Document jZyM8N834mNZpY7vRG4GxRMk
CC: W. F Wagner D Snee
December 7, 1983
TO: FROM:
D. W. MARQUARDT 3. M. MINOR 3. M. LUCAS W. H. FELLNER C. A. FUNG S. P. BAILEY R. K. HENDERSON CT. AJ
C. G. PFEIFER
BLOOD LEAD/GASOLINE LEAD DRAFT REPORT
In an informal seminar in September, I discussed our analyses of blood lead data from a four-year national survey (NHANES II). Our goal is to quantify the portion of a reported decline of 5-6 ug/dl in blood lead levels attributable to survey design and exposure to gasoline lead. Attached is a partial draft of a report that was recently sent to Dr, Ralph Bradley for reyiew prior to a Dec. 15, 1983 meeting with him. Ron and I would welcome any comments you may have on this draft by the end of the year. The deadline for submission to EPA is 3anuary 15, 1984, Also attached is a copy of a Petroleum Laboratory report based on earlier results that will provide a quick overview of the problem.
Sections of the draft report are:
II. NHANES II and the Reported Blood Lead Decline
III. Effect of Survey Design on Reported Blood Lead Decline
IV. Gasoline Lead Exposure
V, Effect of Exposure to Gasoline Lead on Reported Blood Lead Decline
Also included are Appendices referenced in Sections III and V,
CGP:mai Atch
TEH 0532551
MTB > >STOP
*** MINITAB *** STATISTICS DEPT * PENN STATE UNIV. * RELEASE 82.1 *
STORAGE USED
3000 STORAGE AVAILABLE 100000
MTB > >CORR CIS Cl6 Cl? C30
/ XI PRIME < X2 PRIME I M2
T2X1 PRIMEX2 PRIME
'-.899...
-.679
.62~0
-.980
.917' .776
MTB > >REGRESS C30 ON 3 PRED Cl6 Cl7 CIS
THE REGRESSION EQUATION IS M2 = 10.2 + 2.26 XI PRIME + 3.19 X2 PRIME
COLUMN
XI PRIME X2 PRIME T2
COEFFICIENT 10.204 2.2642 3.1863
-4.8362
ST. DEV. OF COEF.
2.932 0.7696 0 .5545 0.4429
T-RATIO = COEF/S.D.
3.48 2.94 5.75 -10.92
S = 4.672
y.,xsT2.
&
-0.31
- L io
R-SQUARED * 98.9 PERCENT R-SQUARED = 98.7 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 3
16
19
SS 32553
349 32902
MS=SS/DF 10851
22
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED
DUE TO
DF
SS
REGRESSION 3
32553
XI PRIME
1
27644
X2 PRIME
1
2307
T2 1 2602
ROW XI PRIME 15 -8 .0
Y M2
-121 .02
PRED. Y VALUE
-112.32
ST.DEV.
PRED. Y RESIDUAL
2.04
-8.70
R DENOTES AN OBS. WITH A LARGE ST, RES.
ST.RES. -2.Q7R
DURBIN-WATSON STATISTIC =1.25
MTB > >REGRESS C30 ON 2 PRED Cl6 Cl 7
THE REGRESSION EQUATION IS M2 - 18.6 + 9.24 X:L PRIME + 5.33 X2 PRIME
COLUMN
XI PRIME X2 PRIME
COEFFICIENT 18.561 9.242 5.331
ST. DEV. OF COEF.
7.982
1.209 1.463
T-RATIO i COEF/S.D
2.33 7.64 3.64
TEH 0532552
f
DUP050033821
R-SQUARED 91.0 PERCENT R-SQUARED 90.0 PERCENT, ADJUSTED FDR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 2
17 19
SS 29950
2952 32902
MS=SS/DF 14975 174
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 2
29950
XI PRIME
1
27644
X2 PRIME
1
2307
DURBIN-WATSON STATISTIC = 1.70
MTB > >REGRESS C30 ON 2 PRED Cl6 Cl7 C31 C32
THE REGRESSION EQUATION IS M2 = 18.6 + 9.24 XI PRIME + 5.33 X2 PRIME
COLUMN
XI PRIME X2 PRIME
COEFFICIENT 18.561 9.242 5.331
ST. DEV. OF COEF.
7.982 1.209 1.463
T-RATIO = COEF/S.D.
2.33 7.64 3.64
S * 13.18
R-SQUARED = 91.0 PERCENT R-SQUARED =90.0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 2
17 19
SS 29950
2952 32902
MS=SS/DF 14975 174
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 2
29950
XI PRIME
1
27644
X2 PRIME
1
2307
DURBIN-WATSON STATISTIC * 1.70
MTB > >NAME C31 'STRES M2',C32 'PRED M2' MTB > >LET C33=C30-C32 MTB > >NAME C3S 'M2 RES' MTB > >REGRESS C33 ON 1 PRED CIS
THE REGRESS 10N-EATI M2 RES = 8.50 is: 0.809 T2
TEH 0532553
DUP050033822
COLUMN T2
COEFFICIENT 8.496
-0.8091
ST. DEM. OF COEF,
5.492
0.4585
T-RATIO -
COEF/S.D. 1.55
-1.76
S = 11.82
R-SQUARED = 14,8 PERCENT R-SQUARED = 10.0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL
TOTAL
DF 1
18 19
SS 435.4 2516.2 2951.6
MS=SS/DF 435.4 139.8
DURBIN-WATSON STATISTIC = 1.59
MTB > >REGRESS C30 ON 2 PRED C26 C27
THE REGRESSION EQUATION IS M2 - 74.9 - 3.1 X1P RES + 6.7 SRES X2P
COLUMN
X1P RES SRES X2P
COEFFICIENT -74.935 -3.11 6.72
ST. DEV. OF COEF.
9.669 18.20 10.46
T-RATIO COEF/S.D.
-7.75 -0.17
0.64
S = 43,24
R-SQUARED R-SQUARED
3.4 PERCENT .0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL To t a l
DF
2 17 19
SS 1117
31785 32902
MS*SS/DF 558
1870
DUP050033823
>MINITAB*MINITAB.MINITAB
IF YOU NEED THE 81.1 VERSION OF MINITAB, IT IS IN *OLD*MINITAB.MINITAB". MINITAB RELEASE 82.1 *** COPYRIGHT - PENN STATE UNIV. 1982 FEB, 9, 1984 *** UNIV. OF WISCONSIN - m&ISON -- MACC VERSION 82.1-UW2.1
STORAGE AVAILABLE 100000
MTB > >RETR 'CAKRDS*TESTS, MTB > >INFO
COLUMN
NAME
Cl T
C2 XI
C3 X2
C4 E
cs M
C6 Y RESID
C7 ST RESID
C8 PRED Y
C9 ST XI
CIO PRED XI
Cll ST X2
Cl 2 PRED X2
Cl 3
XI RESID
C14 X2 RESID
CIS T2
CIS Xl PRIME
Cl 7 X2 PRIME
Cl 8 M PRIME
Cl 9 El
C20 M+El
C21 STRES MP
CONTINUE? >
C22 PRED MP
C23 RESID MP
C24 SRES XIP
C25 PRE XIP
C26 XIP RES
C27 SRES X2P
28
PRE X2P
C29
X2P RES
C30 M2
C31 STRES M2
C32 PRED M2
C33 M2 RES
COUNT 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
20
20 20 20 20 20 20 20 20 20 20 20 20
CONSTANTS USED: K1
K49
MTB > >REGRESS CIS ON 1 PRED CIS C34 C35
THE REGRESSION EQUATTt XI PRIME - 1.52 tO,484,
TEH 0532555
DUP050033824
COLUMN T2
COEFFI'CI'ENT
-1.5158 -0.48421
OF COEF.
0.6650 0.05551
COEF/S.D.
-2.28 -8.72
S = 1.431
R-SQUARED = 80.9 PERCENT R-SQUARED = 79.8 PERCENT, ADJUSTED FOR D.F,
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 1
18
19
SS 155.92
36.88
192.80
MS-SS/DF 155.92 2.05
DURBIN-WATSON STATISTIC =1.74
MTB X XNAME C34 ' STRESXlP'',C35 'PRED X1P' MTB > XLET C36=C16-C35 MTB > XNAME C36 "X1P RES2" MTB X XREGRESS Cl7 ON 1 PRED Cl5 C37 C38
THE REGRESSION EQUl X2 PRIME - 2,93
COLUMN T2
COEFFIC l ENT -2.9263
-0.30226
ST. DEV, OF COEF.
0.9229 0.07704
T-RATIO = COEF/S.D,
-3.17 -3.92
S = 1.987
R--SQUARED =46.1 PERCENT R-SQUARED = 43.1 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 1
IS 19
60.711
71.047 131,800
MS=SS/DF 60.753 3.947
DURBIN-WATSON STATISTIC = 2.95
MTB X XNAME C37 STRESX2P',C38 'PRED X2P' MTB X XLET C39=C17~C38 MTB X XNAME C39 'X2P RES2" MTB X XCORR CIS C36 C39 C30
f [ XIP RES2
i X2P RES2 ^___ M2
T2X1P RES2X2P RES2
.000
.000 .029
-.980
.080 ,150
I j
MTB X XREGRESS C30 ON 3 PRED C36 C39 CIS
THE REGRESSION--EQU&f I ON IS M2 - 2,55 -4^2.26 J1P RES2
2P RES;
ST. DEV.
T-RATIO =
rirti-r* xn
TIH 0532556
DUP050033825
X1P RES2 X2P RES2 T2
-2.552 2.2642 3.1863 -6.8957
2.170 0.7696 0.5545 0.1812
-1.18 2.94 5.75
-38.06
S = 4.672
R-SOUARED =98.9 PERCENT R-SQUARED 98.7 PERCENT, ADJUSTED FOR D.F.
DIALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 3
16 19
SS 32553
349 32902
MS =SS/DF 10851 22
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 3
32553
XIP RES2
1
211
X2P RES2
1
721
T2 1 31621
ROW X1P RES2 15 0. 78
Y M2 -121.02
PRED. Y VALUE
-112.32
ST.DEV.
PRED. Y RESIDUAL
2.04
-8.70
ST.RES. -2.Q7R
R DENOTES AN OBS. WITH A LARGE ST. RES.
DURBIN-WATSON STATISTIC = 1.25
MTB > >SAVE 'CAKRDS*TESTS.' MTB > >ST0P
*** MINITAB *** STATISTICS DEPT * PENN STATE UNIV. * RELEASE 82.1 *
STORAGE USED
3000 STORAGE AVAILABLE 100000
TEH 0532557
DUP050033826
MTB > >STQP
*** MINITAB *** STATISTICS DEPT * PEW STATE UNIV. * RELEASE 82.1 *
STORAGE USED
3000 STORAGE AVAILABLE 100000
MTB > >REGRESS CIS ON 3 PRED Cl6 Cl7 Cl
THE REGRESSION M PRIME =7.17
PRIME
PRIME 6:..23Tf
COLUMN
XI PRIME X2 PRIME T
COEFFICIENT 7.166
-0.058 2.8012 -6.230
ST. DEV. OF COEF.
3.670 1.897
0.5729 1.092
T-RATIO = COEF/S.D.
1.95 -0.03
4.89 -5.71
S = 4.516
R-SQUARED = 99.0 PERCENT R-SQUARED = 98.9 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
-0,/ 6
7.os
DUE TO REGRESSION RESIDUAL TOTAL
DP 3
16 19
SS 3357?
326 33903
MS=SS/DF 11192-\
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN
DUE TO
DF
SS
REGRESSION 3
33577
XI PRIME
1
31353
X2 PRIME
1
1560
T 1 664
ENTERED
IN THE
ORDER GIVEN \i w >
DURBIN-WATSON STATISTIC = 1.34
MTB > >CORR Cl6 Cl7 Cl CIS
XI PRIMEX2 PRIME
X2 PRIME
.620>7
/
T -.383/ -.679/
M PRIME V.I62*) (3^-764
MTB > >REGRESS CIS ON 2 PRED CIS Cl7 Cl9 C20
THE REGRESSION M PRIME = 21.1
PRIME +14.38 !2 PRIME
COLUMN
XI PRIME X2 PRIME
COEFFICIENT 21.122
10.5057 4.3838
ST. DEV. OF COEF.
4.623 0.7004 0.8472
T-RATIO = COEF/S.D.
4.57 15.00
5.17
S " 7.633
R-SQUARED = 97.1 PERCENT R-SQUARED = 96.7 PERCENT, ADJUSTED FOR D.F.
^ 11 ,
TEH 0532558
DUP050033827
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 2
17 IS
SS 32913
SSO 33903
MS-SS/DF 16456 58
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
OF
SS
REGRESSION 2
32913
XI PRIME
1
31353
X2 PRIME
1
1560
ROW XI PRIME 14 -8,0 15 -8,0
Y M PRIME
-96.28 -121.02
PRED. Y VALUE
-80.46 -106.76
ST.DEV. PRED. Y
3.03 3.28
RESIDUAL -15.83 -14.26
ST.RES, -2.26R -2.Q7R
R DENOTES AN OBS. WITH A LARGE ST. RES,
DURBIN-WATSON STATISTIC 1.64
MTB > >NAME CIS "ST M PR',C20 'PRE M PR" HTB > >INFO
COLUMN Cl C2 C3 C4 C5 C6 C7 C8 09 CIO Cll Cl 2 Cl 3 C14
CIS Cl 6 Cl? Cl 8 CIS C20
NAME T XI
X2 E M Y RESID
ST RESID PRED Y ST XI PRED XI ST X2 PRED X2 XI RESID X2 RESID T2 XI PRIME X2 PRIME M PRIME
ST M PR
PRE M PR
COUNT 20 20 20 20 20 20
20 20 20 20 20 20 20
20 20 20 20 20 20 20
CONTINUE? > CONSTANTS USED: K1
K49
MTB > >LET C21=C18--C20 MTB > >NAME C21 'M PR RES" MTB > >REGRESS C21 ON 1 PRD Cl
THE REGRESSION EQUATION IS
AM PR RES 1.68 0.160 T
c o l u mn
T
COEFFICIENT 1. (583
-0.1603
S - 7.353
ST. DEV. OF COEF.
3.416
0.2831
T-RATIO COEF/S.D,
0.49 -0.56
TEH 0532559
DUP050033828
R-SqUARED * 1.7 PERCENT R-SOUARED - .0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 1
18 19
SS 17,08
973.26 990.34
MS'-SS/DF 17.08
54.07
CONTINUE? >
ROW T 14 14 .0
Y M PR RES
-15.83
PRED. Y
VALUE -0.56
ST.DEV.
PRED. Y RES1DUAL
1.92
-15.26
R DENOTES AN OBS. WITH A LARGE ST. RES,
DURBIN-WATSON STATISTIC * 1.67
MTB > >INFO
COLUMN
NAME
Cl T
C2 XI
C3 X2
C4 E
C5 M
C6 Y RESID
C7 ST RESID
C8 PRED Y
C9 ST XI
CIO PRED XI
Cll ST X2
Cl 2 PRED X2
Cl 3 XI RESID
Cl 4 X2 RESID
Cl 5 T2
CIS
XI PRIME
Cl 7 X2 PRIME
Cl 8 M PRIME
C19 ST M PR
C20 PRE M PR
C21 M PR RES
CONTINUE? >
COUNT 20 20 20 20 20
20 20 20 20 20 20 20 20 20 20 20 20 20
20 20 20
CONSTANTS USED; K1
K49
MTB > >REGRESS CIS ON 1 PRED Cl C22 C23
THE REGRESSION EOUATION IS XI PRIME - 1.04 - 0.529 T
COLUMN T
COEFFICIENT -1,0421
-0.52932
ST. DEV. OF COEF.
0.2787 0.02326
T-RATIO * eOEF/S.D.
-3.74 -22.75
S = 0.5999
R-SOUARED * 96.6 PERCENT R-SQUARED *96.5 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO
DF
SS
A rtrt
MS=SS/DF
A AA
TEH 0532560
DUP050033829
RESIDUAL TOTAL
18 19
6.48 132.80
0.38
DURBIN-WATSON STATISTIC =2.27
MTB > >REGRESS Cl7 ON 1 PREP Cl C24 C25
THE REGRESSION EQUATION IS X2 PRIME = - 2.33 - 0.302 T
COLUMN T
COEFFICIENT -2.9263
-0.30226
ST. DEV. OF COEF.
0.9229 0.07704
T-RATIO = COEF/S.D.
-3.17 -3.92
S = 1.387
R-SQUARED =46.1 PERCENT R-SQUARED 43.1 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 1
18 19
SS 60.753 71.047 131.800
MS=SS7DF 60.753 3.947
DURBIN-WATSON STATISTIC = 2.88
MTB >
MTB > MTB > MTB > MTB >
>NAME C22 '.ST X1PR',C23
>LET C26=C16-C23 >LET C27=C17-C25 >NAME C26 'XIP RES',C27 >INFO
'PRED XIP 'X2P RES'
,C24
'ST X2PR',C25
'PRED X2P'
COLUMN
NAME
Cl T
C2 XI
C3 X2
C4 E
C5 M
C6 Y RESID
C7 ST RESID
C8 PRED Y
C9 ST XI
CIO PRED XI
cii ST X2
Cl 2 PRED X2
Cl 3 XI RESID
Cl 4
X2 RESID
CIS T2
-^C16
XI PRIME
--9>C17
X2 PRIME
CIS M PRIME
Cl 9 ST M PR
C20 PRE M PR
21 M PR RES
CONTINUE? >
C22 ST XI PR
C23
PRED X1P
C24 ST X2PR
COUNT 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
20 20 20
TEH 0532561
DUP050033830
C26 C27
XIP RES X2P RES
20 20
CONSTANTS USEDi K1
K49 K50
NTS > >REGRESS CIS ON 3 PRED C26 C27 Cl
THE REGRESSION EQ!
IS
M PRIME = - 0,97 O.OSiXlP RES + 2.80 X2P RES -jl 7.051 T
COLUMN
X1P RES X2P RES T
COEFFICIENT -0.971 -0.058 2.8012
-7,0462
ST. DEV. OF COEF.
2.098 1.897 0.5729 0.1751
T-RATIO = COEF/S.D.
-0.46 -0.03
4.89
-40.23
S = 4.516
R-SOUARED - 99.0 PERCENT R-SQUARED f 98.9 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL
TOTAL
DF 3
16
19
SS 33577
326 33903
MS=SS/DF 11192 20
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE
DUE TO
DF
SS
REGRESSION 3
33577
X1P RES
1
72
X2P RES
1
488
T 1 33017
WHEN
ENTERED
IN THE
ORDER
DURBIN-WATSON STATISTIC * 1.34
TEH 0532562
DUP050033831
/wc
(5
.ooosu^t .oaomio
non% 11.%%
TEH 0532563
DUP050033832
DUP050033833
DUP050033834
TEH 0532566
DUP050033835
MTB > >PLOT 02 CIS XI
12.00+
--
**
* **
8.00+ --
* **
* *
* **
4.00+
***
*
***
00+
+----------- -------I--------------------( ------------------ )-------------------- I------------------- KT2
.00
5.00
10.00
15.00
20.00
25.00
MTB > >PLOT 0.3 CIS X2
12.50+
9.00+
* k it
* **
**
5.50+
**
kk
k
*k
k
k
2.00+ *
.00
*
5.00
*
10.00
15.00
20.00
25.00
MTB > >PLOT C5 CIS M
180.00+
120.00+
kk k
k ** *k * ** k
SO.00+
k
*
kk
.00+
+------- --------+-------------- -+------------------- b--------------- -+--------~-------+T2
.00
5.00
10.00
15.00
20.00
25.00
TEH 0532567
DUP050033836
MTB > >PLOT C3 C2 X2
12.50+ 'J
9.00+
*** *** * *
-* * 5.50+
**
-* * * *
O m
2.00+ * +-------
2.00
* 4.00
* 6.00
8.00
10.00
12.00
MTB > >C0RR CIS C2 C3 C5
in XI X2
#M
T2 .899
.679 .930
XI
. 620 .969
X2 .764
m 9
MTB > >REGRESS C5 ON 3 PRED C2 C3 Cl5
THE REGRESSION EQUATION IS
M * 0.63 + 8.85 XI + 3.67 X2 + 1.11 T2
<i
ST. DEV.
T-RATIO =
COLUMN
COEFFICIENT
OF COEF.
COEF/S.D.
0.632
3.266
0.19
XI
8.8536
0.8572
10.33
X2
3.6658
0,6177
5.94
i T2
1.1063
0.4934
2.24
^
*5
ii
0
S * 5.204
R-SQUARED * 98.7 PERCENT R-SQUARED =98.4 PERCENT, ADJUSTED FOR D.F
ANALYSIS OF VARIANCE
i
DUE TO REGRESSION RESIDUAL TOTAL
OF 3
16 19
SS 32049
433 32482
MS=SS/DF
10683 27
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 3
32049
XI 1 30511
X2 1 1402
T2 1 136
0 ROW
4n
xAi
Y PRED. Y ST.DEV.
M VALUE PRED. Y RESIDUAL
AA AA
AA
ft
ST.RES.
A ftAD
TEH 0532568
DUP050033837
R DENOTES AN 08S. WITH A LARGE ST. RES DURBIN-WATSON STATISTIC * 1.17 HTB > >SAVE 'CAKRDS*TESTS.'
TEH 0532569
DUP050033838
\
u
cl
TEH 0532570
DUP050033839
TEH 0532572
DUP050033840
MTB > > REGRESS C5 ON 3 PRfi.D C2 C3 Cl
TEH 0532573
DUP050033841
THE JREGRfSSJIJMJiQUAT, M =K.17\+(4.0yXl -I
3.77
COLUMN
XI X2 T
COEFFICIENT 7.166
4.058 3.1988
3,770
ST. OF COEF.
3.670
1.897 0.5729
1.092
T-RATIO = COEF/S.D,
1.95 2.14 5.58 3.45
S 4.516
R-SQUARED = 99.0 PERCENT R-SQUARED 98.8 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
OF 3
16 19
SS 32156
326 32482
MSSS/DF
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 3
32156
XI 1 30511
X2 1 1402
T 1 243
DURBIN-WATSON STATISTIC =1.34
MTB > >REGRESS CS CN 2 PRED C2 C3
THE REGRESSION EQUATION IS M = - 1.28 + 10.4 XI + 4.16 X2 )
COLUMN
XI X2
COEFFICIENT -1.279
10.4498 4.1564
ST. DEV, OF COEF.
3.506 0.5312 0.6424
T-RATIO = COEF/S.D.
-0.36 19.67
6.47
S = 5.788
R-SQUARED = 98.2 PERCENT R-SQUARED = 98.0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 2
17 19
SS 31913
569 32482
MS=SS/DF 15956 33
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 2
31913
XI 1 30511
X2 1 1402
TEH 0532574
DUP050033842
DURBIN-WATSON STATISTIC m 1.81
MTB > >REGRESS C5 ON 2 PRED C2 C3 C7 C8
THE REGRESSION EQUATION IS M = - 1.28 + 10.4 XI + 4.16 X2
COLUMN
XI X2
COEFFICIENT -1.279
10.4498 4.1564
ST. DEV. OF COEF.
3.506 0.5312 0.6424
T-RATIO = COEF/S.D.
-0,36 19.67
6.47
S * 5.788
R-SQUARED = 98.2 PERCENT R-SQUARED = 98.0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 2
17 19
SS 31313
569 32482
MS=SS/DF 15956 33
CONTINUE? >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 2
31913
XI 1 30511
X2 1 1402
DURBIN-WATSON STATISTIC * 1.81
MTB > >LET C6=C5-C8 MTB > >NAME C6 'Y RESID' MTB > >REGRESS C6 ON 1 PRED Cl
THE REGRESSION EQUA1________
Y RES ID =?= - 1,02 +Co To 97 T
i i rmin'iiii i
--^
COLUMN T
COEFFICIENT -1.018 0,0970
ST. DEV. OF COEF.
2.598 0.2169
T-RATIO = COEF/S.D.
-0.39 0.45
S = 5.594
R-SQUARED * 1.1 PERCENT R-SQUARED - .0 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 1
18 19
SS 6.25 563.22 569.48
MS-SS/DF 6.25
31.23
p u n%rs til t tA>r< v p ml <
at
A _ 41 AA
TEH 0532575
DUP050033843
MTB > >NAME C7 "ST RESID' ,C8 'PEED Y'
MTB > >PRINT C1-C8
ROW
T XI X2
E
M Y RESID ST RESID
11 22 3 3 4 5 5fl 6 7h 8 jf *8.
9 9 "SL 10 7 IrO
11 11 12 12 13 16 "*a. 14 14
15 15
18 17 17 18 2 *a
19 19
20 IS'SO
2 2 2 4 4 4 4 6 8 8 8 8 8 8
8 10 10
10 12 12
2 -0.7534 4 -7.4820 8 -1.3071 4 1.4994 8 -2.9768 2 2.5257 8 3.5950 4 -1.7794 2 3.5611 8 4.1898 6 -0.2868 8 3.2994 8 4.1078
4 -8.2845 10 -10.0171
8 -5.3341 8 -3.7320
10 -0.3987
8 2.6184 10 -2.1740
24.247
28.518 45.693 51.493 58.023 56.526 80.595 72.221
76.561 100.190
94.713 113.299 113.108
99.715 120.983 122.666 135.268 149.601 155,618 161.826
-3,68651 -7.72786
1.13428 -5.64616 -7.43510
7.69290
6.82393 -5.82468
6.82856 5.51902 8.35525 -2.27098 5.85014 0.77053
-2.90030 -5.49145 -1,20207
4.81847
-1.75138 -3.85658
-0,71087 -1.45731
0.22226 -1.02394 -1.35695
1,46730 1.32969 -1,05581 1.34372 1.01186
1.48297 -0,40850
1.04722 0.14508 -0.55506
-1.03019 -0.22019
0.91234 -0.34056 -0.75305
MTB > >PLOT C2 Cl XI
12.00+
**
***
PRED Y
27,933 36.246 44.559 57.146 65.458 48.833 73.771 78,045 69.733 94.671 86.358 115.570 107.258 98.945 123.883 128,157 136.470 144.783 157.370 165.683
8.00+
****
*k**
4.00+
* * * kkk
.00+
.00
5.00
10.00
15.00
20.00
25.00
MTB > >PLOT C3 Cl X2
12.50+
9.00+ 5.50+
k kk
* **
kk
*k
kk
k
kk
k
k
TEH 0532576
DUP050033844
--------FT
.00
5.00
10.00
15.00
20.00
25.00
MTB > >PLOT 05 Cl M
180.00+
**
120.00+
*
** **
** *
60.00+
**
**
**
**
.00+
+------ ------------+-------- --------- +---------- ----+------
Oo or l
. 00 5.00
15.00
--t--20.00
25.00
>PLOT C3 C2 X2
12.50+
-
9.00+
*** * * k * *
ifl - * * * * * 5.50+
-* * * *
2.00+ *
k
+------ --------
2.00
4.00
*
----h-----
6.00
-------- h----- ---
8.00
10.00
---+X1 12.00
MTB > >CORR Cl C2 C3 C5
T XI X2
XI .983
X2
.679
. 620
M
.935
.969
.764
MTB > >SAVE *CAKRD8*TESTS.' MTB > >STOP
*** MINITAB *** STATISTICS DEPT * PENN STATE UNIV. * RELEASE 82.1 *
STORAGE USED
3000 STORAGE AVAILABLE 100000
TEH 0532577
# # # # # #
Cl
DUP050033845
1!
RUNID: CAK
ACCTs 156015
CAK
FIN
TIME!
TOTAL: 00:00:13.061
CPU: 00:00:01.206
CC/ER: CO:00:05.698
PROJECT: Q*Q*Q*
CBSUPSi 004956066 I/O: 00:00:06.155 WAIT: 00:17:02.879
SIMS USED:
257 SUAS REMAINING:
99995983
IMAGES READ: 40
PAGES: 9
START:
11:09:37 FEB 08,1984
FIN: 11:26:53 FEB 08,1984
^TERMINAL INACTIVE*
>MINITAB*MINITAB.MINITAB
*WAIT-LAST INPUT IGNORED*
IF YOU NEED THE 81.1 VERSION OF MINITAB, IT IS IN "0LD*MINITAB.MINITAB". MINITAB RELEASE 82.1 *** COPYRIGHT - PENN STATE UNIV. 1982 FEB. 8, 1984 *** UNIV. OF WISCONSIN - MADISON -- MACC VERSION 82.1-UW2.1 STORAGE AVAILABLE 100000
MTB > >RETR ' CAKRDS*TESTS. * MTB > >INFO
COLUMN Cl C2 C3
C4 C5 C6 C7 C8
NAME T XI X2 E M Y RESID ST RESID
PRED Y
COUNT 20 20 20 20 20 20 20
20
CONSTANTS USED: K49 K50
MTB > >REGRESS C2 ON 1 PRED Cl C9 CIO
o THE REGRESSION EQUATION IS XI =* 1.04 + 0.529 T
COLUW T
COEFFICIENT 1.0421
0.52932
ST. DEV. OF COEF.
0.2787 0.02326
T-RATIO COEF/S.D.
3.74 22.75
S = 0.5999
R-SQUARED * 96.6 PERCENT R-SQUARED 96.5 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO
REGRESSION
RESIDUAL TOTAL
DF 1
18 19
SS 186.32
6.48 192.80
MS*SS/DF 186.32 0.36
0 DURBIN-WATSON STATISTIC - 2.27
'0
MTB > >
uxn v v k iAur e*n s a t
n / rshriN
/
TEH 0532578
DUP050033846
MTB > >REGRESS C2 ON 1 PRED Cl Cll C12
THE REGRESSION EQUATION IS XI = 1.04 + 0.529 T
COLUMN T
COEFFICIENT 1.0421
0.52932
ST. DEV. OF COEF.
0.2787 0.02326
T-RATIO COEF/S.D
3.74
22.75
S 0.5999
R-SQUARED =96.6 PERCENT R-SQUARED = 96.5 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION RESIDUAL TOTAL
DF 1
18 19
SS 186.32
6.48 192.80
MS=SS/DF 186.32 0.36
DURBIN-WATSON STATISTIC = 2.27
MTB > >REGRESS C3 ON 1 PRED Cl Cll C12
THE REGRESSION EQUATION IS
X2 " 2.93 *+!#>** 0.302 T
COLUMN T
COEFFICIENT 2.9263
0.30226
ST. DEV. OF COEF.
0.9229
0.07704
T-RATIO < COEF/S.D
3.17 3.92
S 1.987
R-SQUARED * 46.1 PERCENT R-SQUARED = 43.1 PERCENT, ADJUSTED FOR D.F.
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 1
18 19
SS 60.753 71,047 131.800
MS=SS/DF 60.753 3.947
DURBIN-WATSON STATISTIC = 2,88
MTB > >NAME Cll 'ST X2',C12 'PRED X2' MTB > > INFO
COLUMN Cl C2
C3 C4 C5
C6 C7 C8 C9
NAME T XI
X2 E M Y RESID ST RESID
PRED Y ST XI
COUNT
20 20
20 20 20 20 20 20 20
I,of
l.%
M3
3 i "2
Ay
f
TEH 0532579
DUP050033847
CU Cl 2
ST X2 PRED X2
20 20
CONSTANTS USED! K4S K50
MTB > MTB > MTB >
MTB > ROW
>1_ET 013=02-010 >LET 014=03-012 >NAME Cl3 'XI RESID >PRINT Cl3 Cl 4
XI RESID X2 RESID
1 0.428571 -1.22857 2 -0.100752 0.46917 3 -0.630075 2.16692 4 0.840602 -0.13534
5 D.311278 1.56241
6 -0.218045 -2.73985
7 -0.747368 2.95789 8 0.723308 -1.34436
9 0.193985 -3.64662
10 -0.335338 2.05113
11 -0.864662 -0.25113 12 0.606015 1.44662 13 0.076692 -0.85564 14 -G.452631 -3.15789 15 -0.981955 2.53985 16 0.488722 -1.76241 17 -0.040601 -0.06466 18 -0.569925 1.63308 19 0.900752 -0.66917 20 0.371429 1.02857
MTB > >REGRESS 05 ON 3 PRED 013 C14 Cl
THE s REEGGRKEESSS16N~QUATI ON M =1 20.8 f (4.061:1 RESID 4(3.20 1X2 RESID +\6.83
COLUMN
XI RESID X2 RESID T
COEFFICIENT 20.755 4.058 3.1988 6.8846
ST. DEV. OF COEF.
2.098
1.897 0.5729 0.1751
T-RATIO * COEF/S.D.
9.89 2.14 5.58 39.31
S = 4.516
R-SQUARED m 99.0 PERCENT R-SQUARED 98.8 PERCENT, ADJUSTED 1
ANALYSIS OF VARIANCE
DUE TO REGRESSION
RESIDUAL TOTAL
DF 3
16 19
SS 32156
326
32482
MS< 107,
CONTINUED >
FURTHER ANALYSIS OF VARIANCE
SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN
DUE TO
DF
SS
REGRESSION 3
32156
XI RESID
1
1
X2 RESID
1
636
T 1 31520
TEH 0532580
DUP050033848
DURBIN-WATSON STATISTIC =1.34 # o-SSSk
>
*111
g'l 5
TEH 0532581
DUP050033849
N 3 3 8 2 8 .0 2
TEH 0532582
DUP050033850
DUP050033851
K
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to Deo)the P dlpeoP-dead? dUods C. Purpose, oP report'
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* " Pot nci<D*~d taifXj dec/o*Cs u%, A/sXcr^<D ^aarttlo *&+<P e&mt*upt/n*
TEH 0532584
DUP050033852
Z23JZ*
A,
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DUP050033853
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** TEH 0532586
DUP050033854
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" AJfl+6 Is-H'W. Cedt(tn<6^j fct&A/.*e*v' ^2J> /^ ^
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TEH 0532587
DUP050033855
/
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f\y{uu*clUu*
TEH 0532588
DUP050033856
&GUr 1~ 7C
f
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TEH 0532589
DUP050033857
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TEH 0532590
DUP050033858
p-ps
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TEH 0532591
DUP050033859
1'
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DUP050033860
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TEH 0532593
DUP050033861
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DUP050033862
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