND POLYNOMIAL REGRESSION ANALYSES.
USAGE
CALL MULTR (N,K,XBAR,STD,D,RX,RY,ISAVE,B,SB,T,ANS)
DESCRIPTION OF PARAMETERS
N - NUMBER OF OBSERVATIONS.
K - NUMBER OF INDEPENDENT VARIABLES IN THIS REGRESSION.
XBAR - INPUT VECTOR OF LENGTH M CONTAINING MEANS OF ALL
VARIABLES. M IS NUMBER OF VARIABLES IN OBSERVATIONS.
STD - INPUT VECTOR OF LENGTH M CONTAINING STANDARD DEVI-
ATIONS OF ALL VARIABLES.
D - INPUT VECTOR OF LENGTH M CONTAINING THE DIAGONAL OF
THE MATRIX OF SUMS OF CROSS-PRODUCTS OF DEVIATIONS
FROM MEANS FOR ALL VARIABLES.
RX - INPUT MATRIX (K X K) CONTAINING THE INVERSE OF
INTERCORRELATIONS AMONG INDEPENDENT VARIABLES.
RY - INPUT VECTOR OF LENGTH K CONTAINING INTERCORRELA-
TIONS OF INDEPENDENT VARIABLES WITH DEPENDENT
VARIABLE.
ISAVE - INPUT VECTOR OF LENGTH K+1 CONTAINING SUBSCRIPTS OF
INDEPENDENT VARIABLES IN ASCENDING ORDER. THE
SUBSCRIPT OF THE DEPENDENT VARIABLE IS STORED IN
THE LAST, K+1, POSITION.
B - OUTPUT VECTOR OF LENGTH K CONTAINING REGRESSION
COEFFICIENTS.
SB - OUTPUT VECTOR OF LENGTH K CONTAINING STANDARD
DEVIATIONS OF REGRESSION COEFFICIENTS.
T - OUTPUT VECTOR OF LENGTH K CONTAINING T-VALUES.
ANS - OUTPUT VECTOR OF LENGTH 10 CONTAINING THE FOLLOWING
INFORMATION..
ANS(1) INTERCEPT
ANS(2) MULTIPLE CORRELATION COEFFICIENT
ANS(3) STANDARD ERROR OF ESTIMATE
ANS(4) SUM OF SQUARES ATTRIBUTABLE TO REGRES-
SION (SSAR)
ANS(5) DEGREES OF FREEDOM ASSOCIATED WITH SSAR
ANS(6) MEAN SQUARE OF SSAR
ANS(7) SUM OF SQUARES OF DEVIATIONS FROM REGRES-
SION (SSDR)
ANS(8) DEGREES OF FREEDOM ASSOCIATED WITH SSDR
ANS(9) MEAN SQUARE OF SSDR
ANS(10) F-VALUE
REMARKS
N MUST BE GREATER THAN K+1.
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
THE GAUSS-JORDAN METHOD IS USED IN THE SOLUTION OF THE
NORMAL EQUATIONS. REFER TO W. W. COOLEY AND P. R. LOHNES,
'MULTIVARIATE PROCEDURES FOR THE BEHAVIORAL SCIENCES',
JOHN WILEY AND SONS, 1962, CHAPTER 3, AND B. OSTLE,
'STATISTICS IN RESEARCH', THE IOWA STATE COLLEGE PRESS,
1954, CHAPTER 8.