A COMPREHENSIVE, MATRIX FREE ALGORITHM FOR
ANALYSIS OF VARIANCE
by
William J. Hemmerle
Institute of Statistics Mimeo Series #1212
A CCMPBEHEm IVE, MATRIlC FREE ALGORITHM FOR
ANA~S
IS OF VARIANCE
SAMPLE PROBLEMS
The following simple examples have been prepared principally to.
illustrate the different features of the program - options, model specification, computations, output - in maIIY different combinations.
They do not
necessarily represent the most likely use of the program in analyzing each
set of data.
The unbalanced data sets used in the first two examples were
taken from Searle [19 ~.
The first data set is llsed in Chapter 7 to illustrate
the two-way classification with interaction.
The second is used in Chapter 6
to illustrate the two-way nested classification.
The third example involving
balanced data with 2 crossed factors, 2 nested factors, and interaction terms
•
a~ars in Appendix B of
T~se
e.
1 1
1
1 1
1';.
1
1", •
1
4
;.
7.
1 4 11 •
1
1
"'"" .:" "
::
2
2
;
The 'final example, a Latin square, was
extracted from Statistical Methods by G. N. Snedecor (5th Edition, page 308).
sample problems have all been rup in batch mode.
F (A .81 l. ( I ( J ) • J (41 ),
CAlA F:RlwAl ANu II\PvT CATA(lx.2IZ.FIl.C)
,'.
C12J .
--- ---- '"
4
4
'"
c.
12.
1.2.
14.
s.
7.
1 ~.
10.
liJ.
14. '..
11 •
1 J.
•
!
j
1
o
C
O.
(S(Sl.2.A.C.R)
CELL SuMS. FRECUE~CIES, A~D ~EANSCELL
SuM
FF<EO.
MEAN
1
C.3000CJOOO 02
3.
0.10000JOOO 02
2
(MISSING CELL)
3
(.120000000 02
1.
O.IZOOOvOOO 02
4
0.180000000 02
2.
0.<;00000000 01
5
C.lbOOOOOOO 02
2.
0.<;00000000 01
c
0.260000000 02
2.
0.130000000 02
7
(MISSING CELL)
8
(MISSING CELL'
S
(MISSING CELL)
Ie
(.160000000 02
2.
0.800000000 01
11
0.300000000 O~
2.
0.150000000 02
12
C.48CeOOeOo 02
4.
0.120000000 02
CLASSIFICPTICN SUMS. FREQUENCIES. AND MEA~S­
1.
2
;:;
C .CCO COO-COD 02
C.440eOOCOo 02
e.<;;40eOOOOo 02
6.
4.
e.480000000
0.420000000
e.42000000(;
(.660(0000D
5.
4.
8.
0.100000000 02
0.11000JOO(; 02
0.117500000 02
.J
2
;:;
..
I
j
•
I,
4
02
02
02
02
0.1<;8000000 03
CFTICNS- S= 8. T=O.0500.
3.
6.
0.96000JOOO
0.105000000
0.140000000
0.110000000
01
02
02
02
18.
0.110000000 02
1=100. R=I. V=O. G=O. P=O
~+A(I)+E(J)+AB(IJ)
E/I; LIST-
ITE"ATIC~
H
2
.::3
4
TrE RA/IIK CF
Aa (1
J'
T~E
~ (;~SIGN MATRIX IS
8
1. SSF(FULL MCOEL'=
0.226000000 04.
SSE (FULL MeDEL)=
0.560000COO 02
E/F LlST-4
2
2
1
TRACE=
4.000000000
I1EFATICN
TRACE=
4.815000000
I1EFAT~C~
TFACE=
5.S4~113426
1IEFA'ICN
lRACE=
5.88t175169
ITEFATICN
TFACE=
5.seS797E08
THE RANK CF T~E r DESIGN MATRIX IS
6
FI;C~ RANK CCMP~TA'ICNSOF(NU~)=
2. OF(OEN)=
10
I'EFATIC~
1. SSFH=
0.1415<;E870 04
ITERATICN
2. SSF<H=
0.le60~~790
04
ITEFATION
3. SShr=
0.203,5(670 04
I1E"~lICN
4, SSF<H=
0.211805740 04
1IEFATIG~
5. SSF<H= 0.215668170 04
11E~ATIJN
6. SS~H= 0.218117400 04
ITE~ATIC~
7. SSF<H=
0.21S47122D 04
ITE~ATIC~
8. SSRH=
0.220344350 04
I1ERATIO~
9. SSF<H= -0.220937140 04
ITEFATICN
10. SSRH=
0.2213e449D 04
1IE"ATICN
11. SS"H=
0.2216=~50D 04
ITERATIC/II
11. F=
3.879 • FROB(F) .GT. 0.0559 VS. F LEVEL OF 0.0500
SSR(~EDUCEC MOOEL)=
0.2216==500 04
ITEFATIC~
~
,II ( 1 )
E.lR LlST-
O.
1.
2.
3.
4.
4
-3
,
1
C. TRACE=
ITE~ATIC~
1. TRACE=
ITE~ATIC~
2. TRACE=
ITERATIC~
3. TRACE=
ITERATIC~
4. TRACE=
TrE RANK CF T~E r DESIG~
ITERATIC~
c.cctcc6c67
7.C~7222222
7.Sc7en4784
7.ESC480000
7.S8S7S7654
MATRIX IS
8
O. OF(OEN)=
DF(~U~)=
10
O. TRACE=
c.(OCCOOOOO
I,ERATICN 1. TRACE=
c.tffeb6667
I1E~ATIC~
2. TRACE=
7.407407407
ITERATIC~
3. TRACE=
7.eeZ944673
ITERATIC~
4. TRACE=
7.SSE432683
ThE ~A~K CF T~E H CESIGN MATRIX IS
8
O. OF(DE~)=
F~G~ ~A~K CCMPUTATICNS- DF(hUM)=
10
FFC~
~ANK
H
caMP~TATICNS-
E(J)
E/R LIST4
::
-2
1
ITERATIC~
O(P)
S= 8. T=C.OSOO. 1=100. R=I.
r.
AS ( I J )
E/o; LISTGFTIG~S-
-4
::
2
V=O. G=O. P=1
1
O. TRACE=
4.000000000
ITERATICN
1. TRACE=
4.E7SCOOOOO
ITERATIC~
2. TRACE=
S.54~113426
IlERA1IC~
3. TRACE=
E.e86175169
ITERATIC~
4. TRACE=
5.SE5797608
THE RANK OF ThE ~ DESIGN MATRIX IS
6
2. OF(OEh)=
10
FRCM RA~K CGMP~TATICNS- DF(~UM)=
ITERATICN
1. SSRH=
0.1415ScE70 04
I1ERATIC~
2. SSRH=
0.IE6053790 04
ITERATICN
3. S5RH=
0.203750670 04
ITERATION
4. SSRH=
0.'11S05740 04
ITERATICN
5. SSRH=
0.215868170 04
ITERATIC~
6. SSRH=
0.21S117400 04
I1ERATIG~
7. 5SRH=
0.219471320 04
ITERATICN
8. S5RH=
0.,20344350 04
ITERATIO~
9. S5R~= 0.220937140 04
ITERATIG~
10. SSRH=
0.'213E4490 04
I1ERATICN
11. SSRH=
0.,21655500 04
ITERATIG~
12. SSRH=
0.221E760S0 04
ITERATICN
13. 5SRH=
0.22203S290 04
I1ERATIC~
14. SSRH=
0.222160910 04
ITERATIC~
15. SSRH=
0.222251910 04
ITERATIC~
16. SS~H= 0.2223201S0 04
ITERATICN
17. SSRH=
0.222371500 04
ITERATIGh
18. S5RH=
0.222410130 04
ITEhATICh
19. S5~h= 0.2224~922D 04
ITERATICN" 20. SShH=
0.22246116D 04
ITEHATICN
21. SShH=
0.222477690 04
I1EhATICN 22. SShH=
0.22249C170 04
ITERATIC~
23. 55RH=
0.2Z249~5S0 04
ITERATICh
24. SSRM=
0.222506690 04
ITERATIC~
25. SSRH=
0.222512050 04
ITEo;ATICh
25. F=
~.114 • PROB(F) .GT. o.oeeo VS. F LEVEL OF 0.0500
SSR(hEOUCEt MOCEL)= 0.22251~050 04
ITERATIC~
C(z.V.G)
OFTIQI\S- S= 8. T=0.0500.
M+A(ll+E(J)
1=100. R=I. V=I. G=I. P=1
TrE
CF TrE ~ OESIG~ ~ATRIX IS
6
64. SS~(FULL MeoEL)=
0.222528570 04.
SSE{F~LL MCOEL)~
0.Y07142850 02
ES1I~ATES OF EXFEeTEO CeLL MEANSCELL
ES~IMATEC MEA~
1
0.571467750 Cl
2
0.855742230 01 (MISSING CELL)
3
0.13285C800 C2
4
0.1028:~COO 02
5
C.l0S2817~0 C2
6
0.110709150 02
7
0.154585740 02 (MISSING CELLI
8
0.124588530 02 (~ISSING CELL)
5
0.976643890 01 (MISSING CELL)
10
C.9S2518~30 01
11
0.143568410 02
12
C.113571210 02
~ANK
ITERATIL~
G-l~VERSE
SCLUTIL~­
A
-".109508470 01
0.111840E40 01
-0.2.23237080-01
8
-0.15705570::> 01
-0.142821260 01
0.295944500 01
-0.275454840-03
2
3
4
0.11380720C 02
F(A.S) L(I(2).J(3»
CATA FORMAT A~O I~PvT OATA(IX.212.F4.0)
1
1
5.
•
1 2
8.
1 2 10.
1 2 9.
2 1
6.
2 1 10.
2 2 6.
2 2
2.
~;;:
1.
2 2 3.
2.3
3
3.
7.
;2
o
0
O.
O(z.C.P.v.G)
CLASSIFICATIWN SU~S.
I.
0.320000000
1
0.400000000
2
.J
0.2.::>0000000
1
0.390000000
2
0.10000000e
3
!
,j
i
i
:1
~
!
I
:\
~
••
1
F~EQvEN(IES.
AND
MEA~S-
02
4.
\)2
8.
0.800000000 01
0.500000000 01
02
02
02
3.
7.
2.
0.766666670 01
0.557142860 01
0.500000000 01
12.
0.600000000 01
C.720000000 02
8. T=0.0500. 1=100. R=I. v=o. G=O.
OPTIa~s- ~=
M+A ( I )+E
E/F< LIST-
(1 J)
p=o
3
<:
1
5
CF ThE ~ DESIG~ ~ATKIX IS
1. SSFO(FULL MCDEL)=
0.516000000 03.
ITEFOATICN
SSE(FlJLL MCDEL)=
0.260JOOOOD 02
H
811,,11
E.lf< LIST-~
_
-<:
1
T~E FOANK CF ThE h oESIG~ MATFOIX IS
2
F~C~ FOA~K CCMPUTATIJNS- DFl~UM)=
3. of(DEN)=
7
ITEkATIC~
1. SSRH=
0.456000000 03
ITERATICN
1. F=
5.38:*. Pf<OB(F) .GT. 0.0311 VS. F LEVEL
SSf«KEOUCEC Mvu~L)= 0.456C(COOO 03
h
Al n
E/K LIST-
n,E.
~
K ANK
2
-:;
ITEf<ATICN
ITEf<ATICN
,f
I
•!I
-2
1
o.
TRACE=
4.1ftt66t67
1. lKACE=
4.305::5556
ITERATIC~
2. TKACE=
4.517746~I4
I1EKATICN 3. TRACE=
4.7fi431~61
ITERATICN
4. TRACE=
4.945912107
T~E KANK CF T~E H DESIGN ~A1KIX IS
5
FkC~ RA~K CCMPUTATICNS- DFCNUM)=
O. of(oEN)=
7
OIZ.V.G)
vFTIC~S- S= 8. T=0.0500. 1=100. R=I. V=I. G=I. p=o
M+A(J)+ElIJ)
THE RANK CF THE M oESIG~ MATf<IX IS
5
ITEf<ATICN
1. SSK(FULL MeoEL)=
0.516JOOOOO 03.
SSECFULL MeoEL)=
0.260000000 02
ESTI~ATES OF EXPECTED CELL MEANSCELL
ES1I~ATfO MEAN
1
(.500COOOOO 01
2
C.SO(COOOOC 01
:;
u.OOGCOOCOO 00 (~ISSING CELL)
4
0.900000000 01
5
C.300COOOOO 01
6
(.5COCOOOOO 01
G-INVERSE SO~UTICN­
B
0.'::'::3333330 CO
0.433333330 Cl
.:: -C.4f666667C 01
4
0.3~~333330 01
5 -C.2t:666667C 01
c· -0.ct666667D 00
1
I
<:
A
1
2
-C.50CCOOOOO 00
0.50(COOOOO 00
1
C.51666t:t:7D 01
ClG)
s= a. T=0.0500. 1=10C. R=I. V=I. G=O. P=O
M+A ( l )
2
T~E kANK CF ThE M DESIGN MATRIX IS
1. SSk(FULL MCOEL)=
0.456000000 03.
ITEkATIC'"
SSE(FULL NCOEL)=
0.860000000 02
ES1I~ATES OF EXPECTED CELL MEANSCELL
ESTl~ATEC MEAN
1
c.eooocooOO 01
2
O.EOOOOOCOD 01
3
c.ecccoooOO 01 C~ISSING CELL)
OPTIC~S-
~F
0.0500
4
e
C
to
Tt-E
F~C~
C.5CCCCOCOD 01
C.5CCCOOCCD 01
C.5CCCCOOOD 01
All)
~A~K
~A~K
CF TtoE t-
CESIG~
COMF~TATIC~S-
ITERATION
SSRl~EDUCEC
1. F=
MCOEL)=
~AT~JX
CFl~U~)=
2.7~1
IS
1
1.
DF(OE~)=
• PROblF)
0.4~2CCOCOD C3
10
.GT. 0.1231 VS. F
LEV~L
OF 0.0500
f.
e
2 1 1 t.3C
2 1 1 f.3~
~
1 1 7.00
;: 1 1 S.05
:: 1 2 t. ~5
:: 1 2 :.90
Z 1 2 :.67
2 1 ;: f.::;O
2 :: 1 ~ •..:O
2 2 2 1 f.l0
;: 2 :: 1 (;.50
2 2 2 1 f.S5
2 2 2 2 t.l0
2 2 2 2 f.l0
2 2 2 2 f.::;O
2 2 (.7:
0 C C 0 0.00
C(Z.A.Cofi.\I)
CELL. SUMS. Ff;EOUEI\CIES. AND ~EA"SFfiEC.
MEAN
SUM
CELL
0.606000000 01
0.242400COO 02
4.
1
0.631250000 01
0.o2502~00COO 02
4.
2
4.
0.69250000D 01
C.277000000 02
3
0.697500COO 01
4
0.27<;00000.:> 02
4.
0.607000000 01
4.
5
C.242800000 02
4.
0.601500000 01
t
0.240600000 02
4.
0.650000000 01
C.260000000 02
7
4.
0.745250000 01
E
C.2<;810000D 02
0.59850ClOOO 01
0.2.39400000 02
4.
S
0.575000000 01
<:.230000000 02
4.
10
4.
0.600000000 01
0.240000000 02
11
4.
0.619750000 01
0.247 ... 00000 02
12
4.
0.71750JOOO vI
12
0.287COOOOO 02
0.610500000 01
14
0.244200000 02
4.
0.f21250000 01
0.24E500COO 02
4.
15
4.
0.631250000 01
0.252500COD 02
16
CLASSIFICATICN SU~So FREQUENCIES. AND MEA"SI JK.
0.4'.>4<;00(.00 02
8.
o .i:l8625000 01
1
0.69500;)000 01
0.~5i>COOOOO 02
8.
2
:;
0.604250000 01
0.483400000 02
8.
0.55810COOO 02
8.
0.697625000 01
4
0.469400000 02
8.
0.586750000 01
5
B.
0.609B75000 01
C.487,"00000 02
6
0.664000000 01
8.
7
0.531200000 02
0.626250000 01
8.
0.501000000 02
E
IJ.L
8.
0.649250000 01
0.519400000 02
0.664.375000 01
8.
2
0.531500000 02
8.
0.628500000 01
0.502800000 02
.3
0.673.375000 01
'I
0.53E700000 02
8.
0.599250000 01
8.
0.479400000 02
5
0.597375000 01
0.477<;00000 02
8.
6
0.669375000 01
8.
7
0.535500000 02
8.
0.620875000 01
0.4<;6700000 02
8
IJ ••
0.656812500 01
0.105C,,"OGOD 03
16.
0.650lii37500 01
16.
0.104150000 03
2
lb.
0.598312500 01
C.<;57;;'00000 02
3
0.t:4512500C 01
0.10::,,20000 C3
16.
4
2
2
2
2
2
2
2
2
.
.. .
,-J
'Ii
41
II
1.KI..
s.
0.606500000
0.616375000
0.67125JOOD
0.721375000
0.65800JOOO
0.592750000
0.610625000
0.625500000
01
01
01
01
01
01
01
01
02
0..3
0;:
02
16.
16.
16.
16.
0.611437500
0.696312500
0.t25375000
0.618062500
01
01
01
01
4
0.102220000
0.lC7020000
0.101490COO
0.574600000
03
03
C3
02
16.
16.
16.
16.
0.f38075000
0.668875000
0.f34312500
0.609125000
01
01
01
01
1
2
0.20<;240000 03
0.1<;8<;50COO 03
32.
':2.
0.653875000 01
0.621718750 01
1
2
3
4
5
f
7
8
0.481800000
0.482500000
0.517COOCOO
0.526900000
0.529600000
0.4E4800000
C.508500000
C.550600000
02
02
02
02
02
02
02
02
1
4
C.C;643COOOD
0.104':90000
0.101460COO
0.105910000
2
.;
4 .
0.<;<;88COOOO
0.100<;40000
C.I03830000
0,.10.3540000
2
3
"
5
f
7
8
0.485200(00
0.4<;;310uJ00
C.53700JOOO
0.577100000
C.526400000
0.474200000
0.4685COCOD
0.500400000
02
02
02
0,
02
02
02
02
8.
8.
8.
8.
8.
8.
0.976300000
0.111410000
C.I0.CC60COD
0 ... 86900000
8.
I.K.
2.
3
4
1 •• L
2
:3
I •••
• JKL
,
1
i
(
,
8.
0.602250000
0.603125000
0.646250000
0.658625000
0.66225,)000
0.606000000
0.635525000
0.68825JOOO
01
01
01
01
01
01
01
01
02
0":
03
0';;
16.
16.
16.
16.
0.602687500
0.6524.37500
0.634125000
0.6619.37500
01
01
01
01
02
03
0;:
03
16.
16.
16.
16.
0.624250000
0.630875000
0.648937500
0.647125000
01
01
01
01
1
2
0.200820000 03
0.207370000 0:::
':2.
32.
0.627562500 01
0.648031250 01
1
2
3
4
0.101160000
0.<;67'::00COO
0.102550(;00
0.1077::;0000
0.3
02
03
03
16.
16.
16.
16.
0.632250000
0.604562500
0.64093750.:»
0.673437500
1
2
0.1<;7890000 0.3
0.210300000 03
'-::2.
0.618406250 01
0.657187500 01
1
2
0.20.3710'00 03
0.204480000 03
'::2..
8.
8.
8.
8.
8.
8.
8.
• .JK.
2
3
• J.L
• .J ••
• .KL
•.K.
1
f
t
~
'!
~2.
01
01
01
01
••• L
32.
0.6365<;;3750 01
0.639000000 01
0.637796880 01
64.
0.408190000 03
OFT 1 C"5- 5= 8. 1=0.0500. 1= 100. R=O. V=O. G=O. P=O
M+A(II+e(IJI+C(KI+AC(IKI+E~(IJKI/
+C( 1JL HCO( IJKL)
E/R L1ST4
2
5
4
11
1. SSRIFULL MCDEL)=
~~EIF~LL MCDEL)=
7
ITEf.<ATICN
~
294
C.2017914::!0 04.
0.195237750 02
7
2
5
4
7
2
5
4
2
All)
E/f; lIST4
7
.2
:
4
11
2
-9
4
1. DF(OEN)=
48
ITERATIC~
1. SSRH=
0.2clc2599o 04
ITERATIC~
1. F=
4.06S*. PROBCF) .GT. 0.046f VS. F LEVEL
SSPCf,EDUCEC MCDEl)=
0.261625990 04
FR:~
RA~~
CCMF~TAIIC~S-
OF(~UM)=
~F
0.0500
H BOJ)
E/R LIST4
7
.2
-5
...
11
2
9
4
7
2
2.
-5
3
RANK CCMP~1~TICNS- DFl~UM)=
2. DF(DEN)=
48
ITEf;ATICN
1. SSR~= 0.2flcl~36o 04
ITERATICN
1. F=
2.18S • PROBCFI .GT. 0.1212 VS. F LEVEL OF 0.0500
SSRCREoUCEC MOoEL)=
C.26161~~6D 04
CCZ)
OPTICNS- 5= 8. 1=0.0500. 1=100. R=O. V=O. G=O. p=o
H CCK)
FRC~ RANK CCMP~TAIIC~SoFCN~M)=
I.DFCOEN)=
48
ITERATION
1. F=
:.916*. PROBlF) .GT. 0.0178 VS. F LEVEL ~F 0.050u
SSRCREDUCEC MCOEL)=
0.261550790 04
H AC I I K)
,
FRC~ RANK CC~FUTATIONSDFCNUM)=
1. DFIDEN)=
48
ITERATIC~
1. F=
8.358*. PROBCF) .GT. 0.0059 VS. F LEVeL uF 0.0500
SSRCREDUCEO MODEL)=
0.261451490 04
4
Fh[~
H B C C I.J~)
RANK CCMPUTATIC~S- oFI~U~)=
2. DFCDEN)=
48
ITERATION
1. F=
0.982 • PROBCF) .GT. 0.3837 VS. F LEVEL uF 0.0500
SSR(REOUCED MeDEl)=
0.2c17J1540 04
H DC I JL)
FRC~ RANK COMPUTAIIONS- DFCNUM)=
4. DF(DEN)=
48
ITERATICN
1. F=
1.131 • PROS(F) .GT. 0.3534 VS. F LEVEL OF 0.0500
SSRCREDUCED MODEL):
0.261607500 04
H CDCI.JKL)
F~C~ HA~K CG~F~TATICNS- OFCNU~)=
4. DFCOEN)=
48
ITERATICN
1. F=
1.605 • Pf;OBlF) .GT. 0.1873 VS. F LEVEL uF 0.0500
SS~lHECUCEO MODEL)=
0.2615J023D 04
FRC~
Ollt.G)
5= e. T=0.0500. 1=100. R=O. V=l. G=I. p=o
"'.AlJ l+CCK) ... CCIKJ
ITERATICN
1. SSRCFULL MCDEL)=
0.261088330 04.
SSECFULL MeDELI=
0.2c5548c60 0,
ESII~ATES OF EXPECTED CELL ME"NSCELL
ESTIMATED MeAN
1
0.6114J750D 01
2
C.611437500 01
3
0.6S6~1250D
Cl
4
0.6S6312500 01
5
0.611437500 Cl
6
0.C1143750C C1
7
C.696J1250D Cl
e
0.6S6J1250D 01
S
0.62537500C 01
10
0.625J7500D 01
11
C.618C62500 01
1,
0.618062500 01
13
0.t2537500D 01
CFTIC~S-
,
Id
~i
F(R.C,T) L(1(3),J(~I,K(3»
CATA FGR~AT A~C l~PUT DATAl1x.;;I2.FtI.OI
1 1 1 ECE.
1 2:2
EES.
1 3::: StlC.
2 1 2
715.
:: :: ::: lC:E7.
2 _
;(;(;.
;:! 1;:
;; 2
E41i.
711.
COO
O.
C(Z.",.V.GI
O~TIC~~- S= 8. T=C.0500.
1~100.
1<=1. v=o. G=O. P=O
~+R(I)+C(J)+T(K)
E.I'" LIST-
e
0
VECTCI'<
1.
VEeTD'"
!;.
VECTOR
S.
VECTOR
11.
VECTel'<
15.
VECTOI'<
Ie.
VECTe" 21.
VcCT'::1'<
22.
VECTOR 2(;.
ThE I'<ANK CF
ITEI'<ATIC~
ITE"'AT1C,,"
I TERATIC""
I1EI'<ATIC~
ITEI'<ATll:i~
ITEf<AllC ....
ITERAT1G~
ITE"'ATIC ....
ITE:RA1ICN
ITEI<ATIO'"
I1E:RATICh
ITERAT1GN
ITEf<ATIC'"
I'lERATIG'"
»'
..
,
O~
5
0
~
:2
ITERATIC"'S
e. TI'<ACE=
ITERATICNS
6. TRACE=
ITERATIG .... S
6. T"'ACE=
ITEf<ATICNS
6. TRACE=
ITERATIONS
6. TRACE=
ITE"'A'lICNS
6. TRACE=
ITERATIC"'S
6. 'll<ACE=
ITEl'<ATICNS
6. TRACE=
ITERA1IC .... S
6. TI'<ACE=
T~E ~ DESIGN MATRIX IS
1. SSRM= 0.34562(;510 07
2. SSR~= 0.4S92:::E290 07
3. SSR~= 0.567510190 07
4. SSI'<~= 0.5S78~3260 07
5. SSRM=
0.611;:!;:SOEO 07
6. SSJ;M= 0.61733276C 07
7. SSRM= 0.61SSS(;620 07
8, SSJ;M= 0.621180560 07
S. SSI'<M= 0.621706750 07
10. SSRM= 0.021940(;20 07
11. SSJ;M= 0.622044560 07
12. SSRM= 0.6220SC750 07
13. SSRM= 0.622111290 07
14. SSI'<M= 0.622120410 07
1
0.771783175
1.54356E350
2.31534S525
3.0E71326SS
3.858915874
4.6::l069C;OtlS
5.402482224
6.1742653S,
6.946048574
7
e
I1EI'A1I:",
llEFiATICI\
ITEFiATIO'"
IIEFiATlC'"
ITEF<ATICI\
ITEI'ATlO'"
llEFiATIC'"
ITEF<ATICI\
ITERATICI\
IIEI<ATIC/'<
ITEI'ATIC/I.
I1ERATIC"
ITEF<A1ICtITEkATION
"
15, 551''''=
0.622124470 07
Ie, S SF<"'= 0.0,212(270 07
17. 5SFiM=
0.62'127C7O 07
IS. 551''''= 0.622121430 07
19, SSF.IWI=
0.622127580 07
20. 55 Fi 001=
0.6221271050 07
0.622121690 07
21. 5SFiIWl=
22, SSI'IWI=
0.622121700 07
23, 5SI< .... =
0.622127710 07
24. SSFi ....=
0.622127710 07
25, SSk/Wi=
0.622127710 07
26, 551''''=
0.622127710 07
27. SSFiM=
C.62212771O 07
27. SSF«FULL MCoEl.)=
0.622127710 07.
S5E(FuLL MCoEL)=
0.48428<;oeo 04
R(I)
E.lR LIST-
coo
-:
0
3
2
1
F<ANK OF T~E ~ DESIGN MATI<IX IS
5
FkC~ RA"K
CC .... PLTATIC/l.5- OF(I\U~I=
2. DF(oEN)=
2
ITEI'ATICI\
I. S5kH=
0.c21E3769o 07
ITEF<AiICN
1. F=
1.218 • PkOS(F) .GT. 0.450S VS. F LEVEL OF 0.0500
S5R(F<EDUCEC MODEL)=
0.621537690 07
~.
CI.J)
E .... " LISTT~E
o
0
e
5
0
_
2
1
ThE FiANK CF THE ~ CESIGI\ MATF<IX IS
5
F~C~ F<A/l.K COMPUTATIC/l.S- OF(I\U/Wi)=
2. DF(DEN)=
ITERATIC/I.
1. SSF<~= 0.617406360 07
ITERATICI\
1. F=
S.74<; • PF<OB(FI .GT. 0.09<;6 VS. F LEVEL OF 0.0500
SSF«REOUCEC MOoEL)=
0.611406360 07
~
l ( K)
E.lR LISl-
o
0
0
5
0
3
-2
1
RANK OF ThE H OESIG/I. .... ATRIX IS
5
FF<C~ RA/l.K CCMPuTATICNS- oFC"U/WI)=
2. DF(DEN)=
ITERATION
I. SSRh=
0.611784090 07
11ERATICh
1, F=
21.358 • PROS(F) .GT. 0.0541 VS. F LEVEL OF 0.0500
SSFilFiEOUCEC IJ.CDEL)=
0.611784090 07
T~E
E