A MANUAL OF GENERAL
STATISTICAL PROGAMS FOR
THE HONEYWELL 400 COMPUTER
BY
THOMAS A. ENTZMINGER
OHIO RIVER BASIN PROJECT
WORK PAPER No. I
U. S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
CINCINNATI, OHIO
1967
-------
DISCLAIMER
Although these programs were tested by the author
prior to inclusion, no warranty is expressed or implied as to
the accuracy and functioning of these programs and related
program material and no responsibility is assumed by the author
in connection therewith.
-------
FOREWORD
This manual is the result of the authors efforts to generate
and assemble a useful group of general statistical programs for the
Honeywell U00 Computer. Each of the programs in the text has been
used in some area of the Public Health Service or the Federal Water
Pollution Control Administration and each was written at the request
of seme member of one of these agencies.
These programs are written in a compiler language called
AUTOMATH, the Honeywell UOO version of FORTRAN II, and can be adapted
through simple modifications to operate on IBM equipment.
It is the authors hope that these programs may serve as an aid
in stimulating both the use and future development of the more complex
statistical computer programs needed for the solution of problems in
the area of environmental health.
-------
CONTENTS
I AXRSOU Determination of Regression Coefficients
DooLittle Method
II AXRS07 Analysis of Variance - factorial design
with Nesting Option
III AXRSO9 Stepwise Multiple Regression
IV AXRS14 Principal Components Analysis
V AXRS28 Linear Discriminant Function Analysis
VI AXRS33 Multiple Regression
VII AXRS38 Least Squares Curve Fit
VIII AXRS^3 General Correlation Program
IX AXRSi+9 Multivariate Analysis of Variance
X AXRS59 Numerical Integration - Trapezoidal Rule
XI AXRS68 Time Series Analysis - Autocovariance,
Autocorrelation and Power Spectral
Analysis
-------
AXRS04
-------
GENERAL ROUTINE AXRSOU
DETERMINATION OF REGRESSION COEFFICIENTS
DooLittle Method
PURPOSE: To find regression coefficients of a matrix of sums of
squares and cross products.
RESTRICTIONS: l) A maximum of 25 variables (independent plus
dependent) can be treated at a time.
2) The maximum number of dependent variables which
can be processed in any one run is ten.
3) Input to computer is on cards.
ACCURACY; Single precision floating point computations with eight
significant digits.
OPTIONS: 1) The complete square matrix and its vectors or
2) The upper right triangularized portion of a matrix
with its vectors may be submitted. (The program assumes that the
first variables treated are independent and the last variables are
dependent).
INPUT: Data may be punched on cards in any format which can be suitably
described by an Autcmath Format statement. A considerable amount of
running time can be saved by arranging the data so that they are
treated by the READ statement in this manner (a) one observation of
each variable in every read cycle (b) observations of all independent
variables should proceed observations of dependent variables in the
same read cycle. Standard card format is seven fields of 10 digits
each; the last 10 digits may be used for identification.
-------
CARD DECK SETUP;
1. Program Source Deck - complete with modified FORMAT statement
(statement #1001).
2. Name Card - Describes run - uses card columns 2-80.
3. Parameter Card - Gives total number of variables (dependent
plus independent) in card columns 1 and 2, the number of dependent
variables only in card columns 11 and 12, number of degrees of
freedom in card columns 21-2U and matrix configuration in card column
31 (1 = square matrix, 0 = right triangular portion of matrix).
U. Mean for each variable (7F10.5)«
5. Total sum of squares for each dependent variable (7F10.5).
6. Data cards with FINIS.
OUTPUT: The following printout is presented for each dependent variable
in the problem: Degrees of freedom - Total sums of squares - Sums of
squares for error - Mean squares for error - Regression sums of squares -
Multiple correlation coefficient (R2) - Each regression coefficient
with standard error - Student's T - Constant regression term - Inverse
matrix solution.
-------
DESCRIPTION &
PROGRAM LISTING
-------
ccmptlEx
TTTLEAXRS04
c determination of regression coefficients
c dcoltttle method
DIMENSION X(25)» A1(325)*R(32 ?1iRFGSS(10)«X0<25)*AVg(25>«AV(26)~
1DIAG(25)«D(2S,25)*C(25»2S)
DIMENSION TSSdO)
C READ SQUARE MATRIX INTO C '4SORsl
C READ TRIANG MATRIX INTO AL MSQR=0
111 PEAD1000.NCI~ND,IDF,M5QR
IF END of FILE 33*3
3 NCsNCI
READ1002*
-------
DO 8lsNl,NC
Aim=Al(I)-Al(K2)*B
-------
JsMC-NN
DC50NFal,NK
D049Nsl,NM
C(I»J)sC{I»J)"D(I»K)#C(KtJ)
1=1-1
K = K-1
N0»N0*1
50 I=NC-NN
NN=NN+1
NMsNM-1
IF(NM)55,55,53
53 NR=NX-NK
D052KKsl,NR
K = iMC-N0
IsNC-NN
DC51Nsl,NM
C
-------
15 NCsNO-NZ
NZ»2
L»NJ-1
MA«3
00 lajoi.L
N0»NC-NA
NC»N0
9 N1®N1~1
DO 16I"N1«NJ
X-«CN0>*X(N1-1)
13 NZsNZ+I
16 NOsNO-NZ
17 NA»NA+1
19 M=M-1
18 NZ=NZ-M
LKsNJ
DC 20 Ial,NJ
XC(I)=X(LK)
20 LKsLK-1
22 11*IT~1
DF*IDF
NCT=NCI-ND+1
nxx=nci-nd
CONST=AV(NCT)
DO 62 1=1,NXX
62 C0NST=C0N5T-X0
RSQR=REGS5(KK)/TSS
SSE=T5S(KK)-REGS5
EMS=SSE/DF
PR TNT 1776,KK
1776 FORMAT(1H1/50B»19HDEPENDENT VARIABLE 12)
PRINT 1777 »IDF»TS5(KK)•5SE»Ems,RfG55C/ //////)
1788 FORMAT(1H /10B»11H CONSTANT sE17,9////)
1888 F0RMaT(1H / 13B ~ 1HB , 17B , lOHREGRfcSSlON 18"3 ,
114HSTANDARD ERROR18B~1OHSTUDENT5 T/
2 309,1IhCOEFFICIENT///)
18 89 F0RMAT(133»I2,3(159,E15.8)//)
PRINT 1666
1666 FORMAT(1H1/68H INVERSE
1 MATRIX SOLUTION////)
no 66Jsl,NXX
66 PRINT 801 ~ (C(I*J)~1 = 1,NXX)
GO TO 111
33 TYPE ,2000
STOP
800 FORMAT(12*13*12)
-------
801 FORMAT(1B«7E17.9)
1000 FORMAT (l2t8Bfl2«8Btl4f6B«Il)
1001 FORMAT(7F10.5)
1002 FORMAT(7F10«5)
2000 FORMAT(8M JOB END)
END
END
J09EMD
-------
SAMPLE
INPUT & OUTPUT
-------
INPUT TEST DATA
TEST doolittle method
06 01 77 1
95.987
166987778 066826433-125134720 000^00000 000000000-1299*1662
066826433 241148995-047857129 066*26433-073171280-304462385
-125134720.047857129 137651808 000000000 000000000 116804144
000000000 066826433 000000000 074161217-158523880-174520723
000000000-073171280 000000000-158523880 498759156 479101401
FINIS
-------
DF TSS SSE
7700 0.95987000E 02 -0,12604857E 0*
DEPENDENT VARIABLE 1
MSE 55R
-0,16369944E 00 0.13564727E 04
R SQUARE
0,14131837E 02
1
2
3
4
5
CONSTANT =
REGRESSION
COEFFICIENT
~0«68568214E 00
-0.34524596E 00
-0.60977730E-01
-0.62409480E 00
-0.2909I332E 00
O.OOOOOOOOOE 00
STANDARD ERROR
O.OOOOOOOOE 00
O.OOOOOOOOE 00
0«26478724E"0Z
0.29642471E-01
0.29642471E»01
STUDENTS T
O.OOOOOOOOE 00
O.OOOOOOOOE 00
-?0.23028954E 02
-0.21054075E 02
-0.98140712E 01
-------
INVERSE MATRIX SOLUTION
0.598846222E-03
-0.998389149E-03
-0.IS6626189E-03
0.437824956E-04
0,155949461F-04
-0«998389149E-03
0,249480300E-02
0.311181&58E-03
-0.140021430E-02
0.169152335E-03
-0.156626189E-03
0.31 U81558E-03
-0.428298861E-04
-0.6893385A2E-03
0.111144314E-03
0.437824956E-04
-0tl40021430E-02
-0.68933854^E-03
-0.536761818E-02
0.109832193E-02
0.155949461E-04
0.169152335E-03
0.11U44314E-03
0.109832193E-02
0.200731841F-03
-------
AXRS07
-------
GENERAL ROUTINE AXKSOY
ANALYSIS OF VARIANCE
FACTORIAL DESIGN V.'ITH NESTING OPTION
PURPOSE: Analysis of variance for a factorial design
METHOD: Least squares estimates
RESTRICTIONS: l) There are no missing values
2) Maximum of 1000 words of data (observation)
3) Input to computer on cards - data punched one
observation per card. This can be modified by changing format state-
ment s in the program.
ACCURACY: Single precision floating point computations truncated to
eight significant digits.
TRANSFORMATIONS: There are two transformations available - log and square
root - others can be easily inserted upon recompilation of the program.
INPUT:
CARD DECK SETUP:
1. Execute card
2. Binary Decks
3• Jobend card
4. Control card
5• Data deck
6. Finis card
Control Card Format
Beginning in Card Column
1
5
Punch
No. of Observations
Levels of Factor A
-------
Control Card Format (cont1d)
Beginning in Card Column Punch
7
Levels of Factor B
9
Levels of Factor C
11
Levels of Factor D
13
Levels of Factor E
15
Computational codes
Transform Number
k6
Run Identification (9
IF the number of factors in a problem is fever than 5) punch 1 for the
number of levels for each unused factor.
COMPUTATIONAL CODES Result
3 Means and sums of squares are calculated
2 Sum of squares is calculated
1 Neither means nor sum of squares is calculated
COMPUTATIONAL CODE ORDER
Card Column Card Column
1. A
15
13. CD
27
2. B
16
1^. CE
28
3- C
17
15. DE
29
k. D
10
16. ABC
30
5- E
19
17. ABD
31
6. AB
20
18. ABE
32
7- AC
21
19. ACD
33
8- AD
22
20. ACE
3^
9- AE
23
21. ADE
35
10. BC
2k
22. BCD
36
11. BD
25
23. BCE
37
12. BE
26
2k. BDE
38
-------
COMPUTATIONAL CODE ORDER
(cont'd)
Card Column
Card Column
25. CDE
39
28. ABDE b2
26. ABCD
29. ACDE 1+3
27. ABCE Ul
30. BCDE
TRANSFORM CODE:
Result
1
Linear
2
Logs of data are taken before computation
3
Square roots of data are taken before computation
DATA CARDS?
1. Observations are ordered with leftmost factor (A) varying most
frequently.
2. Punch one or more words per card depending on format statement in
main program deck - (generally set to handle one word per card).
OUTPUT:
1. Complete listing of transformed data by row.
2. Grand Average.
3. Identification number and averages for each combination with Code 3.
U. Each line includes the identification number, number of observations
per sum, degrees of freedom*, sum of squares*, degrees of freedom**,
sum of squares**, for each combination with code 2 or 3. Identification
numbers 31> 32, and 33 do not require code 2 or 3 request.
*The degrees of freedom and associated sum of squares are adjusted
only for the grand mean.
**The degrees of freedom and associated sun of squares adjusted for
each interaction and the grand mean*
-------
Internal work order and output identification number are:
Identification Number Combination Identification Number Combination
1
A
IT
BCD
2
AB
18
C
3
ABC
19
CD
k
ABCD
20
D
5
BCDE
21
AC
6
CDE
22
ACD
7
DE
23
AD
8
E
2b
ABD
9
ACDE
25
BE
10
ADE
26
CE
11
AE
27
BDE
12
ABDE
28
BOB
13
ABE
29
BD
1^
ABCE
30
ACE
15
B
31
Adjusted Total
16
BC
32
Correction Term
33
Unadjusted Total
For problems with fewer than five variables duplication of computing may
be avoided by using Code 1 for the highest order combination in the problem.
Code 1 should additionally be used for all combinations which would have
no meaning.
-------
DESCRIPTION &
PROGRAM LISTING
-------
^'EWSTACK
COPTi ES
SUBROUTINE PRAMOv
C CCRRFCT ANO PrfTNT SU^ SC'lAPE* AM0 DE'RFES OF FPEEOOw IN ANr)V A
PI^E^STOM 55(33),NO(5) »^S(33) ,W(33),Z(33>•AS(33),M(33)»A2(33)
^ I ^F^IST Cfct CODE ( 33 )
COMMON SS,'!C «'MPS» "IDF ~ CODE
OC3l=l ,33
3 AS (I)= SS(1)
ASSIGN 11 TO ) -BCO-riCE-BPfc-C^E-er-RD-C^-RE-CE-DE-R-C-D-F
APCDE = As(il)-APCF-A«Dt-ACDE-HC0E-CnE-8nE-RCt-
lACF-ACE-ABF-DE-CP-t5E-AE-ABCD-3CD-ArC)-APD-
2CD-BD-Ap-ABC-riC-AC-A3-A-fl-C-0-E
40 2 (1 )s A
7(2)=AB
7(3)=APC
7(4)sABCH
7(5)rrtCDE
7(6)=COE
Z (7)=r3E
7 ( 9 ) s E
7(O)sACDF
-------
11
10
7(10)= ADF
7 ttn bae
7(t2)=AB0E
7(;3)=apr
7(14>=ASCE
7(15)=*
7(16)sf»C
7(17)=RCD
7(18)sC
7M 19) =CD
7 <201 =r>
7(21)=AC
7(22J=AC^
7(23)=4D
7(24)=ARO
Z(25)sRE
7. (26) = CE
7 (2 7)sBCF
7(28)sRDE
7(29)=^0
Z(30)= ACE
7(31)sARCOr
7(32)sSS(32)
7(33)= SS(33)
rc TO »NDF(3l> * S M 31) »M ( 31) «A 2 (31)
PRINT 2401 , (MPS (3?) »NQF(3?) »SM?2) »"(32) *A2(32)
PR TNT 2402, «\PS (33) «NDF<33> • SS ( 33 ) ~'1 ( 33) »A2 ( 33)
2400 FORMAT ( 8X1SHAUjUSTED TOTAL 1?BI 3»I?BI 3~F17.7,6XI 3«F17,7)
2401 FORMAT (7X16HCQ3RFCTI0IM TERM 1 2X I 3 • 1 2X I 3 ~ F 1 7 . 7 »6X \ 3 t F1 7 . 7)
2402 PCBMAT(6X17HUNADJUSTF0 TnTAL 1?XT3,12XI3~F17.7~6X13~F17.7)
dETUPN
2009 FCDMAT(1M1/93H
1 CF SUM OF DEGREES Oc SUM OF/
2Q4h SOURCE OF V«P!ATI°M OBSERVATIONS FREEDOM
31JARES FRFEDOv SQlJAPES///^
2000 FORMAT (l4t3A8,12BI3*12B,T3»F17.7,*,3T3»Fl7.7)
FNO
FN T
JC?END
rC^PTlFX
T I TLEAXRS07
rCMMCN S5»"C»NPS ~CODE
WJMRER OF
DEGREES
S3
-------
C . FACTORIAL ANALYSTS Or \Z*PT'V,|CF,
C MAXT'vU^ FTVr FACTORS.
CI MEMS TOM SS(33)»MO(5) ~ NSER^O)
rs I MEM'S TON V (1000) »NPS (33) »MD* (331
nivEMSTOM TITLE(IO),C0DE(3B)
Pt AD <*400»CC?E
4400 FORMAT(20A4)
301 PEAD 4002.TITLF
<~002 FCRMATU0A8)
tf end of file 333*208
333 TY"E.2001
STOP
208 PEAD?005»M»NC(1) ~ MO(2)»N0(3) »ND(4) ,N0(?) •
lNSPR(l) »NSERC15) •MSER (IS) «NSP!?(
1?0) ,WSFP(8) »\'SFR(2) »MSER(2l) ~MSE°(23) »M5ER(ll> »
2M5ER(16)»NSER(29)~MSER(25)«NSEP(19)»NSFR(26)*
3MSER(7)«MSrR(3).MSER(24)•NSE"(13)»MSERf22)«
4MSER(30)«NSER(10)*MSER(17)»NSE9(27)»MSFR(28)»
5^SFR(6) *NSrR
6.NTRAM
209 HO 215 T = 1 * 33
MPS (!)=0
^CF (T1=0
215 SS(I)=0.
FNsN
suv=p.
nc 203 lsl,N
READ2006,X(I)
303 r,c. TP (203,307*306)«MTRAM
30^ X (I)=LOGF(X(I))*.434294481
r^C TO 203
306 X ( T)=SORTF(X(I))
203 SU'V = SU,J, + X ( T )
PRINT 2SS5.TITLE
255*5 FORMAT(IH1/64H FACTORIAL ANALYSIS
1 OF \/ARIA-NCE///10Afl//53H PR
2 0 G R A m TNPUT//)
2005 FORMAT(I4t5l2»?lT1)
PRINT2010*(X(I)*T=1*N>
2010 FORMAT(10F12.5)
PRINT 4003
4003 FORMAT(54H PROGRAM OUTPUT/)
PAVG=SUM/FN
229 PRIMT2002»GAVG
230 SS (32) sSUM*GAVrn
MPS(32)SN
MCF(32)=1
MDF(31)=N-1
MPS(33)=1
MDF(33)= M
f^C 204 1 = 1 ,N
X(T)= X(T)-W,
204 SS(3l)=SS(31)*X(n*X(I)
SS(33)=5S(32>*S5(3l)
C SETUP LOOPS FOR A«A^ , ABC»AflCD.
-------
JUMP=I
lOL'Tal
TBAC<=1
T 2 = 1
T 3=1
JAHDsNI-1
JP5 = N
DC 1 l\IS=l,4
T2si?*mo
-------
MPS (MS) =.)PS
«C TO 12
in CCN'TTNUE
C 5F.TI.JP LOOPS FOR Anop,A«E.
! BACK a T BACK~1
1CLJT = T OUT + 1
K3=Ne<1)#NO(2)
JA0D=K3-1
T3 = K3
JP5=1
OC 13 NS=12 »1 3
JP5=JPS*NOr NS-^)
T 3= T 3#MO(N5"9)
MTESTsNSERtNS)
GO TO(13 »14 » 3) ,i\1TEST
14 KADDsI3-1
MPS (NS)sJPS
GC TO 12
13 CONTINUE
C SETUP FOR ARCF.
I ClJTa T OUT + 1
tback=iback+i
KJ 5 a 14
MTESTaMSER(14)
GC TO (15~16 ~ 3)»NTEST
1* T3sN/N0(5)
KADO = T 3-1
K3 = 13/NO(4)
• JADD = K3-1
JP5sNO<4>
PS (14)ajPS
C SUWATTON LOOPS FOR ACDE »AOF « AE • ARDE ~ *3F , ARCE •
12 DC 17 T=1»M»I3
j2= T~JADD
no 17 J=r»J2
SUMbO.
K2=J+kADD
DC IP K=J.K2»K3
1« SUMaSUM+X(K)
GC TO 101
1^ ccnttnije
GC TO(10,13*15),I BACK
C SETUP LOOPS FOR B,8C,*CD.
15 tback=i
jump=jljmp+i
T CIJT= I OUT ~ I
JPSaN
I3sN0(1)
!2sN0(1)
KA[)D= T 3-1
DC 1<9 MS=15»17
JPS=JPS/mO(NS-13)
T2 = I2#N0(N5-13)
NTESTsMSFR
-------
20 VP5sjPS
GC TP 21
19 continue
C St TUP LOOPS FOR c,cn.
I BACK= IBACK +1.
lOUTsI0UT+1
JPS = N
I3=N0(1)*N0(2)
I 2= T 3
KADD= T 3-1
DC 22 MS=1P*19
JPS=JPS/M0(N5-15)
T2sI2#N0(NS-15)
NTESTsNSER(NS)
GC T0(22,23,3) ,,NTEST
23 flPS (MS) =JPS
GO TO 21
22 CONTINUE
C SETUP FOR D.
tback=tback*i
ICUTsI OUT + 1
\'S = 2P
NTFSTsMSFR(20)
GO T0(2
-------
GO TO(28«29»3),NTEST
29 MPS(NS)=JP5
<3=12
GO TO 30
28 CONTINUE
C SETUP FOR AD,A0O.
ibac<=ipack+i
TOUTbIOUT+1
I3=N0(1)*N0(2)*NC(3)
I 2s J 3#N0(4)
K 3= I 2
J3s 1
KAD0=N-1
LADD=T3-1
13=1
JPS=N/N0<4)
DO 31 MS=23»24
L3=L3#N0(NS-22)
JPSaJP5/N0(NS-?2)
NTEST=NSEH(NS)
GO TO(31«32 « 3)»NTE5T
32 NPS(NS)=JP5
JADD = L.3-1
GO TO 30
31 CONTINUE
C SETUP FOR BE.CE.
TBACKslBACK*l
I0UT=T0UT*1
12r N
I3 = N/N0C5)
L3= 1
*N0<4)
DO 33 NSs25*26
K3=K3*N0(N5-23)
J3=J3*N0(N5«24)
NTESTsNSER(NS)
GO T0(34»35»3> »NTEST
35 NP5(NS)=JPS
JADD=K3-l
LADDsJ3-1
GO TO 30
3^ JP5sN0(1)»N0(2)#N0U)
33 CONTINUE
C SETUP FOR BCE.BDE,
IBACK=IBACK+1
T0UT=T0UT*1
I2sN
J 3 = NO(1)
LAD0SJ3-1
L3«l
K3«N0(1)
I3sN0(1)*N0(2)
-------
JP5=MO(1)*NO(3)
DC 36 NS=27~ 28
13= 13*N0 (N5—2<~)
K3s<3*M0(N5"25)
NTESTsNSEK(NS)
GO T0(37*3B«3),NTE5T
38 NP5(NS)=JPS
JADD=K3-1
KADD=T3-1
GO TO 30
37 JPS=N0(1)*M0(4)
36 CONTINUE
GO TO 41
C SUMMATION LOOPS FOR AC»ACD«ADtAR0,3F»CE«BCE»^^E.
30 DO 39 I = 1 ~ 12»I 3
J2si~jADD
DO 39 Jsl~j2»J3
SUMsO.
K2sj*kADD
DO 40 <=JiK2»K3
L2=K+lADD
DO 40 L=<*L2»L3
40 SUM = SUM*X(|_>
GO TO 101
39 CONTINUE
GO T0<28«31»34»37)»IBACK
C SETUP AND SUMMATION FOR BD.
41 JUMPsjUMP+1
lOtJT=IOUT*l
NS=29
NTESTsNSER(29)
GO TO(42 »43»3)»NTEST
43 j3sN0<1)
L3sN0(1)*N0(2)
I3=L3#N0(3)
12*13#N0(4)
JADDSL3-1
LADD=T3-1
MADD=J3-1
NPS(29)sNO(1)*N0(3)*N0(5)
jPSsNPS(29)
DO 44 181,12,13
J2sI~jADD
DO 44 Js I • J2 » J3
SUMsO.
DO 45 K=J»N»T2
I_2sK + L ADD
DO 45 L=K»L2»L3
M2sl+MADD
DO 45 Vsl»«2
45 SUMsSUM+X(M)
GO TO 101
44 CONTINUE
C SETUP AND SUMMATION FOR ACE,
42 TOUT= TOUT+1
-------
JUMPsJUMP*1
NSa30
NTESTbNSEROO)
GO T0<46,47»3),NTEST
47 M3sN0(l)
j3«N0(1)#N0(2)
L3»J3#N0(3)
I3«L3«N0(4)
JADDsl3-1
KADD=M3-l
LADDbT3-1
MAODsJ3-1
NPS(30)sN0(2)*N0(4)
JP5sNPS(30)
DO 48 Ib1»N»!3
j2cI~JADD
DO 48 JsJ,J2,J3
K2xj*kADD
DO 48 KbJ«<2
SUMsO.
L2»K*LADD
DO 49 L*K*L2«L3
M2sl+MADD
DO 49 M»L«M2,M3
49 5UMs5UM*X(M)
60 TO 101
48 CONTINUE
46 CONTINUE
DO 95 I«1,30
IF (NPS(I))95,95,96
96 NDF(I)cN/NPS(I)-1
95 CONTINUE
CALL PRANOV
SO TO 301
C COMPUTE AVERAGES AND SUMS OF SQUARES,
101 REClPsJPS
REClPsl./REClP
AVGsSUM#RECIP
SS(N5)aSS(^5)~5UW*AvQ
GO TO (102,102,103),NTE5T
103 AVGsAVG*GAVG
105 PRINT2032»AVG
102 GO T0(8,17,26,39,44,48>,JUMP
C IDENTIFY AVERAGES BY CODE NUMBER.
3 PRINT 2003, CODE(NS)
IF{IOUT-9)106*106,107
106 GO T0(2»6«ll»l4,l6.20,23,25t29),IOUT
107 IOUT2slOUT-9
GO TO(32,35*38,43,47),I0UT2
2000 FORMAT(3I10»F16§5)
2001 FORMAT(8HJ0B END)
2002 FORMAT(5X11H GRAND MEAN/F16.5)
2003 FORMAT(4XA8)
2006 FORMAT(Fl2,5)
2032 FORMAT(F16»5)
END
END
OVERLAY
STACKPRANOV
JOB END
-------
SAMPLE
INPUT & OUTPUT
-------
tnpjt test data
A AB ABCABCDBCDe COE DE EACPE *DE AeABDe ABeABCE B BC BCD C CD D
ac acd ad abd be ce bde bce ace
TEST PROBLEM 6-8
006002050302013333133313313H3313113111311111
122.
110.
108.
85.
108.
60.
66*
50*
80.
60.
332.
330.
276.
310.
248.
295.
248.
275.
276.
310.
640.
500.
612.
500.
543.
450.
612.
610.
696.
610.
192.
170.
136.
130.
-------
122.
85*
108.
75.
136*
73.
386.
363.
333.
330.
318.
330.
472.
330.
499.
390.
810.
725.
779.
670.
810.
750.
893.
890.
1820*
890.
FINIS
CARDS 572
-------
FArTIRIAl AV-LYSIS OF VARIANCE
r ST ^CILFM h-tf
PRnQPAu I MPJT
122.OOC00
3^2.mcoo
b^o.oncon
192.00000
396.O0C0O
sio.occoo
no.o^ooo
330.00000
500.00000
170.00000
365.00000
725.0^000
lOB.onooo
276,00000
612.00000
i36.ocooo
333.00000
7?9.0.">000
«5.CO0O0
310.00010
5)00.00000
130.00000
330.00000
670.00000
PROGl?A^ i
LOS.00000
2^8.O0O0O
543.00000
122.00000
318.00000
810.00000
PRANO VFftN
392.68333
A
426.03333
359.33333
AB
*13.66667
366.66667
3T*,00000
337.50000
358.16667
328.3333?
399.83333
375.00000
584.50000
389.16667
ABC
157.00000
14C.00000
122.00000
107.50000
116.00000
72.50000
87.00000
*>2.50000
108.00000
67.50000
359.00000
347.5000C
304.500CC
32C.0000C
283.00000
312.500C0
36C.OOOOC
312.500CC
3P7.5P0C^
350.00000
r?D.ooooo
tl2.50000
b*> 5.50^00
60.00000
295.00000
450.00000
n5.00000
330.00000
750.00000
66.00000
248.00000
612.00000
108.00000
472.00000
893.00000
50.00000
275.00000
610.00000
75.00000
350.00000
890.00000
&0.00000
276.00000
696.00000
136.00000
499.00000
1820.00000
60.00000
310.00000
610.00000
75*00000
390.00000
890.00000
-------
5^5.00000
676.50000
60C.00000
7*52.50000
750.00000
1258.00001"
7*0.00000
abcd
122.00000
lie.ooooo
108.00000
S5.00000
108.00000
fO.OOOCO
66 .00000
50.00000
AC.OOOOO
6C.OOOOO
332 .OOOOO
330.00000
276.00000
310.00000
248.00000
205.OOOOO
248.00000
275.00000
276.00000
3-10.00000
640.0^000
500.00000
612.00000
500.00000
543.00000
4*50.00000
612.00000
61C.OOOOO
606.OOOOO
610.00000
192.00000
170.00000
136.00000
no.ooooo
122.00000
85.00000
108,00000
75.00000
136.00000
75.00000
3A6.OOOOO
365.00000
333.00000
330.00000
318.00000
330.00000
472.00000
350.00000
-------
499.0OO00
3PC.00000
H1C.00000
7?5,00000
779.00000
670.00000
tilO.00000
750.00000
893.00000
890.00000
lB?C,00000
boo . ooooo
b
390.16667
355.75000
343,25000
3P7.41667
4P6, 83333
1*8.50000
114,750°0
93.75000
74.75000
*7,75000
353.25000
312.25000
297,75000
336.25000
368.75000
666.750n0
640.25000
638.25000
751.25000
1004.00000
BCD
116.00000
96.50000
e4.OOOOO
58.00000
70.00000
331.00000
293,00000
271.50000
261.50000
203,00000
570.00000
556.00000
406.50000
6] 1 .00000
653.00000
181.00000
133.00000
103.50000
91.50000
105.50000
375,50000
-------
3*1
3?4
41 1
/6 7
7?A
rpc
501
] 3S£>
c
•> r -
w • • ./
3?3
7AC
c:;
«<~
b
fl>
3^1
303
J??C
<+1 5
a r* f
36^
313
3^2
2 qfi
2«jy
268
308
50000
ncn^'"
nonoo
5nnnn
5or,^
5 0 0 C '*
nno^n
5onor
000 no
:jOO0(.
6t>C'00
50000
<30000
OOOOO
ROOOO
50000
500n0
50(J0n
80000
0000O
OOOOO
OOOOO
60oor
ooooo
ROCOO
OOOOO
60000
OOOOO
<*ooor
oooro
13333
6666 7
9333?
OOOOO
66667
3333?
OOOOO
33333
66667
33333
66667
-------
311.66667
3*C,66667
3?6#66667
<~62.66667
«?c,ooooo
Mfc.OOOOC
376,6666 7
M6.66667
3A8.3333*
<~01 .oonoo
W.3333?
81e. 33333
1 ,6666 7
C'L>
339.00000
31S.16667
28<*.OOOCO
3 K. 16667
338.66667
^41.33333
396.33333
*02.500^0
^64 .66667
fc 35.0000^
-------
"'UML' F ^ OF
fCL^CF HP T TOM nns£.0-*/^TI Jw5
dfgrffs of sum or degrees of sjm of
FPE'EPOM 5QuAr«FS FREEDOM S^lKRES
A
30
1
66733.3499700
1
66733.3499700
A :j
*
9
282081,4832000
4
6287^,9003000
* ec
?
29
4862948,4680000
8
99749.6910000
ARC 3
1
59
5f.33]80, 9560000
8
^790«.2305000
*
J
12
4
1«?2472.2330000
4
152472,2330000
nQ
4
14
4564708.2250000
8
255092,3700000
nro
?
29
53*380*,468^000
8
112 781,5585000
c
20
2
4157143.6220000
2
4157143.6220000
CD
10
5
473515^.8740000
2
237954.4355000
D
3°
1
340054.8165000
1
34005*.8165000
AC
in
5
4292758.2740000
2
68881 #3030000
Art)
«?
U
4906609,7750000
2
12751.4335000
AfJ
15
3
429876.9H33000
1
23088.8169000
3
19
800916.316^000
4
67:87.7669000
rr,
A
9
580830.4(126000
4
88303.4331000
AlijU^TF Tr.TftL
0
'*) 9
5833180,9560000
51
574^272.7640000
C^i-RECTT^' TERM
*9
1
9252012.0150000
012
92520 12.0150000
< i a f' J LJ S T r*r% TOTAL
1
6 0
150°519?.9700000
192
15085192.9700000
-------
AXRS09
-------
GENERAL ROUTINE AXRS09
STEPWISE MULTIPLE REGRESSION
PURPOSE; To obtain the "best fit of a set of observations of independent
and dependent variables by an equation of the form
Y = bQ + + bgX2 + + bnxR where Y is the dependent
variable x-^ x^ are the independent variables; and
are the coefficients to be determined.
This program computes a sequence of multiple linear regression
equations in a stepwise manner. At each step one variable is added
to the regression equation. The variable added is the one which
makes the greatest reduction in the error sum of squares. Eauiv-
alently it is the variable which has highest partial correlation
with the dependent variable partialed on the variables which have
already been added; and equivalently it is the variable which if
it were added would have the highest F value. Variables can be
added to the regression equation and automatically removed when
their F values become too low. Regression equations with or
without the regression intercept may be selected.
RESTRICTIONS; l) A maximum of 30 variables (independent plus
dependent) can be treated in each run.
2) Input to computer is on cards
ACCURACY: Single precision floating point computations with eight
significant digits.
-------
-2-
OPTIQNS: Transformation of any variable can be made by inserting
the proper automath statements between the two transform
comment cards in the source program deck (i.e., X(l) = LOGF X(l)
or X(6) = SQRTF (X(6)) or X(l3) = A + B * X(l3) where A and B
have been defined on preceding transform cards.
INPUT: Data may be punched on cards in any format which can be
suitably described by the Automath Format statement. The
standard card format is seven fields of ten. digits each; the
last 10 digits may be used for identification.
CARD DECK SETUP:
1. Compilex card
2. Program source deck - complete with modified Format statement
(#1001), Transform Statements, overlay card, Binary Subroutine
Decks and Jobend card.
3- Name Card - describes run-uses card columns 2-80
4. Control card
Parameter Card Column
No. of variables (NCl) (Max 30) 1-2
1 + degrees of freedom for error
for matrix calculated from Residual SS-
otherwise use the count (DEFR) observations 3-6
Tolerance - usually .001 (TOL) 7-12
F - Level for entering a variable (EFIN) 13-18
F - Level for dropping a variable EFOUT 19-24
maybe F-level for entering
-------
-3-
5- Data - Cards punched in most any form can be
handled by this program (several variables per
card or one per card) and is described by a
FORMAT statement included in the program source
deck.
6. Finis card
7. Repeat steps 3-6 for each additional run.
8. FINIS card
*Note: When generating additional variables (transforms)
allow for reading them in the FORMAT statement.
-------
DESCRIPTION &
PROGRAM LISTING
-------
NEWSTACK
COMPILES
SUBROUTINE C0RR3
COMMON A1.5S.AVG.HCI
COMMON DFFP»T0L.EFTN,EF0UT|AM
DIMENSION Al(465)•AyG(30)*SS(30)iR(465)
C COMPUTATION of correlation matrix
PPTNT1222
ttC=NCI
NCOsNC
K = 1
MCA sO
ru = i
NEsl
DC 456 L=1,NC
DO 454 IsNl,Ncn
»I=NL»NN)
HO 7 JbNIiNN
7 A1 CJ)=P I J)
Ml=NN*l
NN=NN*NCJ-NE
6 NE = NF>1
RFTUBN
1990 FORMAT (5M POW 12)
2000 FORMAT(1Ri7E17»9//)
122? FORMAT (1HI/79H MATRIX OF SIMP
1LE CORRELATION COEFFICIENTS////)
END
END
JCF1END
COMPILES
SUBROUTINE STEP
CCMM0N Al,SStAVG»NCl
COMMON DEFR»TOL.EFIN,EFOMT,Am
DIMENSI0N A1(465)«AvG(30)»S5(30)» A130*30)% INDEX(30)*CoEFN<30)»
1S I1
DC4Ia 1,NC
-------
0C4JsI,NC
27 KKsKK*1
A(I * J)sAl(KK)
4 A(J*I)=A(I»J)
DEFHbDEFP-UO
NCVMJ=NC-1
noent=o
NSTEPs-l
1000 NSTEP«NSTEP*1
SIGy = S0RTF(A(NC»NC1/^EFR)#SS(.MC)
DECR=DEFP-1.0
IF(DFFP)1017»1017.1020
c OUTPUT Nn.l.DEGREES OF FREEDOM reduced to ZERO
1017 PRTNT100,NSTEP»DFFR
GO TO 1580
1020 VWTNsO.O
VMAXsO.O
NOTNsO
D01050I=1»N0VMI
IF(AII»I))1042«1050.1060
C OUTPUT NQ.2.R(I«I) IS NEGATIVE MAJOR DIAGONAL
1042 PRINT200»NSTEP*1
GO TO 1580
1060 TF (A (I , D-TCL) 105 0»1050»10R0
1080 VAP=A(T,NC)*A(NC»I)/A(I,n
IF(VAR)1100»1050»1110
1100 NOINsNOIM+1
INDEX(M 0 T N)si
CCEFM(MOIN)sA(I.NC)*SS(Nr)/Sc (I)
5l^CO(NOlN)=SQRTF(A(i,i) > *S I r-Y/SS (I)
IF(VMIN) 1 lfeO »1170 «904
C OUTPUT N0.3.VMIN IS POSITIvE.PROG RESETS
904 PR INT300 »VMIN
RETURN
1170 VMNsVAR
nomin=i
GO TO 1050
1160 IF(VAR-VMlN)1050«1050,1170
1110 IF(VAR-VMAX)1050»1050*1210
1210 VMXsVAR
N0VAXs T
1050 CONTINUE
IF (N0TM)903»124Q,125°
C FRROR-NOTN IS NEGATIVE
903 RETURN
C OUTPUT.5.STANDARD DEVIATION of y
1240 PPINT400 , SIGY
GO TO 1350
1250 CNSTsAVG (
-------
C K»FLEVL,S.D.OF Y»C0NSTANT,i-t?2
1311 PPINT500,NSTEP«K
60 TO 20
C OUTPUT.7. VARIABLE K ENTERED, PRTNT 6
1313 PRINT500,NSTEP»K
20 PRTNT600»FLEVL»STGr,CN5T»A(rjr,fl|C)
DC*J*1.NOIN
9 PPINT700iINDEX »COEFN(J)»SI3C0(J)
GC TO H 320»1580),M
1320 FLEVL sVMIN*OEFR/A(NC»NC)
IF (EFOLJT*FlEvl) 1350,1350,134ft
13*0 K=MOMIN
MCFNTsO
GC TO 1301
1350 FLEVL sVMAX *DEFR/(A(NC»NC)~V^AX)
TF(EFIN-FLEVL J 1370, 1370, 1380
1370 KsMQMftX
NCENT»K
1391 IF(<)1392,1392,1400
1392 PRINT500,N5TEP»K
RETURN
i400 DCU 101 = 1 »IVC
IF ( I-K)1430,1410,1430
1430 DC 1440Js1, NC
TF[J-K)1460,1440,1460
1460 A(T,J)sA(I,J)-A(I,K)*A(K,J)/i(l<,<)
1440 MC*NC
1410 NCsNC
0C1480T=l,NC
IF 1540*1520,1540
1540 AU»J)bA(K,J)/A(KiK)
1520 CONTINUE
A
RETURN
100 FCRMAT(IB•12,£17.9)
101 FCRMAT(8R»t2,15B»E16.9)
102 FGRMAT(27H DIAGONAL ELE^ENT5//34r| VAp.NO.
I VALUE//)
200 FCPMAT(1R,I2,38,I3)
300 FCRMAT tlB,El7.9)
400 FORMAT (30H STANDARD F3P0P OF Y s£l6.9)
500 FCP^AT(17H STEP NO. H/29W VARIABLE ENTERING 12)
600 FORMAT (21H F LEVFL E16.9/30H STANDARD FRROR OF
1 Y =F16.9/22H CONSTANT E16.9/15H CORR s£l6.9/)
700 FCRMAT(8PH VARIABLE COEFFICIENT
-------
1 STD ERROR OF COEFFICIENT/33H
2X- I2*9B«E16,9«98*E16.9)
900 FORMAT (IB 2)
FND
END
JOBEND
compilEx
TITLEAXRS09
C STEP WISE MULTIPLE REGRESSION
COMMON A1,SS»AVG,NCI
COMMON defr,tol»efin»efout*am
dimension title CIO)
DIMENSION A1(465)»AvG(30),SS(30)»X<30)
100 REWIND 6
PRINT 2003
2003 FORMAT(1M1)
READ 2002»TITLE
PRlNT2002tTITLE
2002 FORMAT(10A8)
C COMPUTATION OF CORRELATION MATRIX
READ 1000*NCI.DEFR»T0L»EFIN»FF0JT
1000 FCRMAT(I2«F4.0»3F6.3)
1001 FORMAT
PRINT 2010
2010 FORMAT(1W0///60H
1 MEANS//)
PRINT 2000»(AVG(I)~Is1*NC)
PRTNT2020
-------
2020 FORMAT(1H0///69H
1BER OF OBSERVATIONS//)
PPINT3000»AN
3000 FORMAT(560tF5«O)
ERASE<(A1(K)»Ka1«NOELM))
8 READ TAPE 6«
-------
SAMPLE
INPUT & OUTPUT
-------
stepwise multiple regression
060068 ,001 ,5 .3
002500002502500001500003400064
013000002102100000870003600063
003500002202200000430004100082
001750000900130001800001500023
00300000230230000200000330°064
002000001000060003300001300016
005500000700140003400001600012
006000000600080005000001100027
001300000800270001500001900048
005000001800360001800002700050
00500000030010000140000140O012
003000000800270001000002500013
002000000600300001500002100020
002000000800100002500001800023
001000002202200001100004600118
004000001301300002800001700050
000500002600120000730004800063
00025000230230000010000360^150
014000000300100003500000500072
002500001500250000280003300054
003500002801400000010004600109
003500000600060005000001000010
002500003503500005700003800125
000500001100200003400001600044
002000001101100000500002000048
007000003203200006600003800105
004000000800100004500001200009
015000002302300000150004900130
001000003803800002200004300160
003500001500500001500003300048
013000000600120003700000900036
002000002502500001000003500150
012000000500170000300002100078
004000000900075001900001700023
003000000700350002600001200042
008000002002000002200003000072
009000000600086002500001500020
006000001200400001200002000036
008000002600160001100003500056
001500001500300001600002900036
007000001000090010000001200026
008000002802800004200004000108
002000003403400000900004200106
006000000400080003600001100016
015000003203200001800004400104
017000001101100002300001400047
016000000200050001800001100027
003000001800160001100003200012
006000000300040001300001500007
014000000800110002000001700018
006000001400090000700002900028
001800001200240001500002100025
015000000300150000800001300011
018000000600550005700000900020
00500000120020000410000160O014
030000001101100002000002200038
0290000008008OOOO1000002200103
001800002402400001100003800106
BIMED TEST EFROYNSON
control data
-------
013000002602600001700003800063
019000002902900048000002900208
011000001701700001600002300032
010000001500500003500001900028
006000001000500001000002600032
005000002202200001200003900100
001000001500500000800002900030
017000000900300013000001000080
005000003003500000900005800063
001300001000130009000001000025
FINIS
CARDS 3*4
-------
VftP'j ISE VMTIPLF RECESSION
ji,!MDi£;i OF VA,? I M^LFS 6
")FoP>¦ F5 3P C7FE00'4 68.
= LF*/CI. TO ^jTE-J x/AHIA!3LE
r LF /r.L TO RiP-OV.; WRIArtLF
^I'lED TEST efr^nson
I.^OOOIOOOOF 00
0.30000000nE 00
SUMS
0.47S7U000UE 03 0.103700000E 04 0. 70f?i 1OOOOF 03 0.210770000E 03 0.172700000E 04 0.386200000E 04
viEA*lS
0.6-V955B824F. 01 0.15Z500000E 02 0. 104251471E 02 0.309955882E Ol 0.253970588E 02 0.567941176E 02
BER OF OBSERVATIONS
68.
SUM OF SQUARES OP DEVIATIONS AND CROSS PRODUCTS
ROW 1
0.2B0793366E 0*
ROW 2
0.5^6^ 75000E 04
ROW 3
0.905758106F 04
ROW 4
0.2409691*^ 04
ROW 5
0. 104342 7<34f.' 05
ROW 6
0.127073117? 06
-0.716225OO1E 03
0.A32733248E 04
0.538022755E 03
-D.704198088E 03
n.2349^5b87E 05
0,2589254 37E 02
0.3786975O0E 03
0.731002101E 04
0.599451383E 04
0.664559868E 03
0.6878249986 O4
0.266678320E O5
-0.105923088E 04
0.204674999E 05
0.154998B24E 04
-------
•'AT^rx Of- Sr^PLr. C'*2r'^r!. AT 11> I CoEFr I C t c" TS
.?
o
Or
1
0.
loO'^OOono!;
•n
-O.Wv+iSi^SjE
00
0. 5' 3-'v228 17F
-02
0. ?5«54R 1790E
Oo
Rn.v
2
0.
1 OO'.HJOOn Tp
n l
0.«h7992T55t
UO
0. loo ri^qp
00
0.3 791 19542E
00
ROW
¦i
0.
1 O")'1') }Ory)c
n 1
0. 12'"»<.5666E
00
0.7S1Q3.697P
00
0.7860^8292E
O0
RO;N
u,
0.
LiL)O0T0n,)r;
r>i
-0.)'t043r.3'>E
00
0.342*6767QF
00
RHrt
¦>
0.
I'VJTioonor
01
0.64*51 /S715^E
00
ROrt
0.
loo^ooorop
01
STAivj/wn cRRoP OF y = 0.435S012B4F 02
STH3 Nr. 1
tf*RT4~LE FNTERIvQ 3
F LFJF.L 0.lOft724O6«E OH
STAM0A30 ERROR SF Y = 0.27123792HE 02
CONSTANT 0, 2^0998 2 22E 02
CCHP - 0.38?112362c 00
VARIABLE
X- 3
STFtJ NO. 2
VARtA-JLT FNTiiP I -Jvl 4
r LTv/FL 0.121820955E 02
STAMOA.O CRUO? OF Y - 0 ,250H21120F. 02
CONSTANT 0.217444916E 02
CCRR = a.32ljOl363E 00
COEFFICIENT
0.294425540E Ol
std ERROR of coefficient
0.284999634E 00
VARIABLE
X- 3
VARIABLE
X- 4
STEP "tr>, 3
VARIABLE ENTERING 5
F LFVEL 0. 7392i>6605E 01
STAK'OARO ERROR OF Y = 0.23932«*2fcr 02
CONSTANT 0.291071750E 01
COSD = 0.288479437E 00
COEFFICIENT
0.29275^921^ 01
COEFFICIENT
0. 179 7678 34E 01
srn error of coefficient
0.265659659E 00
STD ERROR OF COEFFICIENT
0.515051891E 00
variable
X. 3
VARIABLE
X- 4
VARIA9LF
X- 5
STFP TOO. 4
VARM3LF ENT£PINvj 1
F LFvEL 0.7'175^637SE 00
STA^'OAPC) FRRO° CF Y = 0.239?2f>65<»E o2
CONSTANT -0.125 2842 38E "1
COEFFICIENT
0.195839757E 01
COEFFICIENT
0.231239125E 01
coefficient
O.1O3553033E 01
5TP ERROR OF COEFFICIENT
0.407973952E 00
STD FRROR OF COEFFICIENT
0.524652O73E 00
STO ERROR OF COEFFICIEMT
0.380859873E .00
-------
= 1.20'+ 51
^'AmIA^le
COEFFICIENT
^ n
rS5J=> IF Coefficient
X- 1
0.H.772077* ^
00
0.43l39^32E 0?
yA;j I A".l.p
coefficient
stt
prrop of coefficient
X- 1
0.1 39676502-
01
0.^l^512080£ 0*
V/AOTAlL^
COEFFlClcVT
sn
ERRU= OF COEFFICIENT
X-
0.22333455'»f
01
0.534995316E 00
V60 T A-'Lf"
COEFFICIENT
s rr»
ERRM DF COEFFICIENT
X- *?
0.111^7^116?
01
0.1=)23159S3E 00
4
stf.- no. ¦'•
vftPTa'-'l.P r 3aF ^1
CC^ = T.2B<»7t77S,5E 00
VArjr AOLF
COEFFICIENT
5 TO
ERRUD r»F COEFFICIENT
r.- i
0.427207760E
on
0• 481394432E 00
COEFFICIENT
sn
FRROQ DF COEFFICIENT
X- 3
0.1 39676592?
01
0.4U512O80E 00
VARIABLE
COEFFI CI EN T
5T0
FRROR OF COEFFICIENT
r- '»
0.22333
0.111&74116E
01
0.392315R53E 00
3IAoOMAl ELEmE'JTS
VAT.'vO. value
1
0.1132?864«»E
01
?.
0. 1029076-J^E
00
3
0.270A03309E
01
A
0.12001313"E
01
5
0.279448337E
01
O.Pa^91775SE
00
-------
AXRS14
-------
2
OUTPUT? l) Computes and prints a matrix of sums squares deviations
and cross products.
2) Computes and prints means and standard deviations of all
variables.
3) Computes correlation coefficients of all variables against
each other and tabulates them as a triangular matrix.
U) Extracts eigenvalues and eigenvectors from the correlation
coefficient matrix.
5) Using the eigenvectors the independent variables are
transformed into principal components (which are ordered as to
importance and which are not interdependent).
6) Computes by least squares the multiple regression
coefficients of each dependent variable versus all of the principal
components.
7) Works backwards from the dependent variable versus
principal component regression coefficient to get dependent
variable versus independent variable regression coefficients and
prints one set of coefficients using each additional principal
component.
References:
-------
GENERAL ROUTINE AXRSlU
PRINCIPAL COMPONENTS ANALYSIS
T. A. Entzminger
PURPOSE: Performs a regression on the principal components of a group
of closely related variables.
RESTRICTIONS; l) A maximum of 20 variables (dependent and independent)
can be treated in each run.
2) Input must be on cards.
ACCURACY: Single precision floating point computations with eight
significant digits.
INPUT: Data may be punched on cards in any format which can be suitably
described by an Autcmath FORMAT statement. Arrange data so that
they are treated by the READ statement in the following manner:
(a) one observation of every variable in each read cycle
(b) observations of all independent variables should precede
observations of dependent variables in the same read cycle.
CARD DECK SETUP;
1. Program decks
2. Name cards
3. Control card Card Column
Total number of variables 1-2
Number of dependent variables 3-^
U. Data deck
5. FINIS card
-------
DESCRIPTION &
PROGRAM LISTING
-------
MEWSTACK
COMPILES
SUBRfiUTIME CCRPEL
n I MENS I ON P(210) ,A1 (210) »DI A* (?0) *11(20,20) ~ si G(2fl>
CC'^MnN A 1. , K|OEL^ «NCI ,ND,nTAS,|.i,SI(;
C rCVD[jTATlOM CF CORRELATION
PPIMT1222
NCsNCI
NCOaNC
K=1
NC*sO
NU1
ME = 1
OC 456 L = UNC
or t=ni»nco
»3 ( I) SA1 ( I ) /SGRTF (AI (Ml) *M (<))
Ks* + f>!CO-NCA
45* NCA=NCA*1
NlsNCO+1
K = M 1
MCCsnCO*NC-NE
456 NE = NF~1
Nl = t
NN=NfI
ME* I
OC 6 Ksl,NCI
PP!NTL998*K
PR T NT2000 »(R(I)»Ism1•NN)
*'l = NN*l
NN=NN*NCI-NE
6 ME=NF*1
DC 171 = 1, NOELM
l7 A1(I)sr(T)
PETlJPN
FORMAT(5M RCto 12)
2000 FCRMA T(1Q»7E17»9//)
1222 FCRMaT(1H1/79H MATRIX OF SI^P
HE CORRELATION COEFFICIENTS////)
EN?
FN 3
JC^ENO
-------
rn'/pTi es
SUBROUTINE EIGFN
DIMENSION H(20«20).U<20.20)»X(?0)«TQ(2Q).Al(2l0).
CCw^ON A1 .noelm.nci»no«dias»u«sig
CCNSTRUCT SQUARE MATRIX HF IMDFPFNOE^T vARlABlFS
k"K = 0
N=NCl-MD
DC 5I=1»M
0C4J=I,N
KKaKK+l
H(I,J)sAl(KK)
4 M(J,I)sH(I»J)
5 KKsKK+ND
10 nCl4T=l.N
ncujsi ,n
IFU-J)12.11.12
11 U(I,J)=1.0
GC TO 14
12 U(I«J)=0*
14 CONTINUE
15 NP*0
IF(N-l)1000.1000.17
17 iWIlsN-1
DC30Tsl»MMH
X < I )=0.
T PL 1 = I~1
DCIOjslPLl»N
IF ( X CI >-AOSF CH f I • J) )l20»?G»3i
20 X ( T)=A3SF t M(T.J))
IC(I)aj
30 GCUTNUF.
pAr3 = 7.4505805g6t-9
HDTESTb1,OF38
40 DC 701 = 1 »N«II 1
IF ( 1-1)60.60,45
45 TFfXwAX-Xd) )60. 70«70
60 XMAXsX(I)
IPTV=I
vJPTV=TS(T)
70 CONTINUE
if(x^ax)iooo.iooo.no
80 TF(HHTPST)90.90,85
85 TF(XmAX-hDTEST>90,<»0»148
90 HDTMTNsAP.SF (H ( 1 »l> )
001101=2.N
IF (HDIMIM-A0SF (H < I»l)))110,n0,100
1 00 HD JWITNsAFISF (H (T.I))
lio continue
HDTEST=H^IMIN*RAP
IF (H0TF5T-XMAX) 148,1000.1000
148 MP=NP*1
-------
150 TANGb5IGNF(2.0» (H (IPI V» If>IV)-W f JPIV«JPI V) ) ) *H (IP I V« JPI V) / UdSF M (I
1PIV»TPTV) -H(JPIV»JPIV/) ) +SQRTF ( (H<1PIV.IPIV)-H(JPIV,JPI V))**2*4 .0-
1TANG#HTI))
H {IPIV,JPlV) =0.
IF (H (IPIV.IPIV) -H ) 1*2.153,153
152 HTEMPsHdPIV.lPlV)
H *COSINf
CCSINEsABSF(SIME)
SINE=HTEMP
153 CCN'TTMUF
D0350I=1.NMI1
IF(I-IPIV)210,350, ?00
200 IF(I-JPIV)210.350.2l0
210 IF(TQU)-IPIV)230,24^.230
230 IF(ir(I)-JPlV)350*24U,350
240 K=IQ(I)
250 HTF:MP = H {I »K)
H(T»K)sO.
T PL I = I~1
x(r)=0.
DC320j=IDLliN
IF(X(I)-ABSF(H 11 * J)))3001300,320
300 X =-SINE*HTEMP*CC5INE»h(I.JPlV)
IF (X ( I ) -AsiSF (H( I .JPIV) ) )4Q0.*3n»S30
-------
480 HTFMPsH(IpI V,I)
H (IPTV« n =C05INE*HTE^P* SINF.*H (jPT V * I)
IF(X(IPIV)-ABSF(H(IPIV*I))500*500
490 X(IPIV)aAB5F(H(IPlVtI))
IG (IPIV) = I
500 H(JPIv,I)=-SINF*HTEMP+C0SINE*M(JPlV*I)
IF(X(JPIv)-AB5F 510,530,530
510 X(JPTV)=Af?5F(H(JPIV*I) )
IG(JPIV)si
530 CONTINUE
540 D0550 I = 1 ,N
HTEMP = U(I %TPIV)
u CI ,IP|V)=CQ5IWE*HTf^P*STNP*U(T,JPTVJ
550 u(I,JPIV)=-5lME*HTEMP*C0SP'E#J(I,JPIV)
f?0T(H0
1000 DO 6001 = 1 1N
600 DIAG(I)=H(I»I)
PETURN
END
END
JCNEND
-------
COMPILES
subroutine regres
c DETERMINATION of regression COEFFICIENTS
DIMENSION X(20)»aH2l0)»B(2l0)*Rt"GSS(in)»x0(20)OlAG(20),U(20»20),
1SIM20)
CC^MnN A1»N0EL^«NCI •MD«DIAG»II.SIG
FRASE(REGSS)
NC=NCI
3 M = r\jC-ND-l
MMsM
mp=nc-md
MJ=NC-MD
NG«NC-ND
NUI
NN=NC+1
NZ = 2
L 2 = 1
NTsNC
MX = 0
DC 12JsNl»NQ
300 DC 5l=Nl«NC
5 R(I)sAl(T)/A1(Ni)
MCXsmC -MD+1
DC 36
3ft NCXsNCX*1
NNC=NC
MM=Nl
NNX=NX
LL2=L2
1 NN'*NN-1
10 12=12*1
MlaNC*l
2 NXsNX*l
MCsNC*NT-MX
K2 = L2
DC 8T=N1,NC
Al(nsfll(I)-Al(K2)*a(L2)
9 K2=K2*1
IF(NC-MOELM)lOtlltll
11 L 2 a LL2 *NS!
MX=NNX*1
Nl»NNC*l
12 MCsNNC*NT-NX
C
C MULTIPLE CORRELATION GOM!»uTATinN
C
DC 37 1=1«ND
37 RE^SS CI» =REG5S CI)/X(I)
PRINT 1
-------
PRINT 801»(REGSS(I)»1=1»ND)
c back SuBSTItutton
r
DC 31 I = 1»NCELM
31 A1 (I)=R(I)
11=0
DC 22 KKrltNO
7 B= 1
IEN=NP
JE=IEN
< = 0
34 DO 35 T = T E3 * IE
4 <=<+1
35 B -B(NO)*X(Nl-l)
13 NZ= NZ * 1
lft N'C*NO-NZ
17 NA=NA+1
19 Msm-1
18 MZsN?-^
LK»NJ
DC 20 1 = 1,NJ
XC ( I)ax
-------
1>45 FORMAT(50B6HUSTNG I2»2lH PRINCIPAL COMPONENTS//)
78 PR I NT 80]»(B(p,I = 1.NJ)
22 TI=IT~1
RETURN
300 FORMAT(I 2 «I 3 «I 2)
1333 FORMAT (IM2/70H I|N1TE
1PNFDTATE SOLUTIONS////)
1444 FORMAT(1H2/70H REGRE
1SST0M COEFFICIENTS////)
1555 FORMAT(1M2/74H MULTIPLE CD
1RRFLATT0M COEFFICIENTS////)
flOl FORMATU«»7E17.9)
END
FIVP
JCBENO
-------
COPILEX
TITLEAXRS14
C REGRFSSION ON PRINCIPAL CO^PrjNrNTS
c ccrrfCted sums of squares an* cross products
COMMON A1 ~NOEL^NCI , ND ~ 0 I AG»IJ,SIG
DIME^STOM x * 2 0 > iAl<2lO) ^IA
100 REWIND 6
REWIND 5
1001 FCRMaT (3F^.UF3.1)
f?EADTOOO*NCI ,MD
IF F.ND OP EILE 2"5 i 30
30 NC=MCI
NC5L« = NC* ,I = UNC>
GC TP 1
<~ end file 6
°EWIMD ft
AS5IGN8 TO M80
ASSIGN 1¦> TC Nil?
50 DC 5 I = 11MC
5 AV^ (T)eAl (I)/AM
ERASE { {A 1 (K) ,K=1«N0ELM> )
GC TO N0O«(3 * 8n)
R READ T APr 6~ (X(I) ~I = l»MC)
IF END OF FlLE^l»b
b Nfcsl
11 = 1
K = 1
nc?i = i i ,mc
TE"P= X{IJ-AVG(I)
PC 7 JsNM»NC
A I(K)=TEMP#(X(J)-AVG(JJ)*A1(<)
y <=<+i
NN = NNJ+ ]
0 II=NN
GO TO MflO«< 3 »80)
ao RFAO TftPr 5, (X (I) • Isl«NC)
IF END OF FILE 4l»*>
PPTNTlllt
1111 FORMAT(lui/82H SUf OF SQUARES
1 DEVIATIONS A^n CROSS PRODUCTS////)
NU1
W = NCI
NE»i
OCAft K=1,MCI
nRT NT199R
1T99 FCRMAT(UH ROx ! 2)
-------
303 A1 (T)sA1(I)*7(T)
ANsAN+l,0
WRITF TAPE 5~ (2(T)~I=l»Nr)
PC TO ?0l
20ft FND PILE 5
R E to IM D 5
AS5IGNB0 TO N80
ASS I R(M 115 TC Ml 15
GO TO 50
115 NCEL^sN*
-------
SAMPLE
INPUT & OUTPUT
-------
INPUT TEST DATA
0401
111112223
141511221
171820292
171718270
I8l9l8?fi'5
181819304
191820311
202121314
23242532A
2525243*0
FINIS
FINIS
FINIS
CARDS 444
-------
S'jM DH bUuArt:5 OF 'J> E VI A T lONb AND CKUSb MRU'J-jCTS
«3-.i i
0. 1 «~ 5 * 0 (J 0 0 0 fc 0 . l^dOOOO'.'e 0 1 O.lblHUOOOOt 01 0,1. 46fc00000fc 02
-nw .?
0, lSCKOUOOOfc, :)1 U#lbl20000i»E 01 0,1341OUOOOE 02
MO W 3
0. iMlftOOOOOt ol 0 , I 5 7 7 0 U 0 0 0 £ 0?.
WOW 4
0. l^S'J'+OUOOL "13
bT^DARD DP.VlATlQrgb
0.^f02^l60R3r *0 0.*0>l7922b9E 00 0. 4*91 968 I 4fc 00 0. 4f>2 1 332011: 01
¦
-------
XI
o
3
o. looocnnnot
0 I
ROW £
o,loooooonot
01
ROW 3
0.lOOOOOOOOt
01
ROw **
0, lOOOOfJOOOE
0.2H8'S153rtc oi
Q.S8526<»6*i9h 00
0.vl<»H9«2C5;>E. 00
O.V7('OZ^23Ht 00
0.9b^219262E-01
0.&H3^1l5R2t HO
0. 00
-0.7^6274q7bt 00
0,!>8()0n7U7^t 00
0 , *~ 7 m 7 365 11 E or)
(J#h5q0g2*>79E 00
A T «I X Oc SIMPLE CORRELATION LQfcFF I C I EN T b
0.9310»0b7^t 00 0,eJ3P3«0X81t On
0 , 906 701 'JO
EI&tNVALJtS
0. 13602720^E-Ol
EIGENVECTORS
0.5t>8 r3 1973E 00
0,817^3524<»e 00
0.93115>5q^E-01
-------
P0V 1
0.2>9'->0 *3f»3t 02 -(j.^gOOOOnOfJP-Oa
POW 2
0.8H6frry f335t "»U J. 1O7Q0000OE-0H
PDW 3
0, 122V6'»^h3E '">•) -').^5^01^y 7lE 00
WOW <~
n. l^s^j^oonot, t-j
0.3<»3i»l«4olK-15
0.226237902E 01 -0 . 2347Q32b8E 01
0.32804^479E O I 0 . 32'19933 lt>F 01
-0. 188Ol9b">0h "11 -'1.27.SQ37BB1E 0).
0.6H6b70S4Ur. 'U
-'J.bySfa U890^E 01
^ OH ^UUAPES OF 3tVl«TIOMb AiMij CKOSb PROJECTS
0.260000000E-OR 0.5y7999961t U2
0,209U018PbE 01
MljL r r pLF. CORRELATION COt^F I C IEiNTS
OES«fc'SSI0N coefficients
0,3 7 0 'J 3 7 6 -v 3 E 01
JSIMG 1 PRINCIPAL CoMpOMENTb
3.2h6*<*1 7*,5t 01
JSINCi 2 PRINCIPAL COMPONENTS
0.^28H30ns8b 01
JSING 1 PRINCIPAL COMPONENT b
0. 7<> 7U63H I bt 00
-------
AXRS28
-------
GENERAL ROUTINE AXRS28
LINEAR DISCRIMINANT FUNCTION ANALYSIS
T. A. Entzminger
PURPOSE: This program performs calculations which aid in discriminating
between two groups of objects or conditions on the basis of several
properties of these objects or conditions. The procedure for
discriminating consists of finding a critical value of the index
such that any object whose index value falls below the critical
value is classified as belonging to one group otherwise to the
other group.
RESTRICTIONS: A maximum of 10 descriptive variables for each group.
ACCURACY i Single precision floating point computations with eight
significant digits.
INPUT: Data may be punched on cards in any format which can be
suitably described by the Autamath FORMAT statement.
CARD DECK SETUP:
1. Program source deck
2. Control card Card Column
Number of variables for discrimination 1-2
3. Data for group 1 variables
Date for group 2 variables
5. Finis card
-------
2
OUTPUT; The program sets up a two way classification of the data to
determine the linear discriminant function Z = f( , x, + 2x2
+ .... n x n) and prints out Z values for each observation entered
along with the coefficients ( 's).
REFERENCE: "introduction to Mathematical Statistics", Paul G. Hoel,
3rd Edition, John Wiley and Sons, Inc., New York.
-------
DESCRIPTION &
PROGRAM LISTING
-------
COMPILEX
TITLEAXRS28
C LINEAR DISCRIMINANT FUNCTION
DIMENSION X<10) tSUM<66) ,0(10) ,r>D(lO) , 8(66),XX(10),X0<10)
PRINT 5000
5000 FCRMATUH1/30X37HLINEAR DISCRI'MnAnT FuNCtION ANALYSIS//)
REWIND 6
READ1000,NV
NC=NV*1
M0FLMsNC*(NC*1)/2-1
FRASEUSUM(I) ,I»l»N\/> ,AN,D,DD)
1 PEAD2000*(X(I),1=1,NV)
IF END OF FILE 5,4
4 DO 31=1,NV
3 SUM(i)=SUM(I)~X )
ANs0.0
11 READ 2001»(X(I),I=1,NV)
IF END OF FILE 6,10
10 DO 13 1=1,NV
13 SUV(t)sSUM(I)*X(I)
AN=AN*1.0
WRITF TAPE 6~ (X ( t ) ,I»1,NV)
GO TO 11
6 FND FILE 6
PR INT4001,AN
REWIND 6
DO 8 Isl,NV
8 DD(I)= 5UM(I)/AN+DD(I)
FRASE((SUM(I)»1=1iNOELM))
1* PEADTAPE6,(X(I),I=1,NV)
IF END OF FILE 20,16
16 NN= 1
11 = 1
K= I
DC19I = 11,NV
TEMP=x{I)-D(I)
DC 17J = NN ,NV
SUM(K)"TEMP#(X(J)-D(J) >*SUM(K)
17 « = <~ I
SUM (K)=D(NN)
K = K* 1
NN=NN+l
19 11=NN
r.OTOI 8
20 PEADTAPE6,(X
-------
11=1
K = l
DC29T = II«NV
TE^PsX(I)-DD(I)
0C27jsNN»NV
SUV <«) sTEMP*(X(J)-00 CJ))*SUM(<)
27 X=K*1
SUM(K)sD(NN)-DD(NN)
K = K*1
NN»NN*1
29 TI"NN
GC TO 20
SIMULTANEOUS EQUATION 5CLUTI0N
31 w=NC-2
NJaNC-1
NG=NC-1
Ml*l
NNsNOl
NZ« 2
L2=l
NT»NC
MXaO
DC 120 JsN]«NQ
DC 50 JsMUNC
50 P(I)xSUM(U/SUM(Nl)
NNCsNC
MNlsNl
MMX=NX
LL2sL2
NNaNN-1
100 L2=L2*1
MsMC* I
M X s N X ~ I
NC = NONT-NX
K2 = L2
DC 80 isNl.NC
5UM(T)=SUM(I)-SUM(K2)* B(L?)
80 k2*K?+1
!F(NC-NOFLM)100,110.110
110 L2=LL2*NM
NXsNNX+1
N1 = NNC *l
120 MCsNMC+NT-MX
UO N1 a 1
NZ = 1
NC»NNC
NOsNC
DC 1*0 IsNltNj
XX (I)=R(MO)
NZ-N7*1
150 MOaNO-MZ
NZ = 2
L=NJ-1
MA = B
DC 1«0 JeUL
-------
NC = NONA
NC = Np
W1«N1*1
DO lftOTsMl.Nj
XX(nsXX(I)-B(NO)*XX002
DC 200 1=1»NJ
xo(i)sxxro
PR INT801»X0(I)
200 K = K-1
PRTNT 4003
XTC=X0(1)
DC 206 I = 1»NJ
XO(J)»XO(I)/XTO
206 PRINT 801»XO(1)
PRINT 401
202 READ TAPE 6»(X(I)»1=1•NV)
IF END OF FILE 2?1*216
216 Z=0.0
DO 219 I=1»NV
?19 Z = Z«-XO(I)*X(I)
PRINT 801»Z
GO TO 202
221 PRINT 402
220 RE&D TAPE 6 • (X ( I ) »I a 1»MV)
IF END OF FILE 230*226
226 Z=0.0
DO 229 Is1»Nv
229 7. = Z + X0(I)*X(I)
PRINT 801 »Z
GO T0220
230 TYPE»803
803 FORMAT(8H THF FND)
STOP
400 FORMAT(4B,E16.9)
401 FORMAT(31H INDICES (Z VALUES) FOP GROUP I)
402 FORMAT(3\H INDTCFS (Z VALUES) FOR GROUP 2)
801 FORMAT(18»7E17.9)
4002 FORMAT(42H COEFFICIENTS OF TME DISCRIMINANT FUNCTION)
4003 FORMAT(55H STANDARDIZED COEFFICIENTS OF THE DISCRIMINANT FUNCTION)
moo format(I2)
2000 FORMAT(2F9.0)
2001 FORMAT(2F9.0)
3000 FORMAT(5F10.3)
4000 FORMAT(17H COUNT GROUP 1 =F9.l)
4001 FORMAT (17H COUNT GROUP 2 =F
-------
SAMPLE
INPUT & OUTPUT
-------
INPUT TEST DATA
02
6.36
5.24
5.92
5.12
5.92
5,36
6.^4
5,64
6.AO
5.16
6.56
5.56
6.64
5.36
6.68
4,96
6.72
5.48
6.76
5,60
6.72
5,08
FINIS
6.00
4.88
5.60
4,64
5.64
4,96
*.76
4,80
5.96
5,08
*.72
5,04
5.64
4,96
5.44
4,88
5.04
4,44
4.56
4,04
5.48
4,20
5.76
4,80
FINIS
FINIS
CARDS 199
-------
LINEAR DISCRIMINANT FUNCTION ANALYSIS
COUNT GROUP la 11.0
COUNT GROUP 2 = 12.0
COEFFICIENTS OF THE discriminant
0.275932185E 00
0.13671153 IE 00
STANDARDIZED COEFFICIENTS OF THE
0.100000000E 01
0.4954533A9E 00
INDICES (Z VALUES) FOR GROUP 1
0.895617565E 01
0.845672125F 01
0.857563006E 01
0.923435700F 01
0.895653939E 01
0.931472073F 01
0.929563006F 01
0.913744871F 01
0.94350R446E 01
0.9534538R7E Ol
0.923690312E 01
INDICES (Z VALUES) FOR GROUP 2
0.841781244E 01
0.789890363E Ol
0.809744871F 01
0.8138176171- 01
0.847690312E Ol
0.821708408F 01
0.809744R71E 01
0.7R5781244E 01
0.7239812Q6E Ol
0.656163161F 01
0.756090415F 01
0.813817617E Ol
FUNCTION
DISCRIMINANT FUNCTION
-------
AXRS33
-------
GENERAL ROUTINE AXRS33
MULTIPLE REGRESSION
T. A. Entzminger
PURPOSE: To find the least squares linear relationship
(y± - y) = b]_ (*3^ - *i) + b2 " *2) + ••• + ^n(*ni-*n)
of p dependent variables y^, (i = 1, ... , p), on the
independent variables xj, (j = 1, ... , n).
RESTRICTIONS: l) A maximum of 25 variables (independent plus dependent)
can be treated in a run.
2) Input to computer is on cards.
ACCURACY: Single precisions floating point computations with eight
significant digits.
OPTIONS; l) Transformation of any variable can be made by inserting
the proper Automath statements between the two transform comment
cards in the source program deck (i.e., x(l) - IXXJF x(l) or x(6) =
SQRTF (x(6) ) or x(13) » A+B*x(13) where A and B have been previously
defined). (The program assumes that the first variables treated are
independent and the last variables are dependent.)
INPUT!
Data may be punched punched on cards in any format which can be
suitably described by an Automath Format statement. A considerable
amount of running time can be saved by arranging the data so
that they are treated by the READ statement in this manner (a)
-------
2
INPUT (cont'd)
one observation of each variable in every read cycle (b)
observations of all independent variables should proceed
observations of dependent variables in the same read cycle.
Standard card format is seven fields of 10 digits each; the
last 10 digits may be used for identification.
CARD DECK SETUP:
1. Program Source Deck - complete with modified FORMAT statement
(Statement #1001), transform statements, overlay card, Binary
Subroutine Decks and Jobend card.
2. Name Card - Describes run uses card columns 2-80.
3. Control Card - Gives total number of variables (dependent plus
independent) in card columns 1 and 2, and the number dependent
variables only in card columns 3 and U. To compute uncorrected
(raw) sums of squares, enter a 1 in card column 5. If sums of
squares are generated externally, enter a 1 in card column 6.
For corrected sums of square and internally generated sums of
squares, columns 5 and 6 must have a blank or zero entered.
4. Data - Card punched in most any form can be handled by this
program (several variables per card or one per card) and is
described by a FORMAT statement included in the program source deck.
5. FINIS CARD
6. Repeat steps 3-6 for each additional run.
7. FINIS CARD
*Note - When using additional transforms allow for reading them in
format statement.
-------
3
OUTPUT:
1. Computes and prints a matrix* of sums of squares (raw or
corrected) and cross products.
2. Computes and prints a matrix* of simple correlation coefficients.
3. Computes and prints the following for each dependent variable:
Degrees of freedom.
Total sum of squares.
Sum of squares for error.
Mean square for error.
Sum of squares for regression.
Multiple correlation coefficient (R2)
Each regression coefficient.
Standard error and Students T for each regression coefficient.
Constant term in the regression.
Analysis of variance Table.
U. Computes and prints the inverse matrix.
5. Computes and prints means and number of observations.
* - Only the upper triangular portion of the sums squares matrix
and simple correlation coefficients matrix is printed.
-------
DESCRIPTION &
PROGRAM LISTING
-------
MEWSTACK
CCWPILES
SUBROUTINE CORREL
DIMENSION) R(325) »A1 (325) «X(2*) tAvG(25) »AV(26)
COMMON X«M1»N0ELw,MCNND,AVG,AV»TRAW,An,I5S»IDF
C COMPUTATION OF CORRELATION MATRIX
PRINT1222
NC=NCI
NCCsNC
K= 1
NCA = o
M 1 = 1
NE*1
DC 456 L=1*NC
DO 454 I=Nl»NCO
Zs A1(N1 )*AI »I=N1»NN)
Nl=NN+l
5 NN«NN*NCI-NE
6 NE=NE*l
RETURN
7 PRINT 3000*Al(N1)*A1(<)»L»I
PRINT 2000» (A1(I)»Ial,NOELM)
STOP
3000 FORMAT(2E16.9.212)
1998 FCMAT (5H ROW 12)
2000 FORMAT(10i7E17.9//)
1222 FORMAT(1H1/79H MATRIX OF SIMP
HE CORRELATION COEFFICIENTS////)
END
END
JOREND
COMPILES
SUBROUTINE OOOLIT
C DETERMINATION OF REGRESSION COEFFICIENTS
DIMENSION X(?5> *A1 (325)«B(325),RFGSS(10)»XO(25)«AVG(25)«AV(2ft),
1DJA6(25)»D(25»25)»C(25»25)»S<10»25)
DIMENSION TSS(JO)
COMMON XtAltNOELW,NCl•ND«AVG»AV,IRAW,AN»ISS«IDF
FRASE(REGSS)
NCsNCI
-------
3 MsNC-fO-l
MMsM
NP«NC-ND
NJ»NC-ND
NG»NC-ND
Nl«l
NN*NC*1
NZ»2
L2al
NT *NC
NXaO
DC 12JsNl»NG
300 DO 5I=N1«NC
5 B(I)sAl (D/AllNl)
C DIAGONAL elements
DIAG(J)sAKNI)
mcx=nC -MO*1
DC 3ft KKR=1»ND
REGSS(KKP)=Al(NCX)*B(NCX)*RtCSS(KKP)
S(ND,J)«A1
-------
391 KKsKK+MO
J = NC
NN»1
M0 = 0
NM«NC-l
NXaNC-l
P040 T = 1»NC
40 C (I»I)=1,0/DlAG(I)
D041KKsl,NX
K=NC-NO
I=NC-NN
DG42N=1«NM
C (I tj)bC (ItJ)-D(I«K)*C(K«J)
42 1=1-1
NN=NN*1
NOaNO+1
41
C START GROUP 2
NTaNC-3
MK* 1
MTaNC-2
N 2 a 2
D054WA=1»MT
N0 = 0
J = J-1
NN»N2
K=NC-NO
D045KZ=1«NK
C(J»J)=C(J*J)-r)(J,<)#C(K.J)
45 KTsK-l
MK*NK+1
MM»NC-NT
KsNC-NO
IsNC-NN
DOUONFs1«NK
R049Nsl,MM
C(t•J)sC(I»J)-0(T»<)*C(K»J)
49 1=1-1
K = K-1
MCsNOl
50 I=NC-NN
NN»NN*l
NMbNM-1
IF(NM)55,55,53
53 MR*NX-MK
DC52
-------
5* N2*N2*1
55
-------
NXXsNCl-MD
CCNST=AV(NCT)
DC 62 I=1*NXX
62 CONST=CON5T-XO(I)#AV(I)
PSQR=RFGSS(KK)/TSS(KK)
SSE=TSSCKK)-REGSS(KK)
EM5sSSE/DF
PRINT 1776 *KK
1776 FORMAT(lHl/50B»19HDEPENDFNT VARIABLE 12)
PRINT 1777tmF.TSS(KK) ~S5E*EWS»REGS5(KK) iRSQR
PR T NT 1888
DC 65 J=1»NJ
5TPERR=5QRTF(EMS*C(J»J))
T=XO(J)/STDERR
65 PRTNT1889.J*XO
801 F0RMAT(1B»7E17.9)
1890 FORMAT(1H1/^7B«26HANALYSIS nF VARIANCE TAB|_E////5B«
119WS0URCE OF VftRlATlOMllB,18MDtGREES OF FREED0M146,
215HSUMS OF SCUARES17B,11HMEAM SQLiApE//)
1»92 FCRMAT(8Pf9HDUE TO 3~12~24B~1Wl«23B.E16.9~1*B»E16,9//)
FNP
FND
JOREND
-------
COMPILES
SUBROUTINE SSCP
C COMPUTES SUMS SQUARES »CROSSPRODUCTS,MEANS
DIMENSION X(25)»Al(325)*AVG
AVC(I)sAVS(I)
IF(IRAW)55,5,55
55 AVC(I)=0.0
5 CONTINUE
ERASE((A1(K),K= 1,NOELM))
8 READ TAPE 6*(X(I),I=1,NC)
IF END OF FILE 42,6
6 NN" 1
11*1
K= I
00^1=11,NC
TEMprX(I)-AVC(I)
DO 7 JrNN,NC
A I(K)=TEMP*(X(J)-AVC(J))+A1(K)
7 K-y*1
NNsNN+1
9 I I= NN
GO TO 8
42 AS5IGN 23 TO 123
NOELM=NC*
-------
12 N2*N2-1
NCELMsNiND*(NlND+l) /2 + M0*NJiMn
NNAsAN
IDFsMNA-(NCI-ND*1)
CALL DOOLIT
PRINT 2010
20]0 FORMAT{1H0///60H
1 means//)
PRINT 2000~ (Av (I) ~IM»NC)
PRINT2020
2020 FORMAT(1H0///69H
1PER OF 0BSFRVATICN5//)
PR T NT3000~ AN
3000 FORMAT(56B.F5.0)
RETURN
1005 FORMAT(1H1/76H
1UARE5 AND CROSS PRODUCTS////)
1006 FOPMAT(1HI/76H
HjARES AND CROSS PRODUCTS////)
2n00 FORMAT(1«»7E17.9//)
FND
FND
JOBEND
UNCORRECTED SUMS OF
CORRECTED SUMS OF
-------
CCMPILEX
TITLEAXRS33
C T• A. ENTZmINGER
C multtplf regression
COMMON X,A1 »MOELm»NCI »ND»A\/G,AV,IRAW,AN,ISS, IDF
DIMENSION X(25)•a I(325)»AVG(25)»AV(26)~ TItLE(10)
C=0.4342945
100 REWIND 6
READ 2003«TITLE
IF END OF FILE 25*30
30 PRTNT2002»TITLE
READ i000«NCl,NDtIPAW,ISS
NCsNCI
NGELMsNC*(NC*1)/2
ERASE((A1(K)»Ksl.NOELM))
AN=0.0
1 PEADlOOl*(X(J)»Isl»NC>
IF END OF FILE 4,2
2 T ND3=IND3
C INSERT TRANSFORMS AFTER STATE^FNT 2
X(1)=L0GF(X(\))*C
X(2)=L0GF(X(2))#C
X(3) =L0GF(X(3))*C
X(4)=LHGF(X(4))*r
1001 F0RMAT(F4.0»F2.0,F4.0,F4.1)
C FND TRANSFORMS here
DC 3 I=1»NC
3 Al(I)sAl(I)*X(I)
ANSAN+1.0
WRTTF TAPE 6» (X(I) ,I = 1»NC)
GO TO 1
4 FND FILE 6
REWIND 6
CALL S5CD
GC TO 100
25 TYPE »802
STOP
H02 FORMAT(8HTHATS IT)
1000 FORMAT(2 T 2•2 11)
2002 FORMAT(1H1/20B•10A8)
2003 FORMAT(10A8)
FND
END
OVERLAY
5TACKSSCP
5TACKC0RPEL
STACKDOOLIT
JCREMD
-------
SAMPLE
INPUT & OUTPUT
-------
INPUT TEST DATA
multiple regression TEST
0401
09^9023553
7.6
0929022713
4.4
0929021809
5.6
0929020904
3.7
0929063553
4.9
0929062713
4.2
0929061809
«.6
0929060904
3.3
0929243553
3.1
0929242713
2.2
0929241809
2.5
0929240904
1.7
1646022713
2.8
1646021809
2.7
1646020904
1.9
1646063553
2.2
1646062713
1.6
1646061809
1.7
1646060904
1.5
1646243553
1.1
1646242713
1.0
1646240908
0.3
2535023553
3.1
2535022713
1.7
2535021809
1.8
2535020908
1.7
2535063553
1.3
2535062713
1.3
2535061809
1.4
2535060908
1.2
2535243553
.7
2535242713
.5
2535241809
.5
2535240908
.3
3869023553
.4
3869022713
.6
3869021809
.5
3869020908
.3
3869063553
.2
38&9062713
.2
3869061.809
.4
3869060908
.03
3869^43553
.3
3869242713
.2
3869241809
.2
3869240904
.1
FINIS
CARDS 445
-------
Ml 'I T 1 PLC r>ERRF«.Sl ONi TEST
uncorrected sums cf squares and cross products
ROW 1
0,251/f379Q6«i Ol 0.337120500E-02 0 .1 <*50 5q9 8 1E-01 -0 . 455995363E 01
ROW 2
0.8 7754*287E 0.1$3649^37F UO -0.377o2?9?7F 01
POW 3
0.233
-------
Dp rSS
f* 2 0.12*91 ?S9F 02
S5E
0.1<>3n3*.3*>E 0*
depfmof:'-it variable i
^<;F S5R R bQiJARE
n,4596l037F-Ol 0.l0*6l405E 0? 0. fl<>*2Z2 1 IE 00
COFKPIC jfnjt
1 -n.1S1^5^9^E
2 -O.^tf^l^OJE
3 0,^94?1A20E
CONST "i'JT = 0,47*&1?932p n 1
STANDARD ERROR
01 0.13520086E 00
00 0.72370238E-01
00 0.1<>U4lUlE 00
students t
-0.13436300E 02
-0.60606961E 01
0• 35197800E 01
-------
MEAN SQUARE
0.S26970362E 01
0.162229702E 01
0.569404441E 00
IMVErSE matrix SOLUTION
0.397712365? 90 -0. 1 5278631IE-03 -0•31*707799E-02
-0.152786311F-03 P.113954162E 00 -0.750O37107E-02
-0«3l4707709E-?2 -0 . 750937107E-02 0.4?8o56354E 00
means
0.329737853E 01 0,8 19892 172E On 0.329511522E 01 0. 24O54565E-01
NUMBER OF OBSERVATIONS
46.
ANALYSIS -IF VARIANCE TABLE
SOUPCF PF V^R T At I PAl Dcr,OEf5 OF FRFrODM 5UMS OF SQUARES
HLF TO 3 1 1 0.826970362E 01
PUF TO a 2 1 0.162229702E 01
HUF TO f 3 1 0.569404441E 00
-------
\
AXRS38
-------
GENERAL ROUTINE AXRS38
LEAST SQUARES CURVE FIT
PURPOSE: This program generates an approximating polynomial by the
least squares technique. The equation so derived contains as
many terms as necessary to bring the standard error of the
dependent variable within a range specified by the user.
RESTRICTIONS: Provision has been made for a maximum of kOO observations
(can be enlarged) and a polynomial expansion up to the 15th degree.
This program is based on the assumption that a set of experimental
data can be fitted to a polynomial of the foxm:
Y * Ao + Ai x + A2 x2 + A3 x^ ———— + A15 x ^
PURPOSE: The linear form Y = Ao + A^ X is tried as a first approximation.
The coefficients axe computed and the standard error of the dependent
variable (Y) is compared to a predetermined tolerance. If the error
is greater than this maximum value the process is repeated, adding
a term of the forn Aq x n (where n = 2, 3 ...., 15) until the error
is within the tolerance.
ACCURACY: Single precision floating point computations with eight
significant digits.
INPUT: The input to the program consists of two types of records.
The first is a control which contains N, the number of pairs, the
tolerance and the highest degree of fit. The next N records are the
observations of X, Y, and the weighing factor W.
-------
CARD DECK SETUP;
1. Control card Card columns
Number of pairs 8-10
~Tolerance 20-30*
Highest degree of fit 39-^0
~Decimal point must be punched on card
2. Data cards
May have any format - programmer must change Format statements
#2000 and #3000 accordingly. Standard format as follows:
Card columns
X value 1-10*
Y value 11-20*
Weighing factor 21-30*
~Decimal points must be shown unless values are integers.
OUTPUT: Program prints tolerance, standard deviation, number of pairs
fitted, least squares coefficients, X values, Y values, predicted Y
values, and the difference between observed and predicted Y values
for each order of the polynomial.
-------
DESCRIPTION &
PROGRAM LISTING
-------
comptlEx
T T TLEAXRS38
C LEAST SQUARES CURVE FIT
C t.a.fntzminger
DIMENSIONX(400) .Y(400) «A(16tl6) »SUmX(31) .SJviY(l5) «W<400)
1 READ1000»N»T0L«LAST
IF END OF FILE 174.18
18 !F(SENSESWITCh1)30»20
20 READ 2000*(X(i),Y(I)»Isl.N)
GC TO 40
30 READ 3000*<* xSUMX UK)
101 A
-------
R = N-L
FTEST=(SS2-S2)*B/S2
SS2=S2
S2 = (S2/B) **.?>
163 PRINT3
PRINT4,N0RD»T0L»S2«N
PRINT1010»FTEST
1010 FCRMAT(1H0/45B*10HF VALUE s Flft.Q//)
PRINTIO
DC 1641cl, L
J-I -1
164 PRINT 5 »J» A(I»KK)
167 PRINT U
DO 1^9 I s 1 ~ |\|
51*0.
S1«A(1»KK)
DO16RJ«1«NORD
168 S1=S1+A(J*1»KK)*X(I)**J
S3*Y(I>-51
169 PRINT 6 • X (!)»Y (I)»51»S3
IF(NORD-LAST)170,173»173
170 IF(S2-T0D173,173»171
171 N0HD=N0RD*1
J=?*NORD
SUMX(J)=0.
SUMX (J+l)=0.
SUMY(N0RD+1)=0.
D0172I«1»N
SUMX(J)=SUMX(J)+X(I)**
1 F t X) Y-F(X))//)
6 FOPMAT(17B«4E21»9)
END
FND
JCREMD
-------
SAMPLE
INPUT & OUTPUT
-------
016
0.5
0.67
1.0
0.87
1.*
1 .04
2.0
1.21
2.5
1.38
3.0
1.55
3.5
1 .72
4.0
1.86
4.5
2.00
5.0
2.14
5.5
2.28
6.0
2.42
6.5
2.56
7.0
2.67
7.5
2.81
fl.O
2.92
FINIS
CARDS
130
INPUT TEST DATA
.001
0.52
0.52
0.57
0.56
0.59
0.59
0.61
0.61
0.63
0.63
0.65
0.65
0.67
0.66
0.66
0,66
0.65
0,66
0.64
0,65
0.63
0,64
0.62
0,62
0.61
0,60
0.57
0,58
0.56
0,55
0.52
0.52
-------
least squares curve Fit
ORDER
1
TOLERANCE
0.100000000F-02
sigma
0.484711646E-01
16
F VALUE s 0.321661260E 04
coefficients
0 0,
614000001E 00
1 0,
298176471E 00
X(I>
Y ( I )
F (X)
Y-F(X))
0.500000000E
00
0.670000000E
00
0.763088236E
00
-0.930B82362E.Oi
O.IOOOOOOOOE
01
0.870000000E
00
0.912176472E
00
-0.421764713E-01
0.150000000E
01
0.104000000E
01
0.106126471E
01
-0.212647060E.01
0.200000000E
01
0.121000000E
01
0.121035294E
01
-0.352942000^-03
0.250000000E
01
0.138000000E
01
0.135944118E
01
0.205588230^-01
0.300000000E
01
0.155000000E
01
0.150852941E
01
0.414705880E-O1
0.350000000E
ni
0.172000000E
01
0.165761765E
01
0.623823530E.O1
0.400000000E
01
0.186000000E
01
0.180670588E
01
0.53294H70E-01
0.450000000E
01
0.200000000E
01
0,195579412E
01
0.442058820E-01
0.500000000E
01
0.214000000E
01
0,210^88235E
01
0.351176470E-01
0.550000000E
01
0.228000000E
01
0.225397059E
01
0.260294120E-01
0.600000000E
01
0.242000000E
01
0.240305882E
01
0.169411760E-01
0,650000000E
01
0.256000000E
01
0.255214706E
01
0.785294100E-02
0.7000000n0E
01
0.267000000E
01
0.270123529E
01
-0.312352940E-01
0.750000000E
01
0.281000000E
01
0.285032353E
01
-0#403235290E-0l
0.800000000E
01
0.292000000E
01
0.299941177E
01
-0.794117650E-01
-------
LEAST SQUARES CURVE FIT
ORDER TOLERANCE SIGMA N
2 0.100000000E-02 0.870826460E-02 16
F VALUE = 0.420742233E 03
coefficients
0 0.493464291E 00
1 0.378533610E 00
2 -0.945378118E-02
X (I) Y(I) F(X) Y-F(X))
0,500000000E no
0.100000000E 01
0.150000000E 01
0.200000000E 01
0.250000000E 01
0.300000000E 01
0.350000000E ni
0.400000000E fU
0.450000000E 01
0.500000000E 01
0.550000000E 01
0.600000000E 01
0.650000000E 01
0.700000000E 01
0.750000000E 01
0.800000000E 01
0.670000000E 00
0.870000000E 00
0.104000000E 01
0.121000000E 01
0.138000000E 01
0.155000000E 01
0.172000000E 01
0.186000000E 01
0.200000000E 01
0.214000000E 01
0.228000000E 01
0.242000000E 01
0.256000000E 01
0.267000000E 01
0,281000000E 01
0#292000000E 01
0.680367651E 00
0.862544120E 00
0.103999370E 01
0.121271639E 01
0.138071219E 01
0.154398109E 01
Oa17025231IE 01
0.185633823E 01
0.200542647E 01
0.214978781E 01
0.228942227E 01
0.242432983E 01
0.255451050E 01
0.267996429E 01
0.280069118E 01
0.291669118E 01
-0.1036765HE.01
0.745587960E-02
0.630100000E-0?
.0,271638700^.02
-0.712185000E.03
~,601890800E-02
U.174768920E-01
0.366176600E-02
-0.542646900E-02
-0.978781400E-02
-0.942226800E.02
-0.432983100E-02
0.548949600E-02
-0« 996428600E*02
0.930882200E-02
0.330882100E-02
-------
LEAST SQUARES CURvt FIT
ORDER TOLERANCE SIGMA N
3 0.100000000E-02 0.776470968E-02 16
F VALUE = 0.435144521E 01
coefficients
0 0,^77829689E 00
1 0.397755512E 00
2 -0. U9396066E-01
3 0.^302608l8E-03
X (I) Y(I) F(X) Y-F(X))
0.500000000E 00
0.100000000E 01
0»150000000E 01
0.200000000E 01
0.250000000E 01
0.300000000E 01
0.350000000E *1
0.400000000E 01
0.450000000E 01
0.500000000E 01
0#550000000E 01
0.600000000E 01
0.650000000E 01
0.700000000E 01
0.750000000E 01
0.800000000E 01
0.670000000E 00
0.870000000E 00
0.104000000E 01
0.121000000E 01
0.138000000E 01
0.155000000E 01
0.172000000E 01
0.186000000E 01
0.200000000E 01
0.214000000E 01
0.228000000E 01
0,2A2000000E 01
0.256000000E 01
0.267000000E 01
0»281000000E 01
0.292000000E 01
0.673026326E 00
0.861075856E 00
0.104230097E 01
0,12l702*37E 01
0.138556875E 01
0.15^825681E 01
0.170541123E 01
0.185735472E 01
0.200440998E 01
0.214689969E 01
0.228514655E 01
0#24l9*7326E Ol
0.255020252E 01
0.26776570IE 01
0.280215944E 01
0.292403250E 01
•0.302632610E*02
0.892414450E.02
.0. 230097 300E«»02
-0.702437300£„02
•0.55687530OE»O2
0.174319200E.02
0.145887670E-01
0.264527600E-02
•0.440997700E-02
•0.6899688OOE-02
•0#51^655000E»02
0.526738000E-03
0.979748300E-02
•0.763701200E-02
0.784055800E-02
-0.403250300E-02
-------
least squares curve fit
ORDER TOLERANCE SIGMA N
4 0.100000000E-02 0.810379424E-02 16
F VALUE = 0.167851096E-.01
COEFFICIENTS
0 0.476346231E 00
t 0.400505548E 00
2 -0.162954878E-01
3 0.673166142E-03
4 -O.U2885480E-04
X(I) Y(I) F(X) r-F(X))
0.500000000E 00
0,100000000E 01
0.130000000E 01
0.200000000E 01
0.250000000E 01
0.300000000E 01
0.350000000E 01
0.400000000E 01
0.450000000E 01
0.500000000E 01
0.550000000E 01
0.600000000E 01
0,65000000QE 01
0,700000000E 01
0.750000000E 01
0.800000000E 01
0.670000000E 00
0.870000000E 00
0.104000000E 01
0.121000000E 01
0.138000000E 01
0.155000000E 01
0.172000000E 01
0.186000000E 01
0.200000000E 01
0•214000000E 01
0.228000000E Ol
0.242000000E Ol
0.256000000E Ol
0.267000000E Ol
0.281000000E 01
0.292000000E Ol
0.672608386E 00
0.861215169E 00
0.10426393IE 01
0.121733209E 01
0.138572338E 01
0.154822160E 01
0.170521375E 01
0.185706538E 01
0.200412063E 01
0.214670220E 01
0.228511134E 01
0.241962788E 01
0.255051023E 01
0.267799535E 01
0.280229876E.01
0.292361456E 01
-0.260838600E-02
0,878483120E-02
-0.263930500E-02
•0.733208800E-02
-0,572337600E-02
0.177840400E-02
0.147862550E-01
0.293461800E-02
.0.412063400E.02
-0.670219900E-02
-O.5111330OOE-O2
0* 372117000E«>03
0.948976900E-02
-0.79953*500E-02
0.770124400E-02
• W.361456400 E-02
-------
AXRS43
-------
GENERAL ROUTINE AXRJ&3
GHIERAL CORRELATION PROGRAM
T. A. Ebtzmlnger
PURPOSE; Ibis program computes simple correlation, partial correlation
and partial regression coefficients of a matrix.
RESTRICTIONS: l) A of 2k variables can be treated in each run.
2) Input to the computer is on cards.
ACCURACY: Single precision floating Jioint - with eight significant digits.
OPTIONS: Transformations may be made on any of the input variables by
inserting the proper automath statements in the appropriate place
in the source program deck.
INPUT: Data may be punched on cards in any format which can be suitably
described by the automath FORMAT statement.
CARD DECK SETUP:
1. Program source deck
2• Name card
3. Control card Card Column
No. of variables 1-2
Calculation route 3
one if simple correlation coefficients are required only.
Blank or zero for simple correlation, partial correlation
and partial regression coefficients.
4 • Data cards
5• Finis card
-------
OUTPUT: l) Matrix (*) of sums of squares deviations and cross products
2) Matrix (*) of simple correlation coefficients
3) Elements of the inverse of the simple correlation matrix
V) Matrix (*) of partial correlation coefficients
5) Matrix (**) of partial regression coefficients
6) Mean value of each variable
7) Total number of observations
* - only the upper triangular portion of this matrix is printed
** - printout for partial regression coefficients in this form:
r11.23^-~n, rll.23^—n, V12.3k—n, r21.3k—n. r13-2li n, etc
Reference - "Methods of Statistical Analysis,
Cyril H. Goulden - 2nd Edition
John Wiley & Sons
New York 1952
-------
DESCRIPTION &
PROGRAM LISTING
-------
NEWSTACK
COMPILES
SUBROUTINE CORREL
DlMENSIONX(24),A1(876) ,g(600) ,f?(8 76)
COMMON X,Al,NOELM,NCI»ND,INDl
C COMPUTATION OF CORRELATION MATpIX
ERASE ((R(I)~I=1«NOEL^))
IF(IND3)2»1 »2
1 PRINT 1221
60 TO 3
2 PRINT 1222
3 NCsNCI
NCOsNC
JJsO
K=1
MCA = 0
Nisi
NE = 1
J=0
Ms I
D0456L=1»NC
D0454IsNl»NCO
J = J*l
P(J)=Al ) * C -1 • 0 >
B(N+1)=(A1*(-1.0)
N = N*2
20 KsK*NCO-NCA
454 NCAsNCA+1
IF(IN03)460,459,460
*59 MsJ+mC
J = J*1
D0455MM=J,M
<~55 R(MM)sO.O
MMMsj*JJ
p(mmm)»i.o
JJsJJ+1
J = M
460 NlsNCO*l
«SN1
NCOsNCO+NC-NE
456 NEsNF+1
Nisi
NN=NCI
NE=1
DO 6 Ksl.NCI
PR INT1999 ,K
PRINT2000,(R(I),IsNl»NN)
IF(IND3>10,8,10
8 NlsrgN+l + NCl
m.nsimn+nci-ne*nci
GO TO 6
10 Ml«NN*1
-------
NNsNN+NCI-NE
6 NE»NF*1
IF (IND3>29»30»29
29 Nl=N0ELM*2
PRINT 1223
PR INT2000 • O(I) »Is I • M1)
GC TO 31
30 D07Isl,N0ELM
7 A1(I)=R(I)
31 RETURN
1998 FORMAT(5H ROW 12)
2000 FORMAT(1Ri7E17.9//)
1221 FORMAT(1M1/79H
1UE CORRELATION COEFFICIENTS////)
1222 FORMAT(1h1/79H
1AL CORRELATION COEFFICIENTS////)
1223 FORMAT(1H1/79H
1IAL REGRESSION COEFFICIENTS////)
END
END
JC9END
MATRIX OF SIMP
MATRIX OF PARTI
matrix of part
-------
compiles
SUBROUTINE INVERT
C MATRIX INVERSION By THE DOOLTTTLE METHOD
DIMENSIONX(24)»A1(876)»B(876).*0(24)
COMMON X,A1»N0ELM,NCI»ND,IND?
PRINT1333
REWIN06
NDaNCl
NC»NCI*2
M=NC-ND-1
MM = M
MPsNC-ND
NJ»NC-ND
NQsNC-ND
Ml* 1
NN«NC*1
NZ = 2
L2 = l
NT = NC
NX so
DO 12J=Nl»NG
300 DC 5lsNl,NC
5 0
-------
34 00 35 1 = IB«IE
K = K + 1
35 B(<)=A1(!)
B(K*l)sAl(III)
K s < ~ 1
IEN=IE-IB-1
lBME«-ND*l
IE«IB*IEN
JF(IEN) 14»34t34
14 Nisi
MsMM
NZ= 1
NC»NNC-NP# =x(lk)
20 LK«LK-1
C PR I NT*WRITE C PRIME MATRIX 0M WOR< TAPE
PRINT 1443,KK
1443 FORMAT(1H /6H ROW 12)
PRINT 801»(XO(I)»131•NJ)
WRITE TAPE6,(XO(I),I=1,NJ)
22 11 * 11~1
REWIND6
N0ELMsNCI*(NCI+1)/2
K = 0
Nl* 1
DO 23 JsltNJ
READ TAPE 6«(XO(I)~I = 1»NJ)
DO 24
-------
23 NlsNWl
RETURN
ROO FORMAT(I?*I3«I2)
801 FCRMAT{1R»7E17.9)
1333 FCRMAT(1M1/70H
1N6ULARIZE0 MATRIX ////)
1444 F0RMAT(1H1/70H
15E ELEMENTS ////)
END
END
J09END
-------
COMPIIEX
TITLEAXRSA3
C CORRECTED SUMS OF SQUARES AND CROSS PRODUCTS
C PARTIAL^ULTIPLE regression+corrflation
DIMENSIONX(2A)»A1(876),AVG(24)
COMMON X»A1«N0ELM»NCI»ND,IND?
C IF KIND IS BLANK-PROGrAM
C FOLLOWS NORMAL PATH-(COMPLETE PARTlALS'
C IF KTND =1 PROGRAM COMPUTES
c ss deviations^ meams and simple
C CORRELATION coefficients only.
100 REWIND 6
READ1000»NCI«KIND
IF END OF FILE 25»30
30 NC=NCI
N0ELM=NC*(NC*1)/2
ERASE((A1(K)»KS1« NOELM))
AN=0.0
1 READ1001*(X(I)»I=1»NC)
IF EmD OF FILE A,2
2 NC»NC
C INSERT TRANSFORMS HERE
1001 FORMAT(AF2»1)
C END OF TRANSFORMS
DO 3 I=1»NC
3 Al (I)=A1(I)+X(I)
ANaAM+1.0
WRITE TAPE 6, (X(I)»lsl,NC)
GO TO 1
A END FILE 6
REWIND 6
DO 5 1 = 1.NC
5 AVG(I)=A1(I)/AN
ERASF<(Al(K)«K=1«N0ELM))
8 READ TAPE 6 « (X(I)~I=1•NC)
IF END OF FILEA1,6
6 NN=1
11 = 1
K = t
DC91 = 11»NC
TEwp=X(n-AVG(I)
DC 7 J=NN»MC
Al (K)=TEMP*(X(J)-AVG(J) ) *A1 (k!)
7 K=K*1
NN=NN*1
9 I I=NN
GC TP fl
Al PRINT 1111
1111 FCRMAT(1H1/82H SUM OF SQUARES OF
1 DEVIATIONS AND CRO5S PRODUCTS////)
-------
45 Nisi
NNsNCI
NE«1
D046 <=1»NCI
PRINT1999
1999 FCPMATI1AH ROW 12)
47 PRINT2000» (Al {I) »I = NUN^)
Nl*NN*l
NN=NN*NCI-NE
46 NE«NE+1
15 JfV03 = 0
NOELMsMOELM + \'C*NC
CALL CORREL
IF(KIND)2003t2003»2005
2003 CALL INVERT
IND3 =I
CALL correl
2005 PRINT 2010
2010 FORMAT(IH0///60H
1 MEAN5//)
PRINT 2000*(AVG(I)• Ia1»NC)
PRINT2020
2020 FCRMAT<1H0///69H NUM
19ER OF OBSERVATIONS//)
PR INT3000 *AN
3000 FORMAT(560,F5.0)
GO TO 100
25 TYPE * 802
STOP
1000 FORMAT(I2»I1)
2000 FORMAT(1B»7E17.9//)
802 FORMAT(8HTHATS IT)
FND
PND
OVERLAY
stackcorpel
stackiiwert
jcbend
-------
SAMPLE
INPUT & OUTPUT
-------
INPUT TEST DATA
04
20711187
43721286
35731385
24841491
50651592
34761193
39871287
36681391
2569U88
27711592
407211*8
46731293
FINIS
FINIS
CARDS 303
-------
^' )'•! L
0.9*c^ )i
0 •
«:);¦; J
0.2<*^SC'J-'JOO£ ¦"):)
^ 0 W H
0.99-51^^6F: "> J
-').l 195*3 33 ife 01
- fSfJOJUOfc 00
"). 13?bOOOOJt 00
* 3«-' sCJiJAWt-S JF OtVlArlONS A'Jf) C«'Ji>b ^JD'JCTS
0.82S>JOO0O()fc.01 0.<»^lfc6h67t 00
0.2*OhJ33 *3h 00
-------
ROW 1
lOO^Ono^OE H -0. id Wf JK^hF. 00
SO.-. ?.
IJ. I'Vj'-'OOOOOc "U -f).^3Td939^<;F On
R D '¦'! -5
0. Ifi0"00!)0 3- CH O.XS^lfWSl^L 00
ROW
0. loj'icuono;: ;
MATRIX Of- M'^LE C'JKPfcl.AT I 3 M 1 C I EM \ b
0.5^9MOHOiifc-Jl n,15CU699^c OQ
0. I^09bni59fe 00
-------
r RI ANQULAKIZtO ma mix
o.iooocoonog n
o.oojocooooe r)
0. lOO'JQOOOOfc T1
0* OOOOC90COE ")J
0.9>>6 16*66 IE TO
0. lOOOCOO^OE 01
0.932*8^77E VJ
0.loo"OonnoE 01
0.9o2*9*M1F. 10
0. lOO'JOOOOOE T L
-0.18:»9«»3H*'JE 00
-0. leH9<»384at 00
-0.2^9dZ9H30E 00
-'J.Ziin57893*fc 00
0.26*>25829536<»^ IE 00
-0.16l"»l823vE 00
-0.1H0B6l<*3:JE 00
-0.539««80''iK-01
-0.539iaa0o3E_01
-0,929^7083819E-01
0.230&27043E-01
0, 15011699*c 00
0.150ll699<»t 00
0, lti39*38<»8t 00
0,1903H5609t 00
0.t 00
0.277301063c. 00
0.2855>36Wt 00
0# 3 1992 9V54t 00
O.lOOOOOOOOt m
O.lOOOOOOOOt 01
O.lOOOOOOOOt PI
0.1U3502026fc 01
O.lOOOOOOOOt 01
0, 1072
-------
RO^ 1
0,1(%7?^^?7£
ROW ^
T'l
ROil 3
0.16'Cn^HlMF-: 00
RCM '~
-0. Is0s6 *VJ
'),lFL 30 -0#ly086l^33t 00
D9270li*t*tA It 00 0.^^062 7U^3t-Ul
0, li6^7!>5»>7fc 01 -0. 319929954L 00
0,319^99 30 0.1l20
-------
j
-0.1 ") L
HOW ~
-0. 10 "i JOrvinfjf; ¦;) l
qO,x 1
-0, 10:)'.i000no^ U
RO,-,
-0, lO JUU'J-jnop
-0 , i 9\T-ll< 01- PARTIAL C W^~LAr I J * v_QdF KICI EN I S
0 , 1<»3:><£0 rniz 00 0,lS47f^3 70t. JO
0.2-i5'Jl>95i-7E:-Jl
-------
MATRIX Oh PARTIAL RtoRfcSSIO^ <-OtFF 1 CI EN T!>
-0. lOOOOoOOOf 01 -0.IOOOOOOOOE 01 -0. 199<*M<*672e 30 -0,l937l7 7Ut 00 -0. 1<*9 i0v033t 00 -0,13 79569^3E 00 0.1682002»0fc 00
0.l6l^lS239E n0 -<).iOOOOOOOOE 01 -0.IOOOOOOOOE 01 -0.2<»3970*6At 00 -0,2S2131862E 00 -0,226343736£-°1 -0.22368381.9Et01
-0.IOOOOOOOOE HI -0. IOOOOOOOOE 01. U. 2 f*s»l 16667E 01 0./3M6666 ?E 01 0, 12 7-jOOOOOE 01 0.894166667t Ol
NUMBER OF gfJSERVATinNS
12.
-------
AXRS49
-------
AXRSJ+9 MULTIVARIATE ANALYSIS OF VARIANCE
PURPOSE; Generalizes the univariate analysis of variance F test to
the problem of testing the significance of differences among groups.
Major computations are of - the null hypothesis of the equality
of g group dispersion matrices, - WHLKS' lambda and F-^ and F2 the
related significance tests.
LIMITATIONS: Ten groups consisting of not more than ten variables.
Input on cards.
ACCURACY; Single precision floating point computations truncated to
eight significant digits.
INPUT: 1. Control card #1 cc
Number of groups 1-2
Number of variables per group 3 -
2. Control card #2 cc
Number of variables per group 1-2
Number of observations per
variable 3 - T
3. Data cards (observations) in
group #1
4. Repeat steps 2 and 3 above for each
additional group to be analyzed.
5- FUJIS CARD
-------
OUTPUT: Printed output includes:
1. Program title and number of groups.
2. Group means, standard deviation and the dispersion matrix for each grout).
3. Log base e of determinant of each group dispersion matrix and corre-
sponding determinant.
U. Loc base e of determinant of pooled within groups estimate \' and
corresponding determinant.
5. Mean, standard deviation, dispersion matrix, and correlation matrix
for total sample.
6. Log base e of determinant of SS matrix and corresponding determinant.
7. Wilks' lambda and correspondine F values.
REFERENCE: This program, which was extracted from a text booh by
Cooley and Lohnes (Multivariate Procedures for the Behavioral Sciences,
Wiley 1962) has been modified for use on the Honeywell 400 computer.
A complete discussion, output symbols and mathematical procedures can
be found in the text.
-------
DESCRIPTION &
PROGRAM LISTING
-------
NEWSTACK
COVPII ES
subroutine ccrr
DIMEMSTONSX UO)*SSO(10»lO)fScno«lO]«DllOtlO)tR(10*ir))*
ixM{io»sn(iO)fH^05t405*375
375 PR I NT 376
376 FORMAT(39H RAW SU^S OF SQUARF5 AND CROSS PRODUCTS*
|NK = 1
GC TP 4
*05 PRJNT406
40* FCPMAT(45H DEVIATION SU-MS OF SQUARES AND CROSS PRODUCTS)
I NK = 2
RC TO 4
430 TF(Ll)700»700»435
435 DC441T=1,M
DC441j=I»M
D(I.J)=5SD(I*J)/(ENG-1«0)
441 D(JtT»sD(I»J)
c oispfrston matrix
450 PRINT451
451 FORMAT < 2?H VARIAMCF-COVARIANCE MATRIX)
I NX s3
r3c to 4
^75 DG486 I=1
D048A.I=I »M
R)
PR I NT 63*
-------
60 TO 26
19 PRINT20*TI*J5EC
20 FORMAT(1H1*A6*9H SECTION 13/)
26 PRINT27*
27 FORMAT(6H0 ROW 3B*lOlil)
DC 29 I = 1 *M
GO TO(231*242.253,264),INK
231 PRINT 30,1,(SS(I,J>,J=Jl,J2)
G0 TP 29
242 PRINT 30,1,(5SD(I,J)*J=J1*J2)
GO TO 29
253 PRINT 30,1 *( D (I ~ J) , J = Jl . J2)
GC TO 29
264 PRJNT 30,I,( R(I *J> *J = Jl*J2)
29 CONTINUE
30 F0RMAT(I6*4B*10F1W2)
TF(J2-M)9 * 32,32
32 GC TO (430,430,475*61)* INK
FND
END
JOBEND
CCMPTi. ES
SUBROUTINE EIGEND
PI MENSIONSX(10),SSO(10»10),SS(10,10),0(10*10) *P( 10,10 ) ,
1XM(10)*5D(10)«H(10»10)*U<10*10)
DI^ENSIOMIO(IO),X(10)
COMMONSX,SSD,SS,n,R,XM,SD,H,U,M,NG,TITLE
N = M
10 D014T=1,N
D014J=1*N
IF(I-J)1? * 11 * 12
11 U(I»J)=1.0
GO TO 14
12 UlI.JjsO.
14 ccnttnue
15 NR=0
IF(N-I)1000*1000,17
17 nMIIsn-I
D030 T = 1,MM I 1
X(I)=0.
I PL 1s T~1
DC30J=IPL1,N
IF(X(T)-ABSF(H(I,J))120*20*30
20 X(I)sftBSF(H(I * J))
IC (T ) = J
30 CONTINUE
PAP=7.450580596E-9
HDTEST=1.0E38
40 P070Isl*NMII
IF(I -1)60 *60,45
45 IF(XMAX-X
-------
GO TO 26
19 PHINT20 ~ TI« J5EC
20 FORMAT (1HUA6«9H SECTION I "3/)
26 PRINT27«(JX
27 FORMAT(6H0 ROW 3B ~ 101 11>
DC 29 T = 1«M
GO TH(231»242»253,264),INK
231 PRINT 30»I • (5S(I «J> »J = JUJ2)
GG TP 29
242 PRINT 30•I«(SSD(T•J)»J=J1«J2)
GO TO 29
253 PRINT 30 «I *( D (I * J)»J = Jl«J2)
GC TO 29
264 PRINT 30 • I » ( R(I~JNJ=Jl»J2)
29 CONTINUE
30 FORMAT(I6«4B«10F11*2)
IF(J2-M)9»32,32
32 GO TO (430»430»475»61)»INK
FND
END
JOBEMD
COMPILES
SUBROUTINE EIGEND
DIMENSIONSX(10)tSS0(l0«10)»SS(IO»10)»D(10»10)»R(10«IO).
1XM(10)«SD(10)«H(10•10)«U<10«10)
DIVENSIOMIO(10)tX(10)
CCMM0N5X~SSD»SS»n,R,XM,SO,TITLE
NsM
10 DO 14 T = 1
PC 14J=1«N
IF(I-J)1?»11 *12
11 U(I.J)=1.0
GO TO 14
12 U
-------
IF(X ma X)1000,1000*80
80 IF (HDTEST)90,90,85
85 IF (XMAX-hDTEST)90,90«148
90 HDIMIN=APSF(H(1»1))
D0110T=2,N
IF(HDIMIN-A05F(H(I,1)))110,110,100
100 HDIMIN = ABSF(W(1.1))
110 CONTINUE
hdtest=hdimin*pap
IF(HDTfST-XMAX)148,1000,1000
148 NfisNR*]
150 TANG = SIGNF(2.0« **2>)
C0SIMF=U0/SCRTF (1.0 + TANr,**2>
5INEsTANG»C0SINE
HII=H(IPTV,IPIV)
HCIPIV.IPIV)=C0SlNfc**2*(HII + TANG*(2,*H(IPtV,JPIV)~TANG*H
-------
390 H(I,JPTV)=-SINE*HTEMP*C0SINE«H=ARSF(H(I»JPIV))
IC(I)s JPIV
(50T0530
420 IF(I-JPIV)430 ,530 ,480
430 HTEMPsH(IPIV,I)
H (TPTV, I ) = CCSINE*HTEMP*SINF.*H (I , JPTV)
IF(X(1PIV)-A85F(H(IPIV,I)))440,450,450
440 X(IPIV)=ABSF(H(IPIV«I)>
IG
IG(IPTV)=I
500 H(JPTV,I)=-SINE*HTEMP*C0SINE*H(JPIV,T)
TF(X(JPIV)-ABSF(H(JPIV*I)))510,530,530
510 X(JPIV)=AB5F(H(JPIV,I))
IC(JPIV)si
530 CONTINUE
540 r>0550T = l,N
HTEMPsU(I»IPIV)
tJ (I ,TPIV) =COSINE#HTEMP*SINE#U(I ,JPIV)
5 50 U(I ,JPIV)s-SINF*HTEMP*C05IME»JU,JPIV)
r;CT040
1000 RETURN
FND
END
JOBEND
CCMPII Ex
TITLEAXRS49
CCWM0N5X,55D,SS,D,R,XM,SD,H,l',M,NG,TlTlE
DIWENSIONSX(IO)»5SD(10•10),55(10,10),D(10,10)»R(10,10),
1XM(10)•5D(10)»H(10•10)»U (10,]0)
DI MENSIONSUMT(10)»W(10»10)*T(10*10)
DIMENSION TITLE(12),X(10)
READ1«K»m
1 FORMAT(2 ! 2)
PR T NT2 ,K
2 FCRMAj(51H GENERALIZED ANALYSIS OF VARIANCE, NO, OF GROUPS = 12)
EN=0.0
ek=k
FRASF (5UMT,Vn,T,HiL0GS,6AlS,FAlS)
CiRCUPS = K
100 READ 2\ »TT,NG
21 FORMAT(F2.0,15)
READ22*(TITLE(I),1=1*12)
22 FORMAT(12A6)
PRINT22,(TITLE(I),1=1*12)
210 m=TT
FNCi = Mfi
002301=1,M
-------
220 5X(I)=0,0
00230.1=1 «M
230 SS(I,J)=0.0
CASES=EN6
240 READl001 ~ (X(I)•Isl*M)
DC 241 Is1»M
XU)=ARSF(X(I))
241 X(I)=LDGF(X(I))#0.43429448
1C01 FORMAT(3F8.0)
DC260l=l,M
5X(I)s 5X(I)*X(I)
D02fe0jsI
260 SS CI »J)=SS(I»J)+X(I)*X(J)
C RAW SUMS OF squares and cross products
CASES=CASES-1.0
IF(CASES)290,280,240
280 PC286 T s1,M
HC286J=I,7
SSD(I,j)sSS(I«J)-SX(I)*SX(J)/ENG
SS(J»T)=S5(I,J)
286 5S0(J«I)= 5SD(I•J)
C DEVIATION SUMS OF scuares ANO CROSS products
D029«5T = 1«M
XM(I)aSX
-------
PRINT9,DETER*
9 FORMAT (29H LOG DETERMINANT 0F GROUP D s FlsSS(I»J)-(SUMT(I)*5UMT(J)/FN)
C T{J «J) IS MOW THE TOTAL DEVIATION CROSS PRODUCTS MATRIX
D037J=1»M
D037 T s 1 ~ M
37 H(I»J)=SSD(I»J)
callftgend
D0371JsliM
D0371T=l»M
D(I»J)sU(I»J)
371 5S0(T.J)=H(l,j)
DETEDM=0.0
D038I=1«M
38 DETEPMsDETFRM+LOGF(SSD(I,I))
PR I NT38I*DETERM
381 FORMAT < 31H LCG DETERMINANT OF POOLED W = F14.7)
OETsFXPF(DETERM)
PRINT391*DET
391 FORMAT(17H DETERMINANT W = F19.7)
FM = M
WATE=LOGF(EN-EK)*EM
PRTNT382.WATE
382 FORMAT(10H WEIGHT = F14.7)
HlLOG=(DETFRM-WATE)*(EN-EK)
PRINT383,H1LCG
383 F0RMAT(9H H1L0G = F14.7)
XMW=M1L0G-H1L0GS
Fl = ."?* { EK-1 *0) *E^* (EM+1 .0)
A1As(FA1S-11.0/(EN-EO))*((2.0*(EM**2#0))~(3.0*EM)-1.0 J
Al=AlA/(ft»0*(E<-l»0)*(EM*l,0))
-------
A2= (GA15-(1.0/CEN-FK)*2.0)>*/(EN-1.0)
C P(I,J) IS NOVv THE TOTAL VARIANCE COVARIANCE MATRIX,
D0450 T = 1»M
D0450J=1»M
«50 R(I,J)sT(I,J)/SQRTF(T(I»T)*T(J,J))
00461s1,M
X M(11= SUMT{I)/en
46 5D{I)sSQRTF (D (I « I) )
PRINT47
47 FORMAT(22H MEANS OF TOTAL SAMPLE)
PRINT25,(XM(I)•Is1,M)
PRINT48
48 FORMAT(37H STANDARD DEVIATIONS FOR TOTAL SAMPLE)
PPINT25, < SD CI>»I = 1*M)
PRINT49
49 FORMAT(44H VARIANCE-COVARIANCE MATRIX FOR TOTAL SAMPLE)
50 PR INT25 <((D(Itj)«I = 1»M)»J=1,M)
PRINT52
52 FORMAT(36H CORRELATION MATRIX FOP TOTAL SAMPLE)
53 PRINT25,((R(I~JJ,1=1»M),J=1,M)
C
D054J=1»M
0C54T=1,M
54 H
-------
XLAMRsEXPF(XLAMBL)
IF(EM-2»0)573*573,57^
573 FU2.0MFK-1.0)
F2=2.0*(EN-EK-1.0)
Y=50PTF(XLAMB)
F=(1.0-Y)*F2/(Y*F1)
GCT0579
57^ 5 = 50RTF ( ( (EM**2)*(
-------
K
SAMPLE
INPUT & OUTPUT
9
-------
0303
0300005
89000.
16000.
25.
46000.
7600.
1.
76000.
300.
7.
69000.
2600.
7.
300000.
13000.
2.
0300005
uooo.
ROOO.
17.
11000.
4700.
42.
61000.
2800.
2.
5200,
300.
1400
18000.
300.
51.
0300005
92000.
1100.
3.
50000.
2100.
36.
240000.
1400.
1.
590000.
3800.
4.
KOOOO,
2200.
6.
locattqm i
LOCATTOM 2
LOCATION 3
CARDS 43fl
-------
GENERALIZED analysis of VARIANCE, no
LOCATION
CORRELATION ANALYSIS FOR
OF GROUPS
1
3
LOCATION 1
NUMBER OF VARIABLES = 3.
number of subjects in this group = 5
means of this group
<~,9617863 3,6181943 0.677*332
STANDARD DEVIATIONS of this group
0,3069251 0.7073527 0.5622055
RAW SUMS OF SQUARES AND CROSS PRODUCTS
500200 SECTION 1
ROW 12 3
1 123.47 90.05 16,7ft
2 90.05 67.46 12.09
3 16.78 12,09 3.47
VARIANCE-COVARIANCE matrix
500200 SECTION 1
ROW
1
1 0,09
2 0,07
3 -0,01
CORRELATION MATRIX .
500200 SECTION 1
0.07
0,50
• 0.04
.0,01
• 0,04
0.29
LOCATION
ROW
1 1.00 0.33
2 0.33 1,00
3 -0,05 -0.11
MEANS 4.96 3.62
STD DEV 0,31 0,71
LOG DETERMINANT OF GROUP D *
DETERMINANT D = 0,0121918
HlLOG FOR THIS GROUP =
FA1 FOR THIS GROUP =
GA1 FOR THIS GROUP a
-0,05
-O.ll
1.00
0.68
0.54
-4.4069946
CORRELATION ANALYSIS FOR
-17.6279782
0,2500000
0,0625000
LOCATION 2
NUMBER OF VARIABLES = 3,
NUMBER OF SUBJECTS IN THIS GROUP =
location
-------
MEANS OF THIS GROUP
4.167B782 3.1953177 1.6016853
STANDARD DEVIATIONS of this group
0.3953076 0.6751475 1.0279227
RAw SUMS OF SQUARES AND CROSS PRODUCTS
/iw/ 00 SECTT0N 1
ROW 12 3
1 87.48 66.86 31.93
2 66.86 52,87 23.82
3 31.93 23.82 17.05
variance-covariance matrix
/W/ 00 SECTION 1
ROW 1 2
1 0.16 0.07
2 0.07 0.46
3 -0.36 -0.44
CORRELATION MATRIX .
/W/ 00 SECTION 1
-0.36
-0.44
1.06
LOCATION 2
ROM
1
2
3
1
l.oo
0.25
-0.89
2
0.25
1.00
» 0 » 64
3
-0.89
-0.64
1.00
MEANS
4.17
3.20
1.60
STD DEV
0.40
0.68
1.03
LOG DETERMINANT OF GROUP D =
DETERMINANT D s 0.0017687
HlLCG FOR THIS GROUP =
FA1 FOR THIS GROUP a
gai for this group =
-6.3374859
-25.3499435
0.2500000
0.0625000
LOCATION
correlation amalysis for
number OF VARIABLES s 3.
NUMBER OF SUBJECTS IN THIS GROUP =
LOCATION
MEANS OF THIS GROUP
5.1919898 3.2863892 0.6P27270
STANDARD DEVIATIONS OF THIS GROUP
0.4085R19 0.2062767 0.5672603
RAW SUMS OF SQUARES AND CROSS PRODUCTS
-------
/W/ 00 SECTION
1
ROW 12 3
1 135.*5 85.49 17.16
2 85.4g 54.17 ll.3fl
3 17.16 11.38 3.62
VARIANCE-COVARIANCE matrix
/W/ 00 SECTION 1
ROW
1
1 0.17
2 0.04
3 -0.14
CORRELATION MATRIX «
/W/ 00 SECTION 1
0.04
0.04
0.04
.0,14
0.04
0.32
LOCATION
ROW
1
2
3
1
l.oo
0.53
—0.61
2
0.53
1.00
0.34
3
—0.61
0.34
1.00
MEANS
5.19
3.29
0.68
STD DEV
0.41
0.21
0,57
LOG DETERMINANT OF GROUP D = -10.3906692
DETERMINANT D s 0.0000307
HlLOG FOR THIS GROUP = -41.5626770
FA1 FOR THIS GROUP s 0.2500000
GA1 FOR THIS GROUP = 0.0625000
LOG DETERMINANT OF POOLED W = 3.1936105
DETERMINANT W = 24,3762791
WEIGHT s 7.4547200
HlLOG = -51.1333135
FOR TEST OF HI M=
F1 = 12.0000000
A2 - A1 SQUARED =
F2 = 123.8498301
FOR TEST OF Hi. F =
Al = 0.3611111
A2 = 0.0173611
B = 189.0728913
MEANS OF TOTAL SAMPLE
4.7738848 3.3666337 0.987*152
STANDARD DEVIATIONS FOR TOTAL SAMPLE
0.5704920 0.5663318 0.8246039
VARIANCE-COVARIANCE MATRIX FOR TOTAL SAMPLE
33.4072852
-0.1130401
2.2149437
-------
0.3254611 0,0943781 -0,3453174
-0.1833733 -0.3453174 -0,1*33733
correlation matrix for total sample
1,0000000 0,2921129 -0,7349*64
-0,3926629 -0,7340464 -0.392&629
LOG DETERMINANT OF T ! 4.3303371
0,0943781
0,6799717
0.2921129
1,0000000
0,3207317
1,0000000
determinant T =
l_ABMDA= 0.3208676
75,9698948
Fl = 6.0000000
F2 = 20.0000000
FOR TEST OF H2. F =
2.5512511
-------
AXRS59
-------
GENERAL ROUTINE AXRS59
NUMERICAL INTEGRATION - TRAPEZOIDAL RULE
T. A, Entzminger
PURPOSE; Confutes the area under a curve having the form
g = f(x) from x = o to n
n
f(x) dx
o
RESTRICTIONS: l) Function may have a maximum of 5 constant values.
2) Program deck must "be recompiled for each new
function by using a programmer defined function statement.
ACCURACY: Single precision floating point with eight significant
digits.
INPUT: Control card Card Column
1st constant 1-10
2nd constant 11-20
3rd constant 21-30
4 th constant 31-40
5th constant 41-50
Intervals for calculations 51-60
Maximum value of the argument (n) 61-70
Interval for printing 71-80
OUTPUT: Program prints the argument (x) and the corresponding area
under the curve "between limits o to n at each print interval
designated by the input.
-------
COMPtLEX
TITLEAXRS59
C NUMERICAL INTEGRATION TRAPEZniDAL &ULE
1 REAO 1000tCl»C2»C3»C4,C5,H»XMAX»PRTN
IF END OF FILE 7,10
10 KTR=n
PR INT3000
X = 0.0
PMAXsPRIN
FUNAsFUNF(Cl»C2»C3»C4«C5»X)/?."
FUNTaFUNA
2 X=X*M
FUNBsFUNF(C1»C2»C3»C4$C5,X)
IF(X-XMAX)3*6,6
3 TF(X-PVAX)5*4,4
5 FUNT=FUNT+FUNB
GO TO 2
6 KTPsJ
4 FUNPs(FUNT+FUNB/2.0)*H-(FUNB-FUNA)/1?.0*H**2
PMAX=X+PRIN
PRINT 2000*X,FUNP
IF(KTR-1)5 »1 ~ 1
7 TYRE,8
8 FORMAT(8HEND JOR)
STOP
1000 FORMAT(8F10.0)
2000 FORMAT(20B«E16,9 *20B~E16,9)
3000 FORMAT(1H1/40B* 2IHNU^ERICAL TNTEGRAT\ON//209»8HARGUMENT20B,
116MAPEA UNDER CURVE//)
FL'MF (C1»C2,C3,C4,C5,X)=SINF (X)
FND
END
JOBEND
INPUT TE5T DATA
.001 3,1415927
FINIS
CARDS 041
-------
ARGUMENT
numerical integration
area under curve
0.500000000E-01
O.IOOOOOOOOE 00
0.150000000E 00
0.200000000E 00
0.250000000E 00
0.300000000E 00
0»350000000E 00
0.400000000E 00
0.450000000E 00
0»500000000E 00
0.550000000E 00
0.600000000E 00
0.650000000E 00
OtTOOOOOOOOE 00
0.750000000E 00
0.800000000E 00
0.850000000E 00
0.900000000E 00
0.950000000E 00
0«100000000E 01
0*105000000E 01
O.ilOOOOOOOE 01
0.115000000E 01
0«120000000E 01
0.125000000E 01
0.130000000E 01
0.135000000E 01
O.UOOOOOOOE 01
0.145000000E 01
0,150000000E 01
0.155000000E 01
0.160000000E 01
0«165000000E 01
0.170000000E 01
0.175000000E 01
0.180000000E 01
0«185000000E 01
0«190000000E 01
0.195000000E 01
0t200000000E 01
0.205000000E 01
0.210000000E 01
0.213000000E 01
0.220000000E 01
0.225000000E 01
0.230000000E 01
0.235000000E 01
0.240000000E 01
0.245000000E 01
0.250000000E 01
0.255000000E 01
0
12«973533E«
>02
0
499582596E-
•02
0
112289U86E*
¦01
0
199334036E-
¦01
0
310875545E-
•01
0
446634816E-
•01
0
606272524E-
•01
0
789389656E-
¦01
0
9955285HE-
¦01
0
122417384E
00
0
147475*16E
00
0
174664315E
00
0
203916123E
00
0
235157726E
00
0
268311036E
00
0
303293187E
00
0
3A0016743E
00
0
378389912E
00
0
A18316782E
00
0
459697557E
00
0
502428807E
00
0
546403725E
00
0
591512397E
00
0
637642076E
00
0
684677^60E
00
0
732500986E
00
0
780993120E
00
0
830032657E
00
0
879497023E
00
0
929262&83E
00
0
979204950E
00
0
102919928E
01
0
107912062E
01
0
112884420E
01
0
11782A573E
01
0
122720174E
01
0
127558986E
01
0
132328915E
01
0
137018039E
01
0
141614637E
01
0
1^6l07220E
01
0
150484558E
01
0
1547357UE
01
0
158850054E
01
0
162817301E
01
0
166627539E
01
0
170271242E
01
0
173739304E
01
0
177023055E
01
0
1801U289E
01
0
183005278E
01
-------
0.260000000E 01
0.265000000E 01
0.270000000E 01
0.275000000E 01
0«280000000E 01
0*285000000E 0l
0.290000000E 01
0.295000000E 01
0«300000000E 01
0.305000000E 01
0.310000000E 01
0.314200000E 01
0.185688798E 01
0,188158140^ 01
0.190407132E 01
0.192430153E 01
0.194222U7E 01
0.195778635E 01
0.197095726E 01
0.198170127E 01
0.198999155E 01
0.199580735E 01
0.199913415E 01
0.199999890E 01
-------
AXRS68
-------
GENERAL ROUTINE AXRS68
TIME SERIES ANALYSIS AUTOCOVARIANCE,
AUTOCORRELATION AND POWER SPECTRAL ANALYSIS
PURPOSE: This program computes the autocovariance, autocorrelation,
power spectrum, cross-variance, cross-correlation and co-spectrum
of tine series.
RESTRICTIONS: l) Card Input
2) 500 discrete data pairs
3) Maximum of 100 lags
ACCURACY! Single precision floating point computations with eight
significant digits.
OPTIONS: Transformation of a variable can be marie by inserting the
proper statements between the transfora comment cards in the source
deck.
INPUT; Standard card format is seven fields of ten digits each; the
last ten digits are used for identification.
CARD DECK SETUP:
1. Execute card
2. Program Desk (Binary)
3. Control Card - Total number of observations of variable pairs
in card columns 1-3 and the maximum lag wanted in columns U-6. A
time interval (usually 1.0) appears in columns 7-17.
U. Data cards
5. FINIS card
-------
OUTPUT;
1. Printout of input data
2. Printout of autocorrelations
3. Printout of autocovariance
4. Printout of power spectral estimates
5. Printout of cross-correlations
6. Printout of cross-covariances
7. Printout of co-spectra
-------
DESCRIPTION &
PROGRAM LISTING
-------
CCMPILEX
TITLEAXRS68
DIMENSIQNW2( 51)«W3 ( 5l)»W4( 51)»W1( 5i)»X(1000)»
lY(lOnO). POWl( 50)»P0W2( 50) «POW3 ( 50) »5P1 ( 50) •
25P2( 50)»SP3( 50)*C1 ( 50)»C2( 50)»C3< 50)»C4( 50)
EQUIVAlENCE(X<1)tPOrtl)~(x( 51)»PfW2).(X(101)»P0w3)~
1C X(151)»SP1)»
-------
PI = B, 1415927
CALCULATE raw fstimates
TERM2=2.0*DELT/PI
2 ERASE(P0Wl.P0u2,POW3>
H=-1.0
POIOIHs1,MP1
HsH+1.0
D09IPsl«MPl
P=IP-1
IF CIP-1)^*5*4
5 EP=0.5
GO TO 8
4 IF(IP-MPi)7,5,7
7 FP*1.0
8 TERM=COSF(H*P*Pl/EM)
POW1(IHibPOWI(IH)*EP*W1(IP)*TEPM
P0W2UH)sP0W2(!H)+EP*W2*TEPV|
9 POW3(IH)sP0W3(IH)+FP*(W3(IP)*rf4(iP))*TERM
POW1(IH)= POWl(IH)*TERM2
POW2(IH)=POW2(IH> *TERM2
10 P0^3(IH)=POW3(IH)*OELT/PI
D015IH=1,MP1
IF (IH-1) 12»U»12
11 SP1.23*P0W1(IH*1)
SP2(IH)s#23*P0W2(IH-1)~,54*Prrf2(TH)+»23#P0W2(IH+1)
5P3 (IH) s,23*P0W3( IH-1) ~,54*P0W"? (IH)+,23*P0W3 (IH+1 )
15 CONTINUE
PRINT1004
COUNTS-1»0
nc?01=l,MPl
CCUNT=COUNT+1.0
20 PR TNT 1005»COUNT, P0W1 (I) »P0W2U> • P0W3U)
PR INT 1007
COIJNTs-1,0
0021t sl,MP1
CCUNT = COUNTM.0
21 PRTNT1006,COUNT,SP1(I).SP2(I),SP*
-------
T3-W1 (1)
DO 31 Is1»MPl
W1(I)=W1(I)/T3
W2(I)«W2(I)/T2
W3 (I)=W3(I)/T1
31 W4(I)sW4(I)/T1
PRINT 1011
1011 FORMAT(1H1)
PRINT 1010
PR I NT 1 OOP » (1^1(1) tW2(I) »W3(I) ,W4(I) »Isl,MPl)
IF0R<=1
GO TO 2
41 TYPE,1003
1003 FORMAT(8H JOB END)
STOP
1004 FOPMAT(1H1/10B22WRAW SPECTRAL ESTIMATES//
118B3hLA6i0B16hP0WER SPECTRUM 1
25B16HP0WER SPECTRUM 26B10HC0 SPECTRA//)
1007 FORMAT(1H1/10B27HSM0OTHEO SPECTRAL ESTIMATES//
11853HLAG10B16HP0WER SPECTRUM 1
25B16HP0WFR SPECTRUM 26B1OHC0 SPECTRA//)
1009 FORMAT(14B37HAUT0 COVArIANCE 1 AuTO COVARIANCE 2
113f3l6HCR0SS C0VARlANCE/56B12MPnSlTlVE TAU8B12HNEGATI VE TAU//)
1010 format(14B38hauto correlation i auto correlation 2
112B17HCROSS CORRELATION/?6912HOOSITIVE TAu8B12HNFGATIvE TAu//)
1005 FORMAT(10B4E20«9)
1006 FORMAT(10B4E20.9)
1009 FORMAT(10B4E20.9)
1000 FORMAT(2I3»F10,0)
3002 FORMAT ( 1m1/40b23HP0wER SPECTej^ ANALVS!S////10Bl0HlNPUT DATA//)
FND
END
jobemd
-------
f
SAMPLE
INPUT & OUTPUT
-------
INPUT TE5T DATA
075030 1
• 0
00*1
070
069
062
061
063
062
062
0*9
060
0062
066
066
066
066
069
066
064
064
063
0063
083
0 R 8
086
086
084
086
091
093
092
0064
080
078
0*7
091
086
083
088
090
089
0071
064
062
062
062
062
062
063
066
072
0061
320
482
482
376
362
415
374
4S1
565
0062
380
478
500
255
349
454
470
4^1
439
0063
376
386
307
356
375
408
474
504
438
0064
485
509
499
530
402
3 94
411
435
4?1
0071
434
448
423
403
525
699
438
438
351
FINIS
059
059
059
061
065
066
UU
060
059
066
071
074
079
Ull
095
094
092
087
079
079
UU
086
088
082
075
069
060
Ull
076
085
084
083
083
085
Ull
498
430
429
444
444
405
A22
410
410
409
424
292
437
A22
440
429
416
413
447
479
A22
411
544
480
435
457
440
A22
356
389
436
367
461
416
A22
CAPDS 161
-------
POwE" SPECTRUM ANALYSIS
INPUT DATA
7,0
6.9
6.2
6.1
6.3
6.2
6.2
5.9
6,0
5.9
5.9
5.9
6.1
6.5
6.6
6.6
6.6
6,6
6,6
6.9
6,6
6.4
6.4
6.3
6.0
5.9
6.6
7.1
7.4
7.9
8.3
8.8
8.6
8.6
8.4
8.6
9.1
9.3
9.2
9.5
9.4
9.2
8.7
7.9
7.9
8.0
7.8
8.7
9.1
8.6
8.3
8.8
9.0
8.9
8.6
8.8
8.2
7.5
6.9
6.0
6.4
6.2
6.2
6.2
6.2
6.2
6.3
6,6
7.2
7.6
8.5
8.4
8.3
8.3
8.5
32.0
48.2
48.2
37.6
36.2
41.5
37.4
45,1
56.5
49.8
43.0
42.9
44.4
44.4
40.5
38.0
47.8
50,0
25.5
34.9
45.4
47.0
46.1
43.9
41.0
41.0
40.9
42,4
29.2
43.7
37.6
38.6
30.7
3 5.6
37.5
40.8
47.4
50.4
43,8
44.0
42.9
41.6
41.3
44.7
47.9
48.5
50.9
49.9
53,0
40.2
39.4
41.1
43.5
47.1
41.1
54,4
48.0
43.5
45.7
4^.0
43.A
44.8
42.3
40.3
52.5
69.9
43.8
43,8
35.1
35.6
38.9
43.6
36.7
46. 1
41.6
-------
AUTO COVARTANCE I
AUTO COVARTANCE 2
0. 134397155E 01
0.128772394E 01
0, 118785858E 01
0.106697289E 01
0.926484780E 00
0.777291300E 00
0.64514535IE 00
0,534<)63738E 00
0.435451329E 00
0.334573899E 00
0.241806906E 00
0.162547195E 00
0.120453842E 00
0.110245650E 00
0,111049210F 00
0.116239556E 00
0,119874773? 00
0.876836172E-01
0#3705066A7E-01
-0,487167929E-01
-0.154606707E 00
-0#255023407E 00
-0.378275957E 00
-0.525489503E 00
-0.677331031E 00
•0.800531553E 00
-0.925i38l757E 00
.0.103444655E 01
•0.108059850E 01
-0,105404402F 01
•0.100200414E 01
0
411686219F
02
0
12593A120F
02
0
601929915c
.01
0
139784444F
01
0
138911048E
01
0
442180318F
01
0
621899518F
00
0
847220915F
00
0
310527828F
01
0
595ft54950F
01
0
4A7067008F
01
0
342359096c
01
0
132452064F
01
0
2S4345018E
01
0
2g2119493F
00
0
109472223F
01
0
5O9O11375c
01
0
178546130c
01
0
4fll67228lF
01
0
3299°4444F
01
0
213984647p
01
0
175472099E
01
0
44394?24lF
01
0
843436582c
01
0
6fl560q626F
01
0
568122222E
01
0
352557459F
01
0
267778888F
01
0
796081040F
01
0
14746A213F
01
0
460577778E
01
CROSS
positive taj
-0.402924444E 00
-0.274706186E 00
-0.110335467E-01
0.661352222E 00
0.104973196E 01
0.125192063E Ol
0.16792780TE Ol
0.256374601E Ol
0.289994534E Ol
0.293843555E Ol
0.288775521E 01
0.256867444E 01
0.228564613E 01
0.222974595E Ol
0.200037362E Ol
0.200691999E 01
04239618545E 01
0.233367157F 01
0.179625778E 01
0.106287683E Ol
0,846720808E 00
0.736472592E OO
0#10471684 ^E Ol
0.160928598E Ol
0.205116497E 01
0.228047645E Ol
0.200327002F Ol
0.120359944E Ol
0,915403876e 00
0.309973720F 00
-0,5l7208889P 00
COy/ARI ANCE
NEGATIVE TAU
-0.402924444E 00
-0.824825105E 00
-0.857645418E 00
-0.704453333E 00
-0.699770391E 00
-0.246959364E 00
-0.155587632E 00
-0.961265348E-01
-0.345720331F 00
-0,3l26l^949E 00
-0.624923760E 00
-0.975160971E 00
-0,121850201E 01
-0,156428416E Ol
*0#139791709E 01
w0,121884000E 01
-0.135245183E 01
-0.141999739E 01
-0.127046971E 01
-0.154963746E °1
-0.186866343E Ol
-0.177900395E 01
-0.154752084E 01
-0.129788837E Ol
-0.552390587E 00
0.185505779E 00
0,5138659^3E 00
0.547774446E 00
0,842064fl71E 00
0.669744737E 00
0.806518520E 00
-------
PAW spectral estimates
LAG POWER
SPECTRUM 1
O.OOOOOOOOOE
00
0
0.100000000E
01
0
0.200000000E
01
-0
o,300noooooF
01
0
0.400000000E
01
0
0,500000000E
01
-0
0.600000000E
01
0
0.700000000E
01
0
0 , 800000000E
01
0
0.900000000E
01
-0
0,100000000E
02
0
0,11OOOOOOOE
02
-0
0.120000000E
02
0
0.130000000E
02
-0
0.140000000E
02
0
0,150000000E
02
-0
0.160000000E
02
0
0,170000000E
02
-0
0,180000000E
02
0
0,190000000E
02
0
0.200000000F
02
0
0,210000000E
02
-0
0.220000000E
02
0
0,230000000E
02
0
0,240000000F
02
0
0,250000000E
02
-0
0,2ftOOOOOOOE
02
0
0,270000000E
02
-0
0.280000000F
02
0
0.290000000E
02
0
0,300000000E
02
0
9R0047562F 00
8ft 11286fl5p 01
H90754R3F 00
2A206fl719E 01
526573766F 00
763278F-0l
331536625F-02
114848712F-01
107112923§~01
194361002F-01
719695123E-02
642pl2749F-02
1 SO132256F-02
123Q83201E-01
POWER SPECTRUM 2
CO SPECTRA
0.505792247E Ol
0,336283569E 02
0,1776650*5F 02
0,544467795e 01
0#272686398E 02
0.184126674E 01
0.43883867iE 02
0.300746600E 02
0.132Q99443E 02
0.260085964E 02
0,100071314^ 02
0,104755052E 02
0.B12977282E Ol
0.285901663E 02
0.925531447E Ol
0.114659656E 02
0.527161593E 01
0.216627062E 02
-0.122484155F 01
0,20902031&F 02
0,139148756^ 02
0,965566924F Ol
-0,148126158E Ol
0.501665321F Ol
0.464321528E Ol
0.945258720E Ol
0,602108585F Ol
-0,l40l23552E Ol
0.700341960F Ol
0.573906102E Ol
0,l65729240E 02
0,826002837E 01
-0»558702618E 00
-0,158408633E 00
-0.605685541E 01
-0.211007279E 01
-0.376337828E 00
-0.247220091E 01
0.335347283E 01
-0.567276577E 00
-0.500709203E 00
0,107297245E 00
-0,236l62l90E-01
-0.676891327E-01
-0.312317845E-01
0.1535271P5E 00
0.203372590E 00
-0.768807726E-01
0.570575963E 00
-0.160270514E 00
0.457357964E 00
-0.101753709E 00
0,186736951E 00
-0.166718740E 00
0.199004696E 00
0.108841576E 00
0.143228990E 00
0.173606870E 00
0.680751459E-01
-0.503536026E-01
-0.248871020E 00
0.503845590E-01
-------
smoothed SPECTRAL ESTIMATE?
lag
0
OOOOOOOOOE
00
0
100000000F
01
0
200000000F
01
0
300000000E
01
0
400000000E
01
0
500000000E
01
0
600000000E
01
0
700000000E
01
0
800000000E
01
0
900000000E
01
0
100000000E
02
0
llOOOOOOOE
02
0
120000000E
02
0
130000000E
02
0
140000000E
02
0
150000000E
02
0
160000000E
02
0
170000000E
02
0
180000000E
02
0
I9OOOOOOOF
02
0
200000000E
02
0
210000000F
02
0
220000000E
02
0
230000000E
02
0
240000000F
02
0
250000000E
02
0
260000000E
02
0
270000000E
02
0
280000000E
02
0
290000000E
02
0
300000000F
02
spectpu^ 1
458241763E 01
-------
AUTO CORRELATION l
AUTO CORRELATION!
0.100000000F
01
0
0.958148210E
00
0
0.8S3842055E
00
-0
0,793895440E
00
-0
0.689363387E
00
-0
0.578353983E
00
.0
0,480029024E
00
0
0.398046921E
00
0
0.324003383E
00
0
0.248944182E
00
0
0.179919661E
00
0
0.120945413E
00
.0
0.896252917E.
-01
0
0.820297496E'
-01
-0
0.826276494E-
-01
-0
0.864895959E'
-01
.0
0.891944276E'
-01
.0
0. 652421676E'
-01
-0
0.275680439E'
-01
0
0 • 36248381 IE'
-01
0
0.1150371S7E
00
-0
0.189753575E
00
-0
0.28l46l2fl3E
00
-0
0,39O99749OE
00
.0
0.503977209E
00
-0
0.595646205E
00
.0
0.688914699E
00
.0
0.769693787E
00
.0
0.804033762E
00
0
0.784275542E
00
0
0.745554580E
00
.0
IOOOOOOOOH 01
305903172F 00
14621O849E-02
3?9541228e-01
3374U718E-01
107407122F 00
15106153^E-01
205792877F-01
75^282785^-01
144686638E °0
113452184F 00
831ft02033F-0l
321730624F-01
617812805E-01
709568306F-02
265Q117g8F-01
I?3fe406l5p 00
4^3694696E-01
116999855F 00
801349254E-01
519776075E-01
426227771P-01
lf)7q35827F 00
204R73650E 00
166536696E 00
137998844£ 00
856374207E-01
650444139F-01
193370825F 00
358205367R-01
111R75928F 00
CROSS CORRELATION
POSITIVE TAU NEGATIVE TAU
-0.541683259E-01
-0,369309294F-Ol
-0.1483327UE-02
0.88910R198F-01
0.141123785E 00
0, 16830561lF 00
0.225758657E 00
0,34466469lE 00
0,38986263^E 00
0,395037176E 00
0.388223815F 00
0.345327260E 00
0.307277522E 00
0,299762417e OO
0.268926077E 00
0.269806158E 00
0.322138198E 00
0,31373396lE 00
0.241485167E 00
0.142890954E 00
0.U3831388E 00
0.990098465E-01
0.140779155E 00
0.216349067E 00
0.275754361E 00
0.306582519E 00
0.269315463E 00
0, 161809^1lE 00
0,l2306499?E 00
0.416722235E-01
-0,695324894e-01
-0.541683259E-01
-0.110887775E 00
-0.115300070E 00
-0»947052437E-01
-0#9407567fl7E-01
-0,332007043E-01
-0.209168782E-01
-0.129230518E-01
-0.464779236E-01
-0.420273048E-01
-0.840134531E-01
-0.131098617E 00
• 0,16381288IE 00
-0.210299115E 00
-0,l8793307iE 00
-0,163858319E 00
-0.181820816E 00
-0.190901502E 00
-0,17079931OE 00
-0.208330043E 00
-0.251219233E 00
-0.239165598E 00
•0.208045489E 00
•0,174485419E 00
-0.742622438E-01
0,249390119E-01
0.690830706E-01
0.736416594E-01
0.113205453E 00
0.900390921E-01
0.108426676E 00
-------
RAw SPECTRAL ESTIMATES
LAG
O.OOOOOOOOOE 00
0.100000000E 01
0#2000000n0F 01
0.300000000P 01
0,400000000F 01
0.500000000E 01
0.600000000F 01
0.700000000E 01
0.800000000F, 01
0.900000000F 01
O.lOOOOOOnOE 02
0.110000000E 02
0,120000000E 02
0.130000000E 02
0,140000000? 02
0.150000000E 02
O.UOOOOOOOE 02
0.170000000E 02
O.leOOOOOOOE 02
0.190000000E 02
0,200000000E 02
0.210000000F 02
0.220000000E 02
0.230000000E 02
0,240000000E 02
0.250000000E 02
0.260000000E 02
0.270000000F 02
0,2BOOOOOOOE 02
0.290000000E 02
0,300000000P 02
SPECTRUM 1
7?92l7490F 00
655615579E 01
140ft84i40F 00
194995734E 01
391804251F 00
5P3<970951F-01
177516296F 00
634374515E»01
l629835g3F 00
690900841F-01
4*6933l99P-0l
406784999E-01
4272l44llP-0l
260o78995F-0l
691562892p^01
2<>5436l55F-0l
368052009E-01
37453Q577F-02
134*46388F-01
986229494p»02
81>767l9lE-02
955957607F-02
122445511F-01
246684263E-02
8?4547lft5F-02
796988037E.02
144ftl6900E-0l
550380073F-02
478367867E-02
111707899F-02
9?25l357lE-02
POWER
0
0
-0
0
0
-0
0
0
0
.0
0
-0
0
-0
0
.0
0
-0
0
0
0
-0
0
0
0
.0
0
-0
0
0
0
POWER 5PECTRUm 2
CD SPECTRA
0.122858678E 00
0.816844366E 00
0,43155451 IE 00
0.132253102E 00
0.6&236464SE 00
0.447250030E-01
0,10659542*E 01
0.730523849F 00
0.323060227E 00
0.631757761E 00
0.243076667F 00
0.254453627E 00
0,197474980e 00
0.694464983E 00
0.224814775E 00
0.278512252E 00
0.128049366E 00
0,52619459^ 00
-0.297518231E-01
0.507717543E 00
0.337997120E 00
0,234539530p 00
•0,359803537E»01
0,121856234e 00
0.112785298F 00
0,22960659
-------
5MP0THED SPECTRAL ESTIMATES
LAG POWER SDECTPUr* 1
0
OOOOOOOOOE
00
0
0
100000000E
01
0
0
200000000E
01
0
0
300000000E
01
0
0
400000000E
01
0
0
500000000E
01
0
0
600000000E
01
0
0
700000000E
01
0
0
800000000F
01
0
0
900000000E
01
0
0
iooooooooe
02
.0
0
110000000E
02
.0
0
120000000E
02
0
0
130000000E
02
0
0
140000000E
02
0
0
150000000E
02
0
0
160000000F
02
0
0
170000000E
02
0
0
180000000E
02
0
0
190000000E
02
0
0
200000000F
02
0
0
210000000E
02
-0
0
220000000E
02
0
0
230000000E
02
0
0
240000000E
02
0
0
250000000E
02
0
0
260000000E
02
0
0
270000000E
02
0
0
280000000E
02
0
0
290000000E
02
0
0
300000000F
02
0
34096091 IE 01
36756A679F Ol
lfl804*658F 01
111073459P 01
646403151F 00
9^8692923^-01
967R80764F-01
112571196F 00
867110348E-01
102270446F-01
U523R154E-02
2090994Q8F-02
771100636F-02
116390122E-01
2«52?68477F-0l
100375903F-01
129083359F-01
9^^414941^-02
868859176F-02
103010707E-01
446936817E-02
471959797E-03
498072888E-02
61138O029F-02
3*4R85612e-02
9R7911814E-03
4710365O2E-02
145438239F-02
l?7424048F-02
392524996F-02
549542962F-02
POWER SPFCTRUM 2
CD SPECTRA
0.442092095E 00
0,56861099lE 00
0.451331853E 00
0.323018082E 00
0.398381874F 00
0,421664845E 00
0.753922524E 00
0.713956205E 00
0.487777292E 00
0.471360676F 00
0.335090019E 00
0.238731838E 00
0.324R87770F 00
0.472137735E 00
0.345184743E 00
0.231555369E 00
0.254229232E 00
0.306753514E 00
0.221733806E 00
0.345063891R 00
0,353237572^ 00
0.196H5203E 00
0.625416347E-01
0.834675034E-01
0.141740512E 00
0,1*3566658E 00
0.123958418F 00
0.543853297E-01
0.116096829E 00
0,2069938AlE 00
0,281509230e 00
0.565097998E 00
0,209948093E 00
-0.216057744E 00
-0.509849461E 00
-0.352102838E 00
-0,16900R015E 00
-0.874179158E-01
0,1494674R0E 00
0.470272305E-01
-0.505726184E-01
-0,842311868E-02
-0#489742849E-03
-0.660993255E-02
0,386857084E-03
0*164682512E-01
0.171340964E-01
0,183497750E-01
0,340889167E-01
0.201493846E-01
0.251005995E-01
0,125289191E-01
0.525508298E-02
-0.175783094E-03
0.1Z6574365E-01
0.184836281E-01
0.191314304E-01
0.191369241E-01
0.875309592E-02
-0.924583339E-02
-0.180662026E-01
-0.11732B020E-01
------- |