• •

ANALYZING EXPERIMENTAL DATA BY REGRESSION X SAS: Annotated Outputs

BU-705-M

May 1980

S. Aref and W. W. Piegorsch Riom0trics Unit, Cornell University, Ithaca, New York

Abstract This annotated output was created to assist the student in learning how to use the SAS computer package. It is intended as an aid to the student in a course covering the methods of data analysis, as presented in Analyzing Experimental Data by Regression by D.M. Allen and F.B. Cady. SAS programs for nine data sets from Allen and Cady's book were developed. They were tied as closely to the text as possible and were written to show several different methods of analysis. Hence, the programs do not always demonstrate the most efficient and logical way of doing the data analysis. Rather, they illustrate different aspects of the methods presented in the book.

•

BU-705-M in the Biometrics Unit Mimeo Series, Cornell University, Ithaca, New York .

• •

Data Set Arsenic Firefly Electricity load Leafhopper Lymphocyte Fat digestibility Protein nutrition Swamp pH Soybean physiology

-TAB-LE -OF CONTENTS
Model 1 variable
2 variable
3 intercepts, 1 variable
1-way analysis
22 factorial
22 factorial 1-way analysis nnequal numbers 2-way analysis unequal numbers covariate analysis

Units in Book~~
4, 5, 6 10,11,13
13 16 17 17 18 18 18

Page 1-9 10-21 22-38 39-44 45-49 50-63 64-71 72-88 89-102

•

*D.M. Allen and F.B. Cady, Analyzing Experimental Data by Regression.
For SAS programs the following version was used: SAS User's Guide (1979). J.T. Helwig and K.A. Council, editors. SAS Institute, Inc., Raleigh, North Carolina .

S T A T I S T I C AL ANAL YS I S S yS T r M
fJOTE: TilE JOB VMPJQ001 HAS BEEN RUN UNDER RELEAS[1._9o2f?_ CF SAS 1\T C_QRtJ(!,L UNI_vERSITY.

2 DATA ARSENIC; (VNl'fS. If,{";')

3 INPUT X1 Yl

If X0=1; Sd 1>. cui~"'"' of / 1( 011]~ fDr __ftrrn-fr~~ tb_t _ _X _r1~+r(~-· _~AS- GJ.M_ sup~lr't.S

5 CARDs;

f~s own.

NOTE: n/\T/\ SET WORK.I\RSENIC HAS 10 OBSERVATIONS AND 3 VARIABLES. ~65 oBS/TRKo NOTE: THE DATA STATrM~NT USED 0.21 SECONDS AND 116Ko

®1167
18

TITLE ARSENIC Pf<OC PRlNTI

DATAl.
Prrtit

-- . X-t"f11l.fr-l.x

for

~e.Ju'l

Wtcde} ·

VARIAE3LES XO I

NCJTE: THE PkOCEOURE PRINT USED Oo13 SECONDS AND 116K AND PRINTED PAGE 1,

~~ ($)-
21 22

PRoc GLM;

./.fopiT~ pr-iwfs Vi1 ~~·,{~,·-~,-)!;,roth. t.

Y~UDOT~GT y- ~~~~~EDWIN1 T

Pt£_ -------
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·------------------- ------
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NOTE: OAT/\ SET WORK.NrW1 ~lAS 10 OBSERVATIONS AND 5 VARI/\8LES. 296 OBS/TRK.

NOTE: THE PROCEDURE GLM USEr. 0.30 SECONDS AND 184K AND PHlNTED PAGE 2o

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24

.NOTE: THE PROCEDURE PLOT USED 0.20 SECONDS AND 124K AND PRINTED PAGE 3•

25 ~ 26 'od:!J

NOTE: THE PROCEDURE PRINT USED Ool6 SECONDS AND 116K AND PRINTED PAGE If,

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28
29 30

PROC GLMI MODEL Y""X1/P I ·fe.~res.s OUTPUT OUT=NEW2 RrSIOUAL=krSID2

NOT~: n.II.T/\ SET ''ORK.NF"\~2 HliS 10 OBSEPV/\TinNS nND 7 VARIABLES. 217 085/TRKo NOTE: Tfl[ PROCEDURE Gt M USED 0.31 SECONDS AND 186K A-ND PKitHED PAGE 5o

31 IP\
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NOTE: THE PROCEDURE PLOT USED o.23 SECONDS AND l24K AND PRINTED PAGE 6o

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34

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NOT[: THE

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OEPENDFNT VARIABLE; Y SOURCE
MODEL _.fe,-:ej.S,.OYI..
ERROR Ruid~~.Als UNCORRFCTED TOTAL

OF
1 9 10

R-SQUARE --------·--
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c.v.
6i>.1813

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ARSENIC DATA

•

GENERAL LINEAR MODELS PROCEDURE

Re~ress YO)'\. Xo (no ,'v..fu-t.tpi)

SUM OF sQUARES

MEAN SQUARE

F VALUE

PR > F

26.50384000 9.22296000

26,50384000

25,86 --- -- -~ .. _000]' _____ --------

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35, 72680_000

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Y MEAN
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SOURCE
xo

OF

TYPE I SS

F VALUE -- --- PR > F

1

26.50384000

25.86

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xo

OF TYPE IV SS F VI\LUE PR > F

1

26,50384000

25.86 · - o.ooo1

PARAMETER
xo

T FOR HO:

FSTIMATE

~ PARAMETER:o

=f -------i~F.2800000

5oOCJ

PR > IT I
0,0007

STO ERROR OF ESTIMATE
·0.32012081

OBSERVATION

OOSERVEo ~ VIILUE ~

-----·- ·--·
1

--- ·- 3.19000000 ·- ---

2 3.26000000

3 1.82000000

,4
5
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1.02000000
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1.34000000

8 0.79000000

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L

1.62800000 1o62B00QOO 1.62800000 lo62A00Q00 1.62800000 lo62800000 lo6280D000 1,62800000 1.62800000 1.62800000

SUM OF RESIDUALS
SUM OF SQUARED RESinUALS
SUM OF SQUARED RESioUALS - ERROR SS fiRST ORDER AUTOCORRELATION OURBIN•WATSON 0

-RESIDUAL~~·-~~~ -=~,--~
1.56200000 1.63200000 Uol9200000 -U.60ROOOOU Do22200000 Oo42200000 -0.28000000 -0.83800000 -0.96800000 -1.32R00000
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ARSENIC DATA
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11 21 31 41 51 61 71 81 91 10 1

2 I+
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DEPENDrNT VARIABLE: Y SOURCE

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SUM OF SQUARES

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•

..- MODEL ERROR

1

6.88257399

6.88257399

23.53 . --- _ -~~·oop

8 2.34038601 0.29254825

CORRECTED TOTAL
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R-SQUAifE--

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b, = M 0 • 0 7 815 0 6 8 ') ..

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0 • 0 01-i

lc.o"'tpC<re '-''-1-h NOTF:S: pp. ~.9-10.

STD ERROR OF ESTIMATE
-- 0,31071996 __ _ 0.01611225

OBSE:RVATION

OBSERVEn

'Jt·----· ------ ---- --- ----------- VALUE

"PREDICTED VALUE _lfi-

1 2
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7
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10

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0.68637679 -0.44102050
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0.3.3603425 0.09493833 -0.29876032 0.11829444
0.22719851

- --- --- -SUM OF RESIDUALS
SUM OF SQUARED RESinUALS SUM OF SQUARED RESioUALS - ERROR SS FIRST ORDER AUTOCORRELATION DURBIN•WATsON 0

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P~UUREGENERAL LINEAR MODELS

fesre ss Y 0~ X, cuvl !.1 ("o

i11terc.e.ft)

SOURCE

OF SUM OF SQU/IRES

MEAN SQUARE

F VALUE

MODEL

2 33.386413'39 16.69320699 57.06

ERROR'
UNCORRrcTED TOTAL
~ow.p()..n
R-SQUARE

8 / 2.34038601

10 ~~5. 72680000

wrfl-, NOTeS: f· &.)
c.v.

STD DEV -·-- -·

0.29254825 Y MEAN

0.93'+'+92

33.2234

0.54087730

1.62800000 z '4

PR > F
0,0001 __
--·-·-- -·. ---·------

•

SOURCE

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1 ?--- 6.88257399
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@ s ____ OF _____ . TYPE

90.60 23.53
F VALUE

1

25.24177252

86.28

1

6.88257399

23.53

>PR F . --------- - - - - - - - - -
0.0001 o.oo13
PR > F
0.0001 0.0013

PARAMETE.R
xo
Xl

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L0 :-2.118622593
bl " - 0 • 0 7 8 1 5 0 6 8

T FOR 110:
---· PA.. RAMETER=O
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PR > Ill
o.ooo1 o.oo13

STD ERROR OF
-ESTI~ATE
0.31071996
o. 01611225

-OBSERVATION

OBSERVED VALUE

PREDICTED VALUE

1

3.19000000

2.72992457

2

3.26000000

2.57362321

~

1.82000000

2.26102050

4

1.02000000

2.10471914

5

1.85000000

1.94841778

6

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7

1.34000000

1.24506167

A

0.79000000

1.08876032

q

0.66000000

0.54170556

10

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,().07280149

SUM OF RESJQUALS SUM OF SQUARED RESIDUALS
SUM OF SQUARED RESinUALS - ERROR SS FIRST ORDER AUTOCORRELATION ·ouRBIN•WATMN 0

RESIDUAL
0.46007543 0.68637f,79 -0.44102050 -1.08471914 -0.098<+1778 0.33603425 0.09493833 -0.29876032 0.1182944'+ 0.22719851
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--·--o
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DEPENDFNT VARIABLE: Y

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GENERAL LINE~R MODELS P EDURE
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MODEL ) EKROR
UNCORRrcTED TOTAL

2 8 10

33,38641399

16.69320699

57,06

2,34038601~

0,29254825

_ 35,72680000 -~OW~f4F€. t-Jifl.. NOT£$: p·b·h·

R-SQUARE 0,934492

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SOURCE
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T FOR HO: PARAMETER:O
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PR > IT I
0,0013 0,0001

STD ERROR OF ESTIMATE
0. 01611225 0,3107199_6

OBSERVATION - - - - - - oBSERVEn --- -- -- - PREDICTED

VI\LUE

VALUE

1

3o19000000

2.72992457

:;>

~.26000000

2.57362321

3
4

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1.82000000 ,.02000000

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1.24506167

A

0.79000000

1.08876032

9

0.66000000

0,54170556

1o

0.30000000

0.07280149

SUM OF RESIDUALS

SUM OF SQUI\qED RESIDUALS

SUM OF SQUARED RESIDUALS - ERROR SS

,,-

FIRST ORDER AUTOCORRELATION

0OURBIN-WAT~ON

-- -- ---

RESIDUAL

0,46007543

0. 686376 79

- 0 • 4 41 02 0~ 0 ----1-------- -1.08471914

-0.09841778 0,33603425

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0,09493A33

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0,11829444

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pr-ecutlt i'l~ i~.~_o
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------
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S T AT I S T I CAL ANAL YS I S S YS T E M

37 38

DATA ~~~~~L~ax 1 .X21 {VNITS.IrJ,/11 13).

39 XO=l;

40 CARDs;··

NOTE: nATA SET WORK.FyREFLY HAS 17 OASERVATIONS AND 4 VARIABLES. 361 OBS/TRK;-NOTE: THE DATA STATtM~NT USED o.07 srcOND~ AND 116Ko

®58
59

TITLE FIREFLY DATAl............. ·············-···--········· PKOC PRirJTI

60 VAR XO X1 X2:

NOT[; THE PROCEDURE PRINT USED Oo14 SECONDS AND 116K AND PRINTED PAGE 9,

61 62 63
NOTE: NOTE:

PROC GLM: M0Df:L y-Xl/PI

~D€~rlSS

y
CM )<, wt:f-4.

i/I,I,TU~f.(JV~'•

.

+rn-OUTPUT o~.IT=NEW3 RESIDUAL=RESID3 PREDICTED=YH_A!31_1g~~ur si:r.t~ tttt.ll f

·--- r.L4ifitAAl plcf. ·

nATA SET WORK.N~W3 HAS 17 OBSERVATIONS AND 6 VARIABLES. 250 OBS/TRKe THE PROCEDURE GtM USED 0.35 SECONDS AND 18~K AND PRINTED PAGES 10 TO 11.

©

NOTE: TilE PROCEDURE PLOT USED 0.20 SECONDS AND 124K AND PRINTED PAGE 12.

66
Y• 67
®68

PROC GLM; MODEL v-Xl X2/P 1

R~9r-er.s

m X. r;.K/. Xz wrU ,-wltr-ttpf.

OUTPUT OUT:NEW4 RESIOUIIL=RESID~ PREDICTED=YHAT41

NOTE: nATA SET WORK.NrW4 HAS 17 OBSERVATIONS AND 8 VARIABLES. 191 OBS/TRKo NOTE: Ttl[ PkOCEDURE GtM USED 0.32 SEcONDS AND 186K AND PRINTED PAGES 13 TO 14.

69

PROC PLOT;

...... --

70 PLOT R~SID4•YHAT41

NOTE: THE PROCEDURE PLOT USED o.2~ srcONDS AND 12'+K AND PRINTED PAGE 15.

71 72

PRoc G~~~ -x X1/ j{@~r:e.s~ . Y()YI Xz. ~~X, wr+t., '"ft'ne.pf :. ..

.. -- . . .

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NOTE: THE PROCEDURE G11V1 USED 0.27 SECONDS liND 162K AND PRINTED PAGES--16 TO i.l,---------- ·----

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PROC PLOT 1

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PLOT X'•Xl Y*X1 Y*X21

(NOTE: -fAts (S 3 A-tPAr'A.ft2 plof..,).

NOTE: THE PHOCEDURE PLOT USED o.38 SfCONDS AND 13'+K AN[) PRINTED PAGES 18 TO 20,

®75 PROC GLMI
76 MODEL Y"'X2/P; 77 OUTPUT OUT:NEW5 RESIOUAL=RESID5

PREOICTEo:yHAT51

NOTE: nATA SET WORK.NtW5 HAS 17 OBSERVATI~NS AND 10 VARIABLES• 155 OBS/TRK. NOTE: TilE PROCEDURE G11111 USED 0.38 SEcONDS AND 184K AND PRINTr_D PAGES 21 TO 22,- -

78 PROC PLOT; 79 PLOT R~SID5•YHAT51
• NOTE: THE PkOCEDURE PLOT USED o.25 SECONDS AND 12~K AND PRINTED PAGt 23, _

-/0-

• •

--------------

FIREFLY DATA

oas xo

X1 -------~~-------------

11 21
31 41 51 61
71
81 91
10 1
11 1
12 1 13 1 14 1
15 1
16 1 17 1

26 21.1

35 23.9

40 17.8

41 22.0

45 22.3

55 23.~

55 20.5

56 25.~

70 21.7

75 26.7

79 25.0- ---------- -87 24.4

100 22.3

100 25.5-

110 26.7

f,30

25.~

14(} 26. ~--------- --------- - - - - - - -

t ) _ .Fr-l------·-h-----~ X' ·F, r-s

•
-11-

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DEPENDrNT VARIABLE: Y

SOURCE MODEL ERROR CORRECTED TOTAL

OF
1 15 16

R-SQUAR£ -- ----- ---

c.v.

Oo1705f.2

1'1.1986

@

FIREFLY DATA •

GENE:RAL LINEAR MODELS PROCE:UUR(
ll'f'r~ss y X,(1)\ IN i-JI.... I" f-e.,.~t.pf.

SUM OF SQUAR£S

MEAN SQUARE

_F VALUE

19'+,4209878~ 9'15.~6136510

194,44:!09878'1 63,03075767

----- 3,08

1139,8623529'1

STD 0£11
7. 93919_125

Y M£AN
•a,35291fue = ij"

SOURCE Xl

OF TYPE: I SS F VALUE PR > F

1

19".~209878~

3,05

0,0994

SOURCE:
- Xl --

OF TYPE IV SS F VALUE PR > F

1

19'~.'+209878'1

-. 3.08

0.099'1

PARAMETER
INT(RCEPT Xl
OBSERVATION
:? 3 4 o; t'. 7 II 9
1n
11 12 13 h
1~
1(, 17

£STH4AT£

T FOR HO: PARAM£TER=o

PR > ITI

STO £RROR OF ESTIMATE:

' l(w;IIA,69620628~
l.,e-0.10308320

10e39 -1.76

o.ooo1
0.099'1

~~fa.N. wd·t.... NOTt: 5: P· I D•.,.,

'1,70&88778 0.05869385

onVsAELRUVEEoy,·

PREDICTED i\
VALUE: 'fi

RE:SIDIJAL
~j~-~-

4c;.oooooooo
IIO.OOOOOOOo 5p,.0000000Q 5o.ooooooao 3],00000000
5:>.00000000 5q.COOOOOOo 3p,.OOOOOOOo IIC.OOOOOOOQ
211.oooooooo 3A.oooooooo
3E..00000000
3F,.0000000(1 'lt;.OOOOOOOQ IIO.OOOOOOOQ 3].00C00000
40.0000000Q

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'15.2802'1411 '14,772671109
'14.6697'141\6 '+'+,257'+b206
43.22663002 '+3,22663002 43,12354681 41.61!036194 41.164?6592 40.75263:310 39,92796746 3.g. 58788580 38,58788580 37,55705376 35,49538966
34.46455761

-1.216011;>95
-5.28829411 t.S.22712t91
5o33020!H2 -1Jo257qf,;>Q6
6,7733&998 10o7733699B
-~.1235q6tll
-1.6803!\l'Jq
-l.i .164%592 -"·75263310 -.5.9279£,746 -2.58786580 7.41211420 ;!,44294624 -4.49538966
~.53544239

OEPE:NCrNT VARIABLE: Y
SUM OF RESTOUALS SUM OF SQUn~EO RESIDUALS SUM OF SQUARED R£SIQUALS - ERROR SS --FIRST ORDER AUTOCORRELATION OURBIN•WATSON 0

o.oooooooo
94~·'+6136510
-o.oooaoooo
-0·09'183671
2e15570071

PR > F
o.o99'+

•
I
~

•
RESI03 I 15.0 •
12,5 •
10.0 +
7.5 +
I I I
s.o +

PLOT OF RESI03•YHAT3
ll44;~l plAt

© •FIREFLY DATA LEGEND: A : 1 OBS• B : 2 OBS•
-k-- Y (M )( 1 t..JtH i~-'~f-tr-t~pt-.

ETC,

I

/A
/

/

/A

/

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A

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2.5 +

A

o.o +
I I
•2.5 +
-s.o +

-~--

~

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A~

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AA
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•
I
~
'

•

OEPEND~NT VAHIABLE: Y

G)

FIREFLY DAlA.

GENERAL LINrAH MODELS P OUR(

y x,fZt~ r-£ H

1M a~ x~

SOURCE

OF SUM OF SQUARES

MEAN SQUARE:

MODEL

2 456, 739'111'15 228,3&970573

ERROR

1'1 683,1'129'11'19

48,79592439

CORRECTED TuTAL

16 1139,88235294

F VALUE 4,68

R•SQUAR[ 0,'100690

c.v.
1F.,8922

STO OEV 6,98540796

Y MEAN '11,$5294118 ::::~

SOURCE
x1 a./one
X2 llti-u )<,

OF TYPE I SS F VALUE PR > F

194,42098784 262,31842361

3.98 5.38

0,0658 0,0361

SOURCE
x1 ,_nu- xl..
X2 ,..f--N_,... )(1

OF TYPE IV 55 F VALUE PR > F

1

0,00500314

o.oo 0,9921

1

262,31842361

5,38

0.0361

-PARAMETER
INTERCEPT Xl X2
OBSERVATION

ESTii-lATE-

T F"OR HO! PARAMETER=o

0~0 ,'11,47445073\.

!.1c 0, D0 0 6 319,:

_

••., .;> ,12752930 .

4o86 0, 01 -2.32

-· r>~ptA.r-e w,.U..

ORSERVEO
V~LUE

PREDICTED VALUE

PR > ITI

STO ERROR OF ESTIMATE

o.oool
Oo9921
0,0361

18,82510332 0. 06633915 0,91759899

NOT£5: pp./0.10-J:J. RESIDUAL

:> 3 - - - -·-·-~--4
!'>
(,
7 p,
9 1o 11 1;:> 1.3 14
1~
16 17

4'i.OCC00000
40.00000000 5p,,00000000
so.ooooaooo
31.00nCOOOu 5;>.00000000
54,00000000
3n.oooooooo
40.00000000 2A.00000000 3A.0000000Q 3r,.OOOOOOOo 3F..00C00000 4r,,0000000o 'IQ,00000)0Q
3t.0000000v 40.00000000

'+6,60157'119 '+0,65072005
5~,6321087.3
44,69717766 4 1l,0616B682 41,94107741 47,891115946 37,2612049'1 45,35550'!13 34,721.31757 38,34080534 39,€>2293683 44,0997'1622 37.29165246 34.74553719 37,312'11213 34.76629666

-1.60157419 .0,65072005
4,36789!27 !>,30202?34 ·13.0616116132 10,0589225';1
6,101840!)'1
0,73879506
-5 • .35550413 -1>.721.31757 -U,340fll''33'1
-S,62293863 -6,09974622
b,70834754 5. 25'14(,281 -b-31241213 5,£3370314

------

D£PENO~NT VARIABLE: Y
SUM OF" Rf5TDUALS SuM OF SQUARED RESIDUALS SUM OF SQUIRED RESioUALS - ERROR SS FIRST ORDER AUTOCORRELATION OuRBIN•WATsON 0

o.oooooooo
683o14294149
.u.oooooooo
------- ---0.20416682
_2.36448237

PR > F
0,0278

•
.......
--1::.

•
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1o.o +
r
7. 5- +
,
;-
5.0 +
2,5 +

PLOT OF R[SlD4*YHAT4
A

(j)

FIREFLY DATA •
=LEGEND: A l OBS, B : 2 OBS• ETC,
R~s1&w..l
A

plot- of

•
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A
BA A

0. ()- +
·2.5 +
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-7.5 +
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·12,5 +

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A

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A

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- ~, .·.t,:...'...... .. Ml.....~..........
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I
~ I

•

DEPENDFNT VARIABLE: Y SOURCE MODEL ERROR CORRECTED TOTAL

OF
2 14 16

® "'"" ""•
GENERAL LINEAR MODELS PROCEUUHE

Rel:jr-ess y (J'\1\ 'iz. ~ XI

SUI' Or SQUARES

MEAN SQUARE

456.73941145

228,.56970573

683.14294149

48,79592439

1139,88235294

F VALUE
lt,68_

PR > F
0,0278

R•SQUAR(
0,4006'!0

c.v.
11'.,8922

<.;TO OEV
6, 9g540796

Y MEAN
'+1,35294118

SOURCE X2 o./o"-f X1 ~Afhr- X'1-

OF TYPE I SS F VALUE PR > F

456, 734'10831 0. 0050031'1

9,.56
o.oo

0,0085 0,9921

SOURCE
X2 aR-u- X,
X1 QJ:/....- 'X-z.

DF lYPE IV SS F VALUE PR > F

1

262,31842361

5.38

0,0361

1

0,00500314

o.oo

0,9921

PARAMETER
INTE:RCFPT
X2
X1

ESTI~~ATE
~0 <"'ll, 4 7445073 ~" -2.1275293'
"b, :;: 0,00069199

T FOR HO: PARAMETER=o
4.86 -2.32
o.o1

PR > I Tl
o.ooo::s
Oo0361 0.9921

STO ERROR OF ESTIMATE
18,82510332 0,91759899 0,06833915

OBSERVATION
1
')
.3
o; 1'. 7 A 9 1o
11 1;> 13 14 1'\ 11'. 17

oBSERVED VI\LUE
'lc;.oooooooo
40,00000000 5A.OOOOU00Q SQ.OfJtJGOOOo 31.00000000 5;>,0000U000 51,,00000000
3p,.oooaoooo
40.0000U000 2A,0000000Q 31!.00000000 31'..0000000J 3f,,000000UO 41'..00000000
4o.oooooooo
31.00000000 40,0000000Q

PREDICTED VALUE
46.60157419 40,65072005 53,632101173 4•1, 69711766 41!, 06168682 'f1,94101741 47,89815946 37.26120•,94 45,35550413 34,72131757 38,34088534 39,62;>93883 '14,09974622 37 ,2'31652'16 34, 7'1553719 37,31241213 34,76629686

DEPENDFNT VIIHIABLE: Y

SUM OF RrSrDUALS
SUM OF SQUARED RESIDUALS
SUM or SQUARED RESioUALS - ERROR SS FIRST ORDER AUTOCORRELATION DURBIN-WATsON 0

RESIDUAL
-1.60157419 -U. 6507;>005
4.36789127 5.302822.5'1 •1.5,06168682 1U,051l9225'J 6,1018405'1
u. 73879506
-5 d55504 13 -6,72131757 -0.340!!8534 -3,f.2293P!!3 -8,09974622
1!,70834754 5,25441;281 -&.31241213 5,2337031'1

_s((~ (.{/.j __ p-r:u.utiJ~
C-L M procJtiM rt- .

o.oooooooo
68.So14294149
.u.ooooooou
-0.20416682 2o36448237

•
I
~ I

•
- l X2
26 +
~
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®• FIREFLY DATA
PL~ = =LEGEND: A 1 OBS, B 2 OBS• ETC.

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I
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FIREFLY DATA •
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A

r
55,0 +

52,5 +

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•

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A

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47,5 +

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PLOT OF Y*X2

(f)
FIREFLY DATA.
= =UEGEND: A 1 OBS, B 2 OBSt ETC,

•

A A

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AA

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1( 27,5 +

1-7·.-5-------1-8·-.5--------1·9-.-5-------2·-0-.5-------+2l-o-5-------2+2-,5--------2+3,-5-------2-'++.5--------2-5·,-5-----·-2-+6,-5-

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1

•

DEPENDrNT VARIAOLE: Y SOURCE
~ODEL
ERROR CORRECTED TOTAL

or 1
15 16

(jj)
FIREFLY DATA.
GENERAL LINEAR MODELS P OUR[
R-f9 f'"4.S s y tM x2- t.J I 'H...

I~ J-u-urJ't .

SUM OF SQUARES

MEAN SQUARE

F VALUE

456.73440831

'+56.734'+0831

10.03

683.14794463

'15.5'+319631

1139.8823529'1

PR > F
o.D06'+

R•SQUA!lE 0.'10061\6

c.v.
11'..319'1

STO OEV 6. 74856_995

Y MEAN '11.35294118

SOURCE X2

--------·-

OF 1

TYPE I SS 456.73'1'10831

F VALUE 10.03

PR > F
0.0064

SOURCE X2

. . --~~---

or 1

TYPE IV SS F VALUE
-456.73440831 - --10.03

PR > F
-0.0064-

PARA~ETER
- lNTERCrPT X2

ESTIMATE
~o" ql. 31\158169 ~z" -?.12144397

T FOR HO: PARAMETER=o
5. 7s •3ol7

PR > ITI
-~--o.ooa1
Oe006'+

STO ERROR OF ESTIMATE
-~15.88243590
0.66990228

OBSERVATION

OBSERVED VALUE

PREDICTED VIILUE

45 .oooooooo

'16.61911386

;;>

40.00000000

40.67907074

3

5A.00000000

53.6191\71\97

.,4

50.00000000

44.7098142q

3t.0000000Q

44.07338109

"' 5;>.0000COOO

41.95193712

7

'54.00000000

47.89198025

A

31\.00000000

:57.20476038

9

40.00000000

45.34624748

1n

28.oooooooo

3•+. 73902761

1t

3A.00000000

38.34548237

1;>

31'..0000000J

39.61634875

1:'1

3;,.00000000

'+4.07338109

14

4;,.00000000

37.28476038

15

40.00000000

34.73902761

1;,

3t.OOOOOOOO

37.26476036

17

40.00000000

34.73902761

DEPENDrNT VARIABLE: Y

SUM OF RrsrnUALS SUM Of SQUARED RESIDUALS
SUM Of SQUARED RESIDUALS • ERROR SS
FIRST OROEP AUTOCORRELATION OURBIN•WATsON 0

RESIDUAL

-1.61911386 .0.67907074
4.38012103
~-29018571
•13.073.31\109 10o0480&;>88 6,10801975 0. 71523962 .5.34624748
-6.73902761 -0.34548237 •3e6lA.341l75 -8,073.16109
a. 71523962
5,;>609723'1 -6,28476038
~.26097239

NOTE: fl...gM ra/HL tu-t.. ~~~t
+*< ..o AM£ aA fAMt. · lor
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u.oooooooo
68-1o14794'1o>3
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RESID5
1o.o +

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415542,77 1119355

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0.1277

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F VI\LUE
2.'+6

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0.1277

F VALUE 2.46

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PARA,..[TfR
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OBSERV t. TION
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l1~~.000QOJOQ l~l~.OOOOOJOu 127~.00000000

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tD92,7~Cl6789 11~5,28174187

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31 3~lt.7sc,'i,U0<:00nt.:u

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M(JU[l Y::: <):JMP-COM STRr"l_LOc
ESTIMATE 'RoW DIFFERENCES' STHM-LOC 1• -1./[; ESTIMATE •COLUMN D!FFERCNCF

~~ .,
STR'-LLCC*SvMP_COM/SOLUTJ.OrJ P;
1'

A S 6.8
A S 7.0
A S 6.8
1\ S 7 • 0 fl. S 6.6

6'• SwMP_COM 0• 1. -1./E;

65 ESTIMATE 'COLUMN DIFFERENCE 2•

SWMP-COM 1• -,5 -,5/[;

NOH: THE PRQCEOURE GLM USED 0.47 SE:ccNOS AND lost< 1\ND PRINTEU PI\GES :>TO 9.

66
®67

f'hJC PPlfiT: V /1 H X0 - X 1 1 ;

:~ ® =!'t, :~c GL "1; 'I, L I ; L L '( >: 1 - X1 1 ; ··JOTE:: Ti If 70

.e-O:tv...eJ ~ I n::rv..:r ·~ Is. I~ i.-v.A I~ l ~ ~
~ ~ rneehl ~ ®

-7:5-

2 <;Tfl I I S T I CAL. II IJ A l Y S I S

:1(~)71 Vl•r\ .xc t3-xs

x~~ x.,-Xll; p,~ X- VYI~ @~ I(Yio-c:kt ·VA

. O l E : Tl:l f'i,lJ([[Jllr<L rfnrJT USED Oo2'1 5lCOrHJS MJf' 116K ANf1 r'RINfEO PAGE 12.

72 73

74 l't ;C F'RltJT:
7':J \:1-:\ Xu-X5;

:; NOTE: TiC: f---t,\.JCEL1UHE PRHJT USEO 0.21 SECOrmS llfJD 116K AND PRINTED PAGE 1~-·---- _
-· '
76 f'FiOC Glr-1; 77 ~~O;JCL 'r=Xt-XS/P;

NOTE: T1 E PROCEDURE GL~ USED 0.2~ SEcoNDS A~rC 162K ANO PHiNTEb PAGf t5.
7R PhuC- PR"Hff:"- -----
79 VAR XO X3-X5 Xl X2;

NOTE: H'E PkuCEDLRE PRINT USED 0·21 SECQtiJDS /'qJO 116K AND PRINTED PAGE 16.

80 PH ,)C GL t"l i

12..D.y~VV\~ ~~~~~-L~ C:...d'~t

(8)81 '-"U;~El Y=X3-X5 Xl X2; Q ~ mo-eW.. ~ tL....o3. U..,...

TIE Pf,JCEDL'RE CLM USED 0.28 SEcoNDS fi~IC 162K AND PKlNTf:O p/\GE 17•

N0 TE : <; i< ~ 1 i-1 S T IT lJ TE I~~ c •
r.o~ tcOX 1(10Gt,
iU\ lEIGH , f•, • C • 2 7 h 0 5

SWAMP PH CATA
GENU~/\L LHrlAR ~0L'[LS PROCEDURE

CLASS llVEL INFORMATION

CLASS

LEVU.S

'VALUES

',

I

AN

s3 ~, f'l

r;l''•PEK OF UbSERVJ\TlOrJS IN 0.1\TI\ SET= 35

• • --•------·------~

@
DEPEflLfi<T V1"~ lliPLE: y souncl MCJorL ERR Of' CORRECTCD TIJTAL
SLliJHCE STRti-LCIC swn•_cor· ST~~-Loc~sW~P-CO~

SWAMp PH nATA GtNERAL Ll~lAR ~OQELS PROCEDURE

OF Sl.'M oF Sc;LAPlS

MEAN SQUARE

5

2.42538095

0.48507619

----·-~-

2')

s.£..5633.3.53

0.194356~2

34 8.06171429 :.To-lc..lS~-R(M)

A~A(I) ~~-IR.Ib

or· >1~--~-TYPE

ss·~--rvALlJl - - - .PR

F

1 R.{LIM): Q.774C7~18 2 RC~lt·-'<;l..l,. 1. 0427,;'377
2 Rt1:1"'-.~.s):: Q.(,0773900

3.9"' 2.61! 1o5b

o.0553 0.0853 o.2266

F VALUE
2.50
OF
1 2 2

PR > F

R•SgUARE

c.v.

0.0536

0.300852

6.6167

STD DlV

Y MEAN

0.44085862

6.66285714

RU-")"' ~s..- '?J."' tt.-s~.,..,

TYPE IV SS

F VALUE

PR > F

1.00971645 0.5090,3840
o.60773',1UO

5.20
1.31 1.56

0,0302 0.2854 0.2266

PAPt.:-~l T[R

ES f Ii·•,qr

T FOR Ho:
PARAMETER=O

PR > IT I

STU [RROR OF
ESTI~AT[

IIH E.f' Cf f' T STPr<.L<;C
sw~~r-co~l
STPM_LOC*~WrP_CO~

g,!. " L1200il000 Ll

. r11f

.fi o.-~

~!.-

~<1.. -- ~

=

.

7nuoncoo 0. OQlJO•lOOO

t:J l:l

~, "{; ... ::--~1.~ r..34<'>66(,6J

N ~'' -s-.~~ 0. 7G~OIJOOO
s o.oo~oucco
A M ~- ~- ~,,._ +i;_,, -O. l19b6C>6b 7

A
-A

s~I

i.32-l-.\l~..-~.~~"f. 3,\

-(o1.•

705Qt10 0 U0 0 0 0

00 00

LJ
[l
s
fl
l3
U . -· ... --·· -- -

31.0'+ 2.':12
1. jQ
.2.tl1.
-l.!i':l -1.&1

lJ,OOU1
.0.0067
0,20'+3 u.U089
•
0,17~6
0.1191

0.!9715797
o·?.6&9'5-H5
0.?.669'5315 0,?.5132808
0. 35 770273 0.43901787

NOTE:

~M

o.oo~ooooo H

~N

o.oo~ocooo ~

N S o.DOUOOOOO U

®no:b..~~~ ~lA~~~ te:r- ~ CJ"'v\

~ .SR'2, ~ t0-..L

Tfl[ TH£ TltE

X'X f'lfiTHJx !illS P.EEf~ DEE~1ED si~iGUL../'.H 1\i'Jo A GENEHIILIZED INVFRSE'It/IS BEEN EMPLOYED To SOLVE THL NOHMAL EQUATIONS. 1\t~OVE [STII-IATES HI:.PR[SlNT or;Ly O~JE: OF Mf1NY POSSIBLE SOLUTrr.NS TO THE NORMAL EQUATimJs. ESTIMATES FOLLOWED BY
LLTTEP. L' ARF [ll/ISED fiNlJ GO iiOT EsTHMrE THE PARI•METI::.k BUT AHE BLUE FOR SOME LirJEAH COMBINATION OF PARAMETERS

~
~~

tOH AI\[ ZEIW>, TilE EXPECTED VIILUE OF TI'E l3IAsED ESTlMATUHs MAY Bt OBTAINED FROM THE GENERAL FORM OF ESTIMABLE

FUi·JCTlur.s. FOR TilE BIASED ESTI•,ATOR<:o Tllr sTD ERR Is THAT OF Tt-'E BIAsED EsTIMAToR AND THE T VALUE H..STS

11u: EIUIIISEU ESTTMAlORl : o. EsTIMATES N0T FOLLOWED BY IHE LETTER B ARE BLUE FOR THE PARAMETER.

I
"'J
~
I

•® 08':>fl-:'v'f\1lOf:

r11. ( r P v t r·. V/'LU[

PRf[ICH:n V1\LUE

•

1 ?
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4 5 6 7
I\
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H 11 1? 13
lt~
1'-J lt-,
17 18 lCJ 20 21 2?
23 24 25 26 27
2A 2g
3ll
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3;;> 33 34
35

(, • h 0 0 0 u0 0 u
7.~0000000
7.20000000 7.00000000
(,.80000000
6.40C00000 7.00000000
b.40GOG0tJ~i
G.nooooooo
7.00C000JQ r:,.;;>OOOO::lUu F, • .?.DOOOOOo f,.LfO(lO."DOo
f .• ?000:J~)()Q
f,.Lf000QJOO
5.?::l000J()J
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6.4000000()
b.l1ooooooo
f.f\0000000
7.ooooo::Joo
(,. ?0 () 0 0 0 () 0
s.E>ooooooo 1.2ooooaoo
7.20000000 7.20000000
r:,. 2 0COOOOo
7.(>0000000 1.?0000000
7.20000000
6.H0000000 7.00000000
6.nooooooo
7.G0000000
6.&0000000

6.82...,00000 6.82...,00000 6.P2S0U000
6.82~00000 6.82~00000
6.82500000 6.82500000 6.6250JC00 h,4(,f,6b6b7
6,4f6b6667
6 • 4 6 h f, 6 6 f, 7 b • 4 £=J, h b 6 h 7 6,1!666b667 h.Lihf,f,f:>bh7
6.1200Ur,OQ f.l200lJOOO 6,1201J0f)00
6.12000Q01) 6.120DJQOO 6,gQOOOOOfJ
6.90000001) 6.7500UQOQ .. 6. 75000l)00
6.75000000 6,750UOQ00 6.75000000
6.7soouooo
6.75000000 6.75000000 6.9000UOOO 6.9DOUUQOO
6.CJOOOOQOO 6.90000000 6,900UUOOO · 6.9oOOOooo

SU~ or RFSIOUALS
SU~ OF SQU/\RED RESIDUALS
Sur.l or SQLJ/\RlD RESIOUi\LS- EkHQR
F 1 RST OR[lER 1\UTOCORHE Ll\ Tl C'fJ OURGI~-Wf\TSON 0 -

SS

•

-7£:-
RESIOUAL
-0.22500000 li.3750000U Ue3750000U 0,17500000
-0.02500000 -U.42500QOU
u.l75oooou -ll.4250nOOll
U.33.5333S.:> u.s33.333j.:>
-0.2b6n6~67
-U.266 0 6Fl6l -U. 066666t:> -, -U.26f,t,bt-b7
U.2800QQOU
-U.92Uucnou u.osu:;oaou u.28ll:JOOO:J
u.2gUJooou
-U.!OOOQIJOU
O.!Oononou
-u.ssooo~oo
-lol50tJ0000
u.4sooooou
u.4soooooo
u.qsoooooo -u.ssooooou
u.45UOOOOU
u.qsuoooou
U.3000000U -U.!00tJ000tJ
u.1ooooooo -u.1ooooooo u.toooooou
-U,3000QOOU
u.oouoooou
:,.63633~3j
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0. lj 0,2 0. 0

+
I I I
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SWIIMp PH DATA

PLOT OF RESIDII*YHATII

LEGEND: A : 1 O~S, B : 2 OBSo ETC.

A

--·--·· - - - - - - - - - - -
c

A

1\ A
c
- - - - - --- ·--- .

•
E B A
B
c
A
c
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---- ---- ----·-----· ·------ --
A
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.

. ·--··--··-·-

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DEPUIDF!IT VIIHIIIflLE: Y SOURCE MODEL EKROR CORHECTr:U lUTAL

DF
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SvUHCE

------- OF

s~~P-Cor
STRM.Lnc
STRM.Lrr•SW~P.COM

2
1 2

,...
• -• ..

SwiiMp PII OAT A GENERAL LlNlAR ~ODELS PROCI:.DURE

SUfi. oF SCI.JIIHI:.S

MEAN SQUARE

2·'12538095

__Q._485076t9

5o63633~33

Ool91J35n:'l2

8o06'l711J29
At-JOV~U4) of f:>.IS.", ·-TYpE I Ss·--·r--VALUI:.-

pR ) F

0,4G187013 lo 33577182 (1of,0773':100

1,24 1'.,87 lo 5b-

0,3044 O,Ot38
o.2266

F VALUE 2,50
OF 2
1 2

PR > F

R•SQUARE

0,0536 __________ 0,300852

STO OlV

0,4~J0858&2

c.v.
6,6167
Y MEAIII
6,66285711t

TYpE IV SS
0,50903840 1,00971645 O,e,0773'JUO

F VALUE
1,31 5,20 lo56

PR > F
0,2854 0,0302 0,2266

PARIIIIii:.TrR

ESlP~ATE

T FUR Ho: PARAMlTER=O

PR > IT I

STD ERROR OF ESTIMATE

INTEkC[I'T
S~<~II.P.Col:

M
-- ----r.J

s

STRM-Loc.

A

STRM_Lnc.•SW~P.COM

N A 1.1

A JJ
AS

N~

~\~ ., 6,120!:10000 u

31,0~

'6,..- \5.~"
~~;~~;-"=

.o0 .073o45oo6o6o6o6o7

B
tf ·-----------

l,jU 2,1:11

ooooonoooo B

~&.>. -s,~-= 0 o 7fl0JOOOO 8
0,00000000 8
'i..t.-'S"~-s,....;,j-o,u<;~66f-.667 B

.2.~2
•1,.1<j

~w-~~~-~·-t-b.f-Oo 7050r.JOOO B___ _

-1,b1

0,00000000 ti

0,00000000 U

0,0001
0,20~J3
------ --Oo0089
0
0,0067
0
0,1756 0,1191:_ -

0,19715797 0,26695315
.Oo25132808
0,26695315
0
Oo35770273 0 ...3901787

NN

O,OOUrJUOOO B

Ns

0,00000000 U

,,

,

®r"'oi;e_ ~ t1.u. ~ c.>e- ~ ~~ ~

I ~~~ OJ:. CS"""' ~

fJOT[:

THE X' X Ml\ TR I X HilS BEEN DEEMFO SI IIGULAR /\No 1\ GCNERALl ZED If~VfRSE HAS BEEN EMPLOYE() To SOLVE TH.E NOHf~IIL [QUI\ TI ONS; T~E 1\LGVE ESTIMATES REPRESENT O~LY ONE OF MRNY POSSIBLE SOLUTIONS TO THE NORMAL EQUI\TJONS, ESTIMATES FOLLOWED BY TfiE LETTER 8 ARE 011\SED AND QO ~OT ESTIMArE THE PAKAMETEK BUT AKE BLUE FOR sOME LINEAR COMBINATION OF PARAMETERS !OR II~( ZEROJ, THE EXPECTED VALUE Or T~E UyAsEO ESTIMIIyUHs ~AY BE OBTAINED FROM THE GENERAL FORM OF ESTIMABLE FUNCT10~S. FOP ~fiE BIASED EsTIMI\TORs, THE sTn ERR Is THAT OF THE BIASED ESTIMATOR liND THE T VALUE TESTS fill! Elt::IASfD FSTIMATORI : 0, ESTh!ATES NOT FOLLOWED BY I"HE LETTER B ARE BLUE FOR TilE PARAMETER,

PARJ\!'~E. TER

ESTI114ATE

T FOR HO: PARAMETER=o

PR > 11"1

STo ERROR OF ESTIMATE

ROW DIFFERENCES
COLU~~N OIFFERETJCE 1 COLur1tJ OlFFlRErJCE 2
\~ ~

0 • 3794U441~
o·. 3 s2 so ooo
-0.07791667
\/\~~

2.28 1.61 -0.48

o.o302
0,1191 0.6340

0.16647454 0.21950893 0.16191929

I
"'......0 (

-
® 20'-lSWAMf~ PH OAlA
as ,xo Xl XC: X3 Xl.f xs Xb X7 XB X9 XlO Xll

I
~
.l

11 1 0 1 0 0 1 0 0 0

21 1 0 1 0 0 1 0 0 0

31 1 0 1 0 0 1 0 0 0

41 1 0 1 0 0 1 0 0 0

51 1 0 1 0 0 1 0 0 0

61 1 0 1 0 0 1 0 0 0

71 1 0 1 0 0 1 0 0 0

81 1 0 1 0 0 l

000

91 1 0 0 1 0 0 1 0 u

10 1 1 0 0 1 0 0 1 0 0

11 1 l 0 0 1 0 0 1 0 0

12 1 1 0 (j 1 0 0 1 0 0

1~ 1 1 0 0 1 0 0 1 0 0

14 J 1 0 0 1 0 0 1 0 ()

15 1 1 0 0 0 1 0 0 1 0

16 1 1 0 0 0 1 0 0 1 0

17 1 1 0 0 0 1 0 0 1 0

18 1 1 0 0 0 1 0 0 1 0

19 1 1 0 0 0 1 0 0 1 0
20 1 u 1 1 0 0 0 0 0 1

.?421 1 0 1 1 0 0 0 0 0 1 22 1 0 1 0 1 0 0 0 0 0 .(3 1 0 1 0 1 0 0 0 0 0 1 01010 0000

25 ]

0101 00 000

2b 1 0 1 0 1 0 0 0 0 0 27 1 0 1 0 1 0 0 0 0 0

28 1 u 1 0 1 0 0 0 0 u

29 1 0 1 0 1 0 0 0 0 0 30 1 0 1 0 0 1 0 0 0 0

31 1 32 1

01
u1

0 0

0 0

1 1

0 0

0 0

0 0

0 0

~3 1 0 1 0 0 1 0 0 0 0

34 1 0 1 0 0 1 0 0 0 0

35 1 0 1 0 ------0 1 0 0 0 0·-~----~

.

·--

~-- --~----~--·---

---·

00 00
00 00
00 00 00 00
00 00 00 00 00 00 00 0, 0 00
00 00 00 00
10
1n
10 10 10 10 10 10 01 01 01 01 01 01

X YY\~ ~ r'rl~ ~-@

•

•
®

•
Sw/\Mp PH rATA

-·-·

GENEHAL LINli\R M08ELS PROCEDURE

OlPUJJ;rrJT Vl\ldi\P.LE: y

Sui 1n cr

DF SUM oF SQ~/\HLS

MEAN SOU/\R£

F V/ILUE

PH > F

R•SQUARE

c.v.

r•.occL

5

2·4?S380Ys

0·~8507619

2.50

0.0536

0.300852

6.6167

ERI~DP.

2<J ~~~'5·6~h33j33

0·194356~2

STO DlV

Y MEAN

C0 I~,-;£ LTr 0 1 0 T1\ L

34

a. or.1714?.9 "' ,.,.-,,. h-- /';;e'! • .,~

n.tttt0851lb2

6.66285714

~{tv\')'= ~s,.yl.. '"IS'f>S. ?q

SQU,;Cl

DF

TYi'[ I '>s

F-VI\LUl

FH > F

OF

TYpE IV ~S

F VALUE

PR > F

Xl

1 ~t..JI+- Q,771JE7218

3.9~

0,0553

0

o,uouooouo

. .X2 0 u.O"::JI)OUtJO

0 o.uouuoouo

)\S )\'+

1 1

R

(~IN ' l),$l1u..00~1202:1:5&.5:+i2SJl

~/ O't28 •

5,2U
0,11

0,0301 O,b8b9

0 0

o.uouoouuo o.uouoouuo

. .x:, 0 u.o .. ouooJo

0 O,OOUOIJOUO

XL

1 ~(Il M,L,Q~[0.2.:>303il.., 8 ).,., ,(.0'?7 1.20

0,2825

0

o,oouooouo

Xl
xu

1

0,314700~2)

1.96

0,1756

0

o,uouooouo

0 O.OvOOliUvO

0 o.ucuooouo

X'J u o.ouoocouo X10 0 o.ouooouco
.Xll () O.OuOC UvO

0 o,oouooouo 0 o,ucuoccuo 0 o.oouooouo

I[_ AI'-.IC\f A (4 ') cr'V\ ~. l 8 • lb

I'ARJir·~lT[R

EST Ir1AT£

T FOI~ 110: PARAI·1fTf H=o

ItJTERC[PT

~u ,.- f.,900000QO B

Xl t:;i','!>- ~'- -0.78000000 B
X2 - - o.oooooooo 8

X3 ':Stl- ~..~=--O,OOO~CCJO 8
..X4 Su-~~ -il.150C:)J')0 B

X~ _

O,OOOOOOoO B

x.:, ~,.-IJ,~-'ida. 1 -t ~-;;. 0,705U00D0 B

X7 1;;,,._--g,,-~...~t ~· 0,49666b67 [3

X8 O,OOOUOOCO B

X'J 0,00000000 B
X10 o,oouuoooo 8 xu 0,00000000 B

t..~~

3fl.S4 -2.Y2 -0,00 -0,63
lobi 1o39
~· \Q,IS'

Pfl .> ITI
o.ooo1
o.aQ67
1.oooo
.0.533b
0,1191 0,1756

STO ERROR OF ESTIMAL-
0,17997978 Oo2b695315
0.35995955 0.23809087
0,43901787 0,35770273

ma-c:kl~
~~--~ nn.u- ~/
~~~~~

NOT[:

THE X'X MIITRIX HAS BEEN Df.EMED SlNGULIIR 111~0 1\ GENEKALlZlD lNVfRSE HAS t:lEEN EMPLOYED To SOLVE THE. NOKMIIL EQUATIONS. Til[ 1\llOVE ESTH~AT[S !~l 0 R[S£NT OtJLY 0'1[ OF '1ANY POS~llJLE SOLUTIONS TO THE NORMAL [QiliiTIOtiS, ESTIMATES FOLLOWED DY THE LlTTER B nRr 811\sED nNU DO NOT ESTIMIIIE THE PAHIIMETlH BUT ARE BLUE FOR sOME LINEAH COMBINATION OF PARAMETERS lOR IlK[ ZERO), THE EXPECTED VALUE OF ThE ~IAsED ESTIMATORs MAy HE OBTAINED FROM TilE GENERAL FORM OF ESTIMABLE
=FUNCTlo~s. FOR Tfl[ BIASED EsTI~ATORs• THE sTO EkR Is THIIT OF THE BIAsED EsTIMATOR liND THE T VALUE TESTS
HU: EIUIAsED ESTl~/\TORl 0, EsTIMATCS NOT FOLLOWED BY THE LETTER 8 ARE BLUE FOR TliE PARAMETER.

----- . ----- ------------

()C)
~

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SWI\Mf' PH r;AT/\

- 22-

):I) )( -~ X•; X!:J Xl X2 X6 X7 X8 X9 XlO Xll

1 () 0 1 u 1 0 0 II 0 ()

u?

(l 0 1 0 1 0 0

00

3 'L

(l 0 1 0 1 0 0 u 0 0

Lf 1

l

00 10 10 0u

0

0

5 1 .J. 0 0 1 0 1 0 0 0 0 0

f, 1

(J 0 1 0 1 0 0 l) 0 0

7 1 .c 0 0 1 0 1 0 0 0 0 0

Rl l 0 0 1 0 1 0 0 n 0 0

9 1 0 1 0 1 0 0 1 0 () 0 0

u10 1 I) 1 0 1 \) 0 1 0

00

11 1 J 1 c 1 0 0 1 0 0

c0

12 1 u 1 0 1 0 0 1 0 (I 0 I)

13 1 0 1 0 1 0 0 1 0 (I 0 0

14 1 0 1 0 1 0 0 l

00

0

0

15 1 0 0 1 1 0 0 0 1 (I 0 0

lb 1 0 0 1 1 0 0 0 1 (I 0 0

17 1 u 0 1 1 0 0 0 1 (l 0 0

18 l

0 0 1 1 0 0 0 1 ll

0

0

19 1 0 0 1 1 0 0 0 1 (I 0 0

20 1 1 0 0 0 1 0 0 0 1 0 0

21 l

100 0 100 01

0

0

2? 1 u 1 0 0 1 0 c 0 u 1 0

23 1 0 1 0 0 1 0 0 0 n 1 0

2.4
.2~

1 1

0 0

1 1

0 0

0 0

1 1

0 0

0 0

0
0

()
0

1 1

0 0

26 1 0 1 0 0 1 0 0 0 0 1 0

27 1 u 1 0 0 1 0 0 0 0 1 n

28 1 J 1 0 0 1 0 0 0 0 1 0

29 1 30 1

0
()

1o·

0 1

0 0

1 1

0 0

0 0

0
0

0 0

1 0

I)
1

31 1 0 0 1 0 1 0 0 0 0 0 1 32 1 0 0 1 0 1 0 0 0 0 0 1

33 1 0 0 1 0 1 0 0 0 0 0 1 34 1 0 0 1 0 1 0 0 0 0 0 1 35 1 0 0 1 0 1 0 0 0 0 0 1

®x-0")~ ~ Mode-l ~

•

®• •SwiiMp PH OATA

GENERAL LlNlAR MODELS PHOCEOURE

[)[P[IJOEi'JT VlliliAfiLE: Y

SOURCE MOOfL [HROH CORRECTED TOTAL

OF SUM oF ~QlJI\H[S 5 2.42538095
29 R~ ... 5·63633S33 34 8.06171'+29

M[AN SQU(IRE 0. 48507f.19 0·19435632

F VALUE 2,50

PR > F
0,0556 STO DlV 0,4408586?

•

R-SQUARE 0,300852

c.v.
6,6167 Y MEAN 6,66285714

SOURCE

OF

Typ[ I Ss - - · F V1\LlJl

pR > F

OF

TYpE IV SS

F VALUE

PR > F

X3 X4
X:~
X1 X2 Xb X7 X8
X9
XlO Xll
PARI\r~ETER

.1
1

) R('2>IN

"

{00..4034q2~3:15'5+H249! :,lf8/1

2,2b 0,22

0 O.OOUUOilUO

.1 Q(LIH,'l.) ...
0

1.335771b2
o.oouuouuo

----·-- 6,87

1 1

A lJ:.l M !) L)=[o, 23 31131\58} ~
' I (i,374-/0042

rJ:J'l °

1. 20 1.9:.

0 o.ooooouuo

0 o.oooooouo

0 o.ooooouuo

0 o.ooo.:ouuo

L At-...JO\JR (_~) avo.~· 1~./b

EST! '1A TE

T FOP 110: PJIRAI-1ElER=o

PR > ITI

0,1435
.0,6433
.0,0138
0,2825 0,1756
.

0 0 0 0
0 0 0 0 0 0
0

STD ERROR or
ESTIMI\:E

o.uouooouo o,uouoouuo o.uuuooouo o,uouoouuo o.uouooouo o.uouuouuo o.uouoouuo o.ouuooouo o.oouooouo o,uouoouuo o,uouuoouo

.

IIJTEI<CEPT i6,.,\. ~ -- -n,90000000 B

:.<3 ~.~.-i;i,.':!. ,. -o.oooooooo s

X<t

~.u.-~.a 3 ~

-0.15000000 8

X5 0, OOOUIJOOO B

X1 ~.~- ~~ ~ -0. 78001'JOOO B

X2 n.oooooooo F3

X6 'E!u-"i&,"!.- ~;,;+ l'3~;-=- n, 705000oO B

X7 ~s- ~l'l>- c:\u. ~lia-s.-:: 0. 4966666 7 B
xa 0,00000000 B

X9 0,00000000 A

XlO n.oooooooo s

Xll 0,00000000 B

tt.. sa~. tlLtb'

38 • .54
-o.oo
-O.b3
.-2.92 1.61 l • .:Sq

o.ooo1
1,0000 o.s33b
.0,0067
0,1191 0 ·1756

0.17997978 0,35995955 0.23809087
.0,26695315
0,43901787 0.35770273

MocLJ.!
~~~~Lu.ot:~j
.~. ~-c,.ej,:~ ( ~~ 'N\~ \

NOTE: TfiE X•x MIITRIX HaS BEEN UEEMEO siNGULAR liND A GENEHALIZEU INVERSE liAS BEEN EMPLOYED To SOLVE THE NOKMAL EQUATIONS,
TttE AuUVE ESTIMATES REPRESENT ONLY ONE OF MANY POSSIGLF SOLUTIONS TO THE NORMAL EQUATIONS. ESliMATEH FOLLOWED BY TilE LLTTFR B ARE BIAsED 1\NO DO NOT ESTIMATE THE PAKA~ETER BUT AHE BLUE FOR SOME LINEAR COMBINATION OF PARAMETERS IOH AilE ZEROI, THE EXPECy[O VALUE OF TI·E tiiASEO ESll~AyUKs MAY BE OBTI\INEO FROM THE GENERAL FORM OF ESTINABLE
=FUNCTIONs. [Qp TilE BIASED EsTI~ATORs• THE sTD ERR Is THAT OF THE BIAsED EsTIMATOR AND THE T VALUE TESTS
HO: EIUIASED ESTIMATOR) 0, EsTIMATEs NOT FOlLOwED BY THE LETTER~B ARE BLUE FOR THE PARAMETER,

00
tN
I

...
•®
•
•

SvJAf'llP PH rATA

ous xo X1 "'2 X3 X4 X5

11 1 0 1 0 0

21 1 0 1 0 0

31 1 0 1 0 0

41 1 0 1 0 0

~1 1 0 1 0 0

61 1 0 1 0 0

71 1 0 1 0 0

A1 1 0 1 0 0

91 1 0 0 1 0

10 1 1 0 0 1 0

ll 1 1 0 0 1 0

1? 1 1 0 0 1 0

13 1 1 0 0 1 0

14 1 1 0 0 1 0

1~ 1 1 0 0 0 1

16 1 17 1

1 1

0
·o

0 0

0 0

1 1

lH 1 1 0 0 0 1

19 1 1 0 0 0 1

20 1 0 1 1 0 0

~1 1 0 1 1 0 0

22 1 0 1 0 1 0

2,~ 1 0 1 0 1 0

24 1 0 1 0 1 0

25 1 0 1 0 1 0

26 1 0 1 0 1 0

t"::".7. 1 0 1 0 1 0

2A 1 0 1 0 1 0

29 1 0 1 0 1 0

~0 1 0 1 0 0 1

.3] 1 0 1 0 0 1

32 1 0 1 0 0 1

.13 1 0 1 0 0 1

34 1 0 1 0 0 1

35 1 0 . -- 1-- 0 0 1

FX -VY)~

c.._~ VV) od.-tJ

®(@) c{-.~ 1/"\r)~~. . ~

2't-

OfJSU{VI\TloN

• •

1
')
<
3
4
5 h
7
H
9
10
1!
1? 13 14 1<=;
lf, 17 lH l'J 20 2}
2?
23 24 25 26 27
~8
29
6()
6]
6?
33 .54
j~

oBSERVE!) VALUE
f1.60000000 7.20000000 7.20000000 7.00000000 6.80000000 6.40000000 7.00000000
n.4ooooooo
6.A0000000 7.00000000 6.;>0000000 6.2oouoooo
t,.t.~OOOOOOO
6.20000000 6.40000000 5.20000000 6.20000000 6.40000000 6.4DD0000u t=..8000000G 7.00000000 t=..2oooooou
~.60000000
7.20000000 7.20000000 7.20000000 6.20000000 7.20000000 7.20000000 7.20000000 6.80000000 7.00000000 6.80000000 ?.OOOOQOOO h.6000U00Q

PpEOlCTEI') VALUE
6.?569'J933 6.75699'133 6.75699933 6.75699933 6.75699933 6.75699933
6.7~69'J933 6.7~b9'J';i33 f1.~9142f,66
f,. "i914266f) o,<;SI42r,66 6.39}42bh6 6,-.;9142666
6.~9142fi6f)
6,:;,}908908 6o""il908']08 .;,,}90A908 6o""i190U908 6o""i1908':30A 7.17200268 7.,7200268 6.80646001 6,"0643001 6.R0b43001 6,R064j001 6.A0643001 6.g0643001
6.~0643001
6.R0643001 6.7340'j243 6.73409243 6.73409243 6.73409243 6.?.340':1<!Lij
6.7340'724~~

RESIDUAL
-0.15699933 0.1+'+300067 0.44300067 0 • 2 4 3 0 0 0 b -, 0,04300067
-0.35699933 0,24300067
-0.356999.3..1 0,40857334 0,608573.34
-0.19142666 -0.19142666
0,00857334 -0,19142666
0,08091092 -1.11908908 -0.11908908
U,080':J}092 U,Q80':J}092 -0.37200268 -0.17200268 -0.60646001 -1.20643001 0,39356999 0,3'j356999 0,39356999 -0.60643001 0.39356999 0.39356999 0.46590757 0.06590757 0,265907:>"7 0,06590757
0.26~90757
-0.13409243

- ~s·-

•

sTI\TISTlCAt

A 1\J A L Y S I :::;

S YS T[ ~ 11:12 SUNOA)

GEnlRAL LTI\iEAK MODELS PROCEDURE

SUM OF R[SIOlJALS SU~ Of SoUAHEU RlSioUALS SU~ OF SQUARED RESroUALS - ERROR
fIRST OFWEH J\UTOCOHHELATIOI\J
U Uf{f] I 1\1 - wJ\ TS n N D

SS

u.oouoooou
6.244072.34
o.ooooooou
u.ll42oo73 1.7647713.3

Q)
OEPUJUrtJT \IArdAOLE: y SOUHC[
MOOE.L
ERHOf< C0Rf<E CT[O lOT Ill
souncL Xl
X2 X3
X4
X')

•
SwAMp PH D/\TA
GENERAL LINl/\R MOOFLS PROClOURE

OF SUM oF SOUf,fiES

MEAN SQUJIR[

F VALUE

3

1.8176'1195

o.605BtJ065

3,01

31

6·2'+407?3'1

0 oi:!Ol42H9

34 8.06171429

ANCNA tc-~~ ~ io~c+ ?· \q,\~

or

TYPE I SS .

.F VALLlt.

PR > F

OF

1 ~(ll f.t)• 0,77487218
0 o.oouuouuo
1 Q ( s j M L):,.[l • o1 0 ~53 4 5( ·I 04 ~
1 I Q,Q322)E-32}- •
0 G,OOOOC('UO

3,8~
s. 02} ~ 5"}
O,tb .

.0,0589
o, 032'+ ns
0,6919

0 0 0 0 0

•

PR > F
0,0451
STO OE.V 0,44880028

R-SQUARE 0.225'+66

c.v.
6,7359
Y MEAN
6,66285711t

TYPE IV !:iS
o,ooooouuo o,uuuoouuo o,uouooouo
O,UOUOuUUO
o,oouoouuo

F VALUE

PR > F

.,

f' ARAI·IL T[R
HlT[RCrPT Xl X2
x3 X4
X~

ESTI~ATE
b,7340'J243 8 -0,41500335 8
(J • 0 (, 0 0 0 0 0 0 8 0,437910;:>5 8
o. Oi23.?7sa o o,ocoooooo 8

T FOR 110:
PARA~ETE.i{=O
43.76
.-2.:,8 2.15 ' 0. 'I 0

PR > ITI
u.ooo1
.U,015U
U,0396 U,691':1

STD ERROR OF ESTl~IA TE
0,15387;>77
.U,l€>115307
0,20384430
0,18087~22

~ IR·- -- - ~·-- -r·- ---· n·- ~

I
--~-~~

~ n:ru.r

~ Vv-.~

NOTE:

TilE X'X MI\TRIX lmS [[EN OEfMED SINGULAR liND A GENEHALIZLD INVERSE HAS BEEN EMPLOYED To SOLVE THL NOKMAL EQUATIONS,
T11E Al,u\1[ ESTJM/ITES NEPRrsENT ONLY ONE OF ~ANY POSSIBLE SOLUT 1CNS TO THE NORMAL EQUATrONs. EslzMAtEs FOLLOWED BY Till llTTlR e 1\PE 8ItsEO RNU DO J~OT ESTIMATE THE PAHAMETEH BUT AHE BLUE FOR sOME LINEAR COMBINATION OF PARAMETERs tON 1\Hl ZfRUl. THE EXPECy[[J VALUE UF T~f BIIIsED ESTI~ArUHs MAY BE OBTAINED FROM THE GENERAL FORM OF ESTIMABLE FUNCllONS, FOR THE BIASED EsTI~I\TORs, TilE ~TO ERR IS THAT ~F THE BIAsED EsTIMATOR AND THE 1 VALUE TlSTS
H~: Elt;li\SED ESTIMATOR) : 0, EsTIMATES NOT FOLLOWEU OY THE LETTER B ARE BLUE FOR THE PARAMETER,

R.a-u.r.s ~ N - N....!/.)

... L o-f-. Sbl~ ~.. )

(~ ~· \J .1«1)

--------- -----------------·-·--- -------

1 ()C>
0

-•- ®
• •

~ ~7-

SwAf_,P PH ['1\TA

s(11J xo X3 Xtt X5 X1 X2

11 1 n 0 1 0

?1 1 0 0 1 0

31 1 0 0 1 0

41 1 0 0 1 0

51 1 0 0 1 0 b1 1 0 0 1 0

71 1 0 0 1 0

A1 1 0 0 1 0

91 0 1 0 1 0

10 1 0 1 0 1 0

1} 1 0 1 0 1 0

1? 1 0 1 0 1 0

13 1 0 1 0 1 0

14 1 0 1 0 1 0

15 1 0 0 1 1 0

16 l

0 0110

17 1 0 0 1 1 0

lll 1 0 0 1 1 0

19 1 0 0 1 1 0

~0 1 1 0 0 0 1

21 1 1 0 0 0 1

22 l

0 1001

23 1 0 1 0 0 1 24 1 0 1 0 0 1

25 1 0 1 0 0 1

;,;t, 1 0 1 0 0 1

~7 1 0 1 0 0 1

:Cf) 1 0 1 0 0 1

29
~0

1 1

- (0J .

1 0

0 1

0 0

1 1

-'1 1 0 0 1 0 1
32 1 0 0 1 0 1
j3 1 0 0 1 0 1

34 1 0 0 1 0 1

3~ 1 0 0 1 0 1 ··--·· ----··----.-

X-m~ ~
© )....\[V).~ \.A.A.,
0... ~ Vv\~
CQ)~~ \...Jv....

•
©
DEP[ftUEitT I.'Ar<IflflLE! y SOUHCE MOO[L
[IHW'<
CORRECTf[) TGTAL
SOURCE X3 .<4 X5 X1 X2

•

SwAMP PH OATil ~ENERIIL LINLIIR MODELS PROCLOURE

OF SU" oF 00UIIRLS

M[AN SQUI\RE

F VI\LUE

3

1· 91 7€: 1-11 95

0.60588065

3,01

31

6·24407?.34

0 .20142H9

34 1\. OC.17!429
AI\JCVA te-'""'t4. ~L...t OVI (oottc,..,.. o+ p. I&. 1@.

OF

TYrE ! Ss· - - r-VI\LUl

PR > F

co1 ~ S.lt--1)=- .Li39~1429-s .,.,4a~~ 2.1eJ 120 0,1'+98 ns.

. .1

'lo.o42ssse4

0,21 • ' 0,6490

0 c.oooooouo

1 0

R. ( L I~.~)::. 1 • 3 3 5771 il2 - 0 • 0 0 0 0 0 0 u0 - -- - - -

6,6j

0,0150

OF
0 0 0 0 0

-•

PR > F
0,04~1
STD DEV
0,44880028

R•SQUARE '. 0.225~66

c.v.
6,7359
Y MEAN
6,66285714

TYPE IV SS
o,oouoouuo o,oouooouo o,uouuouuo o,uouoouuo o,uuuooouo

F VALUE

PR > F

P1\f~ 11 1!t H. R
IfJTE.ilC[f.'T X3 X4
.11!:> Xl
X2

ESTI'~ATE
F.,73409243 A 0,43791025 8 o,072337'J'l A n,ooouoooo R -0,41500335 8 n,OOOUOOOO A

T roR HO: P11 R11~~ET EH=o
43.76 ----2.15
.Oo40
-2,5H

PR > IT I
o.ndol U,IJ3<Jo
.u.~,91~
0,0150

STO ERROR OF [ST H1ATE
0,15387277 0,20384430
.0.18087522
0.16115307

.~~ ..
~u...o-1 l{r\~ "=:, l ~ ~~'S.
ttru.r~

NOTE:

TilE X'il M/ITHilt' tillS RE'EN OEEr1ED sirrGULI\R 1\rJD A GEr.rEKALI7lO INVFRSE HAS BEEN EMPLOYED To SOLVE THI:: NOHMAL EQUI\TIONS. THE ALOVE [STI~AT[S RlPR[SlMT ONLY ONr OF MANY POS~IBLE SOLUTIONS TO THE NORMAL [QUIITIONS, ESTIMATES FOLLOWED BY
TilE Lt TTEfl 8 APf RIIIsED MID DO fJ0T ESTI!t.flfE THE PARAMETlR BUT /IRE BLUE FOR SOME LINEAR COME:!INATlON OF PARAMETERs tuR A~[ ZEFOJ, TilE EXPECTED VALUE Or THE 8II\sED ESTIMATORs MAy BE OBTAINED FROM THE GENERAL FORM OF EsTIMABLE FUNCTIONS. FOR THE BII\SED EsTiwJ\TORs• Tft[.sTO ERR Is THAT OF THE BIAsED ESTIMATOR AND THE T VALUE TlSTS
IlL: EI~IASED fSTTMATORI : O. EsTIMATES NOT FOLLOWEU HY THE LETTE~ B ARE BLUE FOR THE PARIIMETEH.

~<; I Q..o-ur.> ~--~
~~~

LN -\/'>

(_ ~ ~· l~LI<:)) ( a.:k £"" &lo. ~ ')

~--Y.lg..__l'=i __ ~ -~ _C..\'R ~- ~ --~

~ J ~--::. -~ s.. te,... ~ ~ .

~

co
00
.)

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•

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NOTE: THE JC 1:3 Vfli:PJQ 0 C1 HAS BEEN KUN UI'JDE H 1tELEASE 79.3 or SAS 1\ T CORNELL

1 lJJ\1/1 SOf:JEAN; l)NlT Jq

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'C' lj"5

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L ' ) ; i..v\ el; C...O..~

7 X3=1-Xl•X2;

l8

X~=Xl*X4;

r....:.._~ ~

f.J Xb=X2*X4; ~~~

10 11

X7=X3*X4;
C/\r<CS;

~121... ~ 1'1-~

NOTE: OAT/\ SET I:~OHK.SOY13EAN HAS 45 0BSER\If1TTOJS 1\Wi 12 'JAFI/WLE:.l. 130 OBS/TRK. NOTE: TilE llATI~ STATEMENT USEO Oe26 srcnNJS /11\0 128K.

57
58 59
®60

GLM;

CLASS LiGHT;

1i.10i.JC::L )'~LIGHT /SuLUT I ON P;

OUT?Ul OUT=I\JEWl

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61 Pi{OC PLOT; 62 PLOT f\[<;!Dl*YII/\Tl;
NOTF: TilE PROCF:DliiU: PLOT USED 0. ~:~ SFr n~WS 1\H! 'UUK M;D ~'h HJTEU P.'IGE 4 •

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OUTPUT OUT:::N[W2

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PRLOIClED=YHAT21

N 0 H: : 0 1\ T 1\ SL T W0 Hr< • NE W2 It/\ S

NOTE: TltE P!WCEDUH[ GL~1 USEU

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P1WC PLO f;

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PLOT Y*X4

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NOT[: TI~E P1WCEDURE PLOT

n'+ 5 Uf3 Sf V/\ TI 0 '~ S fll\1 U 1 6 V.'I R I 1\ 1:3 L[ <:; •
Q.t~Lf SECOf1IOS :HJC ldOK Al\18 PKINTUJ

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NOTE: THE PROCEDURE GL~ USEU 0.47 s~=CLHJDS f\NL lb4>( Af'JO PKINT£0 PAGES l.i ro 14 •

®75 !'HOC PLOT;
76 PLOT RESID3*YHAT3;

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NOTE: TilE F'HOCEnUHE PLOT USE f) 0. :~4 c~r 01\liJS II r1 D 1 3 0 t< Ai\JD f--'KINTLU PAG[ 1~.
X- mo..~

©

• •

'X :a. I I0

I I 00

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I I 00

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II

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II

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1 () 0 I
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.;"0 0
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55 0

'!iY 0
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4~ 0
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'II 0
f.7 0 '10 0 sg 0
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"2.~2. 0 0

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0
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0 0
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0

0 0

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0
0 XI) Xl.f X 1 Xa.X.3

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@ .0
0
0~
0 "• Xy x, xl. ><s 'Xs~X.,
0

0

0

0

0
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0 0

0

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~

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S'''-2. S'2..

.; ®

S T AT ~ ~ T I C AL

•
Af,ALYSIS

s Y S T E t~

GENERAL LINLAR WQDfLS PROCEDURE

CLASS LLVEL Il<f.'UI<MATION

cu.s~

LE'IL:LS

VI\LUE"S

LIGHl

~ CLS

HU~1EJEK OF Ul:lSfRII,;TlOI,;:, ll'l llAT/1 SET : 45

•
rn~ YY)~
LJ:a"" f"~- f €.~R._

~

S T 1\ T 1 S T l C A L A I• A L t S l S S Y S T E !'4 GEM[HI\L LINli\R MOGEL~ PROCEDURE--

~1:13 ~RIDAYt APRIL 18, 1980

2

DEPENDE~T VARIABLE: Y

SOURCE MODEL

OF .. __ 2._ _

ERROR

42

CORRECTED TOTAL
UM.~ tA::t....J.

44
~.~~

SOURCE

GF

L!GH1

2

_SUti oF SQUI\I<ES 301.8.579377ll 12.921093j3 314.7::,go3111
7'1a9. '-a -;1<>,' ,,,,,- r ~s
jlll.Pd793.//IJ

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0.958~49

11.4173

STD DEV

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o.s54b5762
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12,~56444'+4
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F VALUE

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66.411 l3,l:lR .31 .26

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u.14321198
0,202~3233
0.20253233

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NOTE:

TilE X1 X Ml\lKJX HAS ElEEN OEf 1\tiUl ~HIGULI\H 1\IJr. I• GUJFHALllt.ll Hi'.JfPSl HAS Bff~J fW-'t.oJYF:Il TO SOLVE TilL NUI<MAL [QUJITlON~,

TilE 1\00VE ESTJ.1J\l[S REPkESUH OI~LY GtJr uF M{ltJY f>n<;SIIJI_f JfJLIJTII1r~<> TO THC f.J(JHI~IIL LQIJAfiONS. ESTIMATf~ FOLLOwEU lJY

TtiE L[ TTER B AilE BIASC8 1\f-JII nr, h0T EST Lrc.lllt lilt: f'l\f'I\Hl:Tl rt LliJT ,\Q( llLUf FUi~ Stll~f- L [IJ[IIR CO'·H3If•AT lOiJ UF PIIRAMETE.R5 (tlR f.f.E. ZEfiOl. yf1[ EXPECrEii VI.U,::: GF TfE ulfl:,lll LSfl,"iAful<..; I•Ar tlt: ullT/1lNE!J f111.m rttl l;[NEI~AL FORI~ 01- ESTIMI\OLE

FtJi-JCTIOr..s. FOR THE BIASFO F•:TPH•TORc:;, Trtf <;TI; [l!f< IS THfd tjf TH> Hl1\~lrl f...;fl,~I\TOI~ lltJil THf T Vt>~Uf HSTS

l·-,Ju,:.,-c ..,,~; lJIJ!/I::;lU t._TJ~f.TOrl:: lJ,

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-D

......

~

OHSUW fl TIOfiJ

• •

1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
:9
20
21 22 23 24
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50
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3')
.36 37 38 69 40 41 42 43 44 45

Of1SER 'J[O VALU[

11.88000000 12.76000000 12.68000000 11.96000000 12.4U0000lJO 12.240000UO 13.25000000 11.39000000 12.45000000 12.!9000000 13.!80000UO 11.46000000 12.370000UU 12.27000000 12.32000000
1~.oooooouo
16.68000000 16.59000000 15.09000000 1f:>.24000000 J5.:+4000000 15.80000000 15.88000000 16.00000000
15.68000000 15.82000000 15.'36000000 14.98000000 16.70000000 15.840000•JO
9.50000000 7.52000000 ').51000000 9.4')000000 9.56000000 10.20000000 8.82000000 10.37000000 8.65000000 10.49000000 8.53000000 ').64000000
9.~8000000
9.85000000 3.17000000

\

I'I~Et,IC fUJ
V1\ L Ut:
12.3200UQOO 12.)200000U 1 2 • ">i 2 0 0 L1 GiJ (I 1? • ~ 2 fJ 0 J !) [) ll 12 • .52rJ0JOCC i2.3200CJono 12.3200•)000
12.~20000(10
12 • .32000000 12.320ll:JOOO 12.3201lOOUil 12.32000000 12. 'S20U'J0lll, 12.)2000000 1?. -)2000000 1 ~ • !l4 ') 0 0 ~ tl 8 15 0 r) q 0 (I 0 0 0 0 lS.HqOOUOOO l 5 • n 1t 0 (l 0 0 0 C i. 5 • '\ 4 0 () 0 0 0 i 1
I':). '''-10l10dLO
l"'J.H400UOOO 1').84000QQO l').BtiOOOOOU
15,.'\1~000000
1 5 • :14 0 l1 0 0 0 0 1 :) • ,'J li 0 ll (J 0 IJ 0
15.G40UOOOlJ l5.E400uoou 15.84000000
9. ')tJCJ3.333j 9.::3093.333.5 y. ')0'1333.36 9.5'J93..:i336 9.50933335 9.5093.3.336 '.J. 'l0933333 9.50933333
s9 • ~i 0 'J .5 3 3 3
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SUM Of RtSIDUALS

-SUM or SQUARED RlS!OUALS
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16.59000000 15.09000000 16.2!JOOOOOG
15.44000000 15.80000000 15.88000000 16.00000000 15.6800000;) 15.820000UiJ
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10.20000000 8.82000000
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1. 1 • 7 [1 0 11 2 2 ~) q 1?.99391182 1?.70512675
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norr:. T•tC X'X MlllRIX HI\~ OEEri fJ[EI1f.n s!tJGULfln I\IJlJ /1 GEI·ILflAt_r7EU HIV[Il:;f: HAS llfOI EMPLOYEfl TO SOLVE Hll:.. NOH~AL EQUATIONS.
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