1
/*
2
*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8;
3
DATA SET TITLE: ATMOSPHERIC CO2 CONC - MAUNA LOA OBSERVATORY, HAWAII,
1958-2001.
4
CONTRIBUTORS: C. D. KEELING, T. P. WHORF (AND THE CARBON DIOXIDE
RESEARCH
5
GROUP), SCRIPPS INSTITUTION OF
OCEANOGRAPHY, UNIVERSITY OF CALIFORNIA,
6
LA JOLLA, CALIFORNIA 92093-0444
7
SCOPE OF THE DATA: THE DATA FILE
CONTAINS MONTHLY AND ANNUAL ATMOSPHERIC
8
CO2
CONCENTRATIONS
DERIVED FROM THE SCRIPPS INSTITUTION OF
9
OCEANOGRAPHY'S (SIO's)
CONTINUOUS MONITORING PROGRAM AT MAUNA LOA
10
OBSERVATORY, HAWAII. THIS RECORD
CONSTITUTES THE LONGEST CONTINUOUS
11
RECORD OF ATMOSPHERIC CO2
CONCENTRATIONS AVAILABLE IN THE WORLD.
12
MONTHLY AND ANNUAL AVERAGE MOLE
FRACTIONS OF CO2 IN WATER-VAPOR-FREE AIR
13
ARE GIVEN FROM MARCH 1958 THROUGH
DECEMBER 2001, EXCEPT FOR A FEW INTERRUPTIONS.
14
DATA FORMAT: ALL CONC. ARE
EXPRESSED IN PARTS PER MILLION BY VOLUME (PPMV) IN
15
THE SIO X99 MOLE FRACTION
SCALE. MISSING VALUES ARE REPRESENTED BY
-99.99.
16
*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8;
17
*/
18
19
options nocenter nodate nonumber ls=80 ps=256;
20
data maunaloa; length month $ 9;
21
title1 'Trend analysis of carbon dioxide levels';
22
infile 'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\maunaloa.co2.txt'
firstobs=15 obs=58;
23
input @1 Year 4. @5 January 7.
@12 February 7. @19 March 7. @26 April 7. @33 May 7. @40
24
June 7. @47 July 7. @54 August 7. @61 September 7. @68
October 7. @75
24
November 7. @82
December
7. @89 Annual 7.;
25
time = year - 1957;
26
CO2Level = January; mo = 1; month = 'January';
output;
27
CO2Level = February; mo = 2; month = 'February'; output;
28
CO2Level = March; mo = 3; month =
'March'; output;
29
CO2Level = April; mo = 4; month =
'April'; output;
30
CO2Level = May; mo = 5; month
= 'May'; output;
31
CO2Level = June; mo = 6; month =
'June'; output;
32
CO2Level = July; mo =
7; month = 'July'; output;
33
CO2Level = August; mo = 8; month = 'August';
output;
34
CO2Level = September; mo = 9;
month = 'September'; output;
35
CO2Level = October; mo = 10;
month = 'October'; output;
36
CO2Level = November; mo = 11;
month = 'November'; output;
37
CO2Level = December; mo = 12;
month = 'December'; output;
38
drop January February March April May June July August September
39
October November December
Annual;
40
run;
NOTE: The
infile
'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\maunaloa.co2.txt' is:
File Name=C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\maunaloa.co2.txt,
RECFM=V,LRECL=256
NOTE: 44
records were read from the infile
'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\maunaloa.co2.txt'.
The minimum record length was 102.
The maximum record length was 102.
NOTE: The data
set WORK.MAUNALOA has 528
observations and 5 variables.
NOTE: DATA
statement used:
real time
0.06 seconds
cpu
time
0.06 seconds
41
42
data maunaloa; set maunaloa;
43
if co2level lt 0 then co2level = .;
44
loglevel = log(co2level);
46
run;
48
*proc print noobs; run;
49
options ls=111 ps=56;
50
proc plot data=maunaloa; plot co2level*time; run;
51
options ls=80 ps=256;
NOTE: There
were 528 observations read from
the data set WORK.MAUNALOA.
NOTE: The
PROCEDURE PLOT printed page 1.
NOTE:
PROCEDURE PLOT used:
real time
0.05 seconds
cpu
time
0.03 seconds
Trend analysis
of carbon dioxide levels
Plot of
CO2Level*time. Legend: A = 1 obs, B = 2
obs, etc.
CO2Level |
|
380 +
|
|
|
|
C
|
B
C D
370
+
A C D C
|
C C C B
|
B
C B B
|
C D D B
|
C
C C A
|
C C C A
360
+
A B C B D C B
|
B
B B
D B
|
C B C C C
|
A C D C B B
|
B
E C B C B
|
C D B B B
350
+
C B C B
|
C
B E B
|
C C D B
|
C D D C
|
B
D D C B
|
B B B C B
340
+
B
C D D B
|
C C
D B B
|
C
B D C B
|
C B D A
|
B C C D C B
|
D C C C C
330
+
B C D D B
|
C C E D A B A
|
D C E C A B
|
B C B C B B
|
C D E D C B
| A C
B E D C B B
320 + B C D B B C C C B
| A C C C C D C C B
| B C D D C C B A
| C D A B A
| B B B
|
310 +
|
---+---------+---------+---------+---------+---------+---------+---------+---------+---------+
0
5
10
15
20
25
30
35
40 45
time
NOTE: 7 obs
had missing values.
53
proc mixed data=maunaloa; classes month;
54
title2 'Basic Analysis of Covariance using PROC MIXED';
55
model co2level = time month time*month / htype=1 3 DDFM=Satterthwaite;
57
run;
NOTE: 7
observations are not included
because of missing values.
NOTE: The
PROCEDURE MIXED printed page 2.
NOTE:
PROCEDURE MIXED used:
real time
0.07 seconds
cpu
time
0.07 seconds
Trend analysis
of carbon dioxide levels
Basic Analysis
of Covariance using PROC
MIXED
The Mixed
Procedure
Model Information
Data
Set
WORK.MAUNALOA
Dependent
Variable
CO2Level
Covariance
Structure
Diagonal
Estimation
Method
REML
Residual
Variance Method
Profile
Fixed Effects
SE Method
Model-Based
Degrees of
Freedom Method
Residual
Class Level Information
Class
Levels Values
month
12 April August December
February January July June March May November October September
Dimensions
Covariance
Parameters
1
Columns in
X
26
Columns in
Z
0
Subjects
1
Max Obs Per
Subject
528
Observations
Used
521
Observations
Not
Used
7
Total
Observations
528
Covariance
Parameter
Estimates
Cov
Parm
Estimate
Residual
3.5033
Fit Statistics
-2 Res Log
Likelihood 2184.8
AIC (smaller
is better) 2186.8
AICC (smaller
is better) 2186.8
BIC (smaller
is better) 2191.0
Type 1 Tests
of Fixed Effects
Num Den
Effect
DF DF F
Value
Pr > F
time
1 497
42276.8 <.0001
month
11 497
45.54 <.0001
time*month
11
497 0.26 0.9927
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
time
1 497
42195.7 <.0001
month
11 497
9.51 <.0001
time*month
11
497 0.26 0.9927
59
proc glm data=maunaloa; classes month;
60
title2 'Basic Analysis of Covariance using PROC GLM';
61
model co2level = time month time*month / solution;
62
run;
NOTE: The
PROCEDURE GLM printed pages 3-4.
NOTE:
PROCEDURE GLM used:
real time
0.08 seconds
cpu
time
0.08 seconds
Trend analysis
of carbon dioxide levels
Basic Analysis
of Covariance using PROC GLM
The GLM
Procedure
Class Level
Information
Class
Levels Values
month
12
April August December February January July June March May November
October September
Number of
observations 528
NOTE: Due to
missing values, only 521
observations can be used in this analysis.
Trend analysis
of carbon dioxide levels
Basic Analysis
of Covariance using PROC GLM
Dependent
Variable: CO2Level
Sum
of
Source
DF Squares
Mean Square F Value
Pr > F
Model
23 149874.8665
6516.2985 1860.02
<.0001
Error
497
1741.1612
3.5033
Corrected
Total
520
151616.0277
R-Square
Coeff Var Root MSE
CO2Level Mean
0.988516
0.550729
1.871722 339.8628
Source
DF Type I SS Mean
Square F Value
Pr > F
time
1 148110.2034
148110.2034 42276.8
<.0001
month
11
1754.7861
159.5260 45.54
<.0001
time*month
11
9.8771
0.8979 0.26
0.9927
Source
DF Type III SS Mean
Square F Value
Pr > F
time
1 147825.9593
147825.9593 42195.7
<.0001
month
11
366.6464
33.3315 9.51
<.0001
time*month
11
9.8771
0.8979 0.26
0.9927
Standard
Parameter
Estimate
Error t Value
Pr > |t|
Intercept
307.1697146 B 0.57410421
535.04
<.0001
time
1.3144369 B
0.02222108
59.15
<.0001
month
April
4.3696829 B
0.82363751
5.31
<.0001
month
August
1.5290698 B
0.81190596
1.88
0.0602
month
December 1.7211416
B
0.81190596
2.12
0.0345
month
February 1.9953236
B
0.84506816
2.36
0.0186
month
January 1.4453398
B
0.83122443
1.74
0.0827
month
July
3.3254757
B
0.81190596
4.10
<.0001
month
June
4.1589625 B
0.83122443
5.00
<.0001
month
March
3.1485337 B
0.82363751
3.82
0.0001
month
May
4.9943340 B
0.81190596
6.15
<.0001
month
November 0.7041332
B
0.81190596
0.87
0.3862
month
October -0.8184642
B
0.83122443
-0.98
0.3253
month
September 0.0000000
B
.
.
.
time*month
April
0.0302079 B
0.03170608
0.95
0.3412
time*month
August
0.0088393 B
0.03142535
0.28
0.7786
time*month
December 0.0344038
B
0.03142535
1.09
0.2741
time*month
February 0.0369158
B
0.03232065
1.14
0.2539
time*month
January 0.0290137
B
0.03198159
0.91
0.3647
time*month
July
0.0155849 B
0.03142535
0.50
0.6202
time*month
June
0.0365205 B
0.03198159
1.14
0.2540
time*month
March
0.0285085 B
0.03170608
0.90
0.3690
time*month
May
0.0280599 B
0.03142535
0.89
0.3723
time*month
November 0.0242607
B
0.03142535
0.77
0.4405
time*month
October 0.0289971
B
0.03198159
0.91
0.3650
time*month
September 0.0000000
B
.
. .
NOTE: The X'X
matrix has been found to be
singular, and a generalized inverse
was used to solve the normal equations.
Terms whose estimates are
followed by the letter 'B' are not uniquely estimable.
64
proc sort data=maunaloa; by mo; run;
NOTE: There
were 528 observations read from
the data set WORK.MAUNALOA.
NOTE: The data
set WORK.MAUNALOA has 528
observations and 6 variables.
NOTE:
PROCEDURE SORT used:
real time
0.04 seconds
cpu
time
0.04 seconds
65
proc means data=maunaloa noprint; by mo;
66
title2 'Calculate and plot means to examine pattern over a year';
67
var co2level; output out=next n=n mean=mean var=var;
68
run;
NOTE: There
were 528 observations read from
the data set WORK.MAUNALOA.
NOTE: The data
set WORK.NEXT has 12
observations and 6 variables.
NOTE:
PROCEDURE MEANS used:
real time
0.05 seconds
cpu
time
0.05 seconds
69
options ls=111 ps=56;
70
proc plot data=next; plot mean*mo; run;
71
options ls=80 ps=256;
NOTE: There
were 12 observations read from
the data set WORK.NEXT.
NOTE: The
PROCEDURE PLOT printed page 5.
NOTE:
PROCEDURE PLOT used:
real time
0.01 seconds
cpu
time
0.01 seconds
Trend analysis
of carbon dioxide levels
Calculate and
plot means to examine pattern
over a year
Plot of
mean*mo. Legend: A = 1 obs, B = 2 obs,
etc.
mean |
343 +
|
|
|
|
A
A A
|
342 +
|
|
|
|
|
341
+
A
| A
|
|
A
|
|
340 +
|
|
| A
|
|
A
339 +
|
|
|
A
|
|
338
+
A
|
|
|
|
A
|
337 +
|
|
A
|
|
|
336 +
|
---+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--
1
2
3
4
5
6
7
8
9
10
11 12
mo
73
proc mixed data=maunaloa; classes month;
74
title2 'Analysis of Covariance and Response Surface - testing';
75
model co2level = time time*time mo mo*mo mo*mo*mo mo*mo*mo*mo
76
time*mo time*mo*mo time*mo*mo*mo
time*mo*mo*mo*mo
77
time*time*mo time*time*mo*mo
time*time*mo*mo*mo time*time*mo*mo*mo*mo
78
month month*time / htype=1 3
DDFM=Satterthwaite;
79
run;
NOTE: 7
observations are not included
because of missing values.
NOTE: The
PROCEDURE MIXED printed page 6.
NOTE:
PROCEDURE MIXED used:
real time
0.07 seconds
cpu
time
0.07 seconds
Trend analysis
of carbon dioxide levels
Analysis of
Covariance and Response Surface
- testing
The Mixed
Procedure
Model Information
Data
Set
WORK.MAUNALOA
Dependent
Variable
CO2Level
Covariance
Structure
Diagonal
Estimation
Method
REML
Residual
Variance Method
Profile
Fixed Effects
SE Method
Model-Based
Degrees of
Freedom Method
Residual
Class Level Information
Class
Levels Values
month
12 April August December February January July June
March May November
October September
Dimensions
Covariance
Parameters
1
Columns in
X
39
Columns in
Z
0
Subjects
1
Max Obs Per
Subject
528
Observations
Used
521
Observations
Not
Used
7
Total
Observations
528
Covariance
Parameter Estimates
Cov
Parm
Estimate
Residual
0.5614
Fit Statistics
-2 Res Log
Likelihood 1415.2
AIC (smaller
is better) 1417.2
AICC (smaller
is better) 1417.3
BIC (smaller
is better) 1421.4
Type 1 Tests of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
time
1 491
263837 <.0001
time*time
1 491
2618.04 <.0001
mo
1 491
820.70 <.0001
mo*mo
1
491 359.17 <.0001
mo*mo*mo
1 491
1435.04 <.0001
mo*mo*mo*mo
1 491
326.95 <.0001
time*mo
1 491
0.06 0.8069
time*mo*mo
1 491
1.27 0.2601
time*mo*mo*mo
1 491
8.25 0.0043
time*mo*mo*mo*mo
1
491 0.15 0.7009
time*time*mo
1 491
0.01 0.9111
time*time*mo*mo
1 491
0.80 0.3728
time*time*mo*mo*mo
1
491 0.14 0.7113
tim*time*mo*mo*mo*mo
1
491 0.00 0.9468
month
7 491
25.76 <.0001
time*month
7 491
0.31 0.9474
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
time
1 491
54.27 <.0001
time*time
1 491
36.19 <.0001
mo
0
.
. .
mo*mo
0
.
. .
mo*mo*mo
0
.
. .
mo*mo*mo*mo
0
.
. .
time*mo
0
.
. .
time*mo*mo
0
.
. .
time*mo*mo*mo
0
.
. .
time*mo*mo*mo*mo
0
.
. .
time*time*mo
1 491
0.09 0.7584
time*time*mo*mo
1
491 0.03 0.8697
time*time*mo*mo*mo
1
491 0.01 0.9357
tim*time*mo*mo*mo*mo
1
491 0.00 0.9698
month
5 491
4.95 0.0002
time*month
7 491
0.31 0.9474
81
proc mixed data=maunaloa; classes month;
82
title2 'Fit of a simplified Response Surface';
83
model co2level = time time*time mo mo*mo mo*mo*mo mo*mo*mo*mo
84
/ htype=1 3
DDFM=Satterthwaite outp=ResidDataP solution;
85
run;
NOTE: 7
observations are not included
because of missing values.
NOTE: The data
set WORK.RESIDDATAP has 528
observations and 13 variables.
NOTE: The
PROCEDURE MIXED printed page 7.
NOTE:
PROCEDURE MIXED used:
real time
0.16 seconds
cpu
time
0.16 seconds
86
quit;
Trend analysis
of carbon dioxide levels
Fit of a
simplified Response Surface
The Mixed
Procedure
Model Information
Data
Set
WORK.MAUNALOA
Dependent
Variable
CO2Level
Covariance
Structure
Diagonal
Estimation
Method
REML
Residual
Variance Method
Profile
Fixed Effects
SE Method
Model-Based
Degrees of
Freedom Method
Residual
Class Level Information
Class
Levels Values
month
12 April August December
February January July June March May November October September
Dimensions
Covariance
Parameters
1
Columns in
X
7
Columns in
Z
0
Subjects
1
Max Obs Per
Subject
528
Observations
Used
521
Observations
Not
Used
7
Total
Observations
528
Covariance
Parameter
Estimates
Cov
Parm
Estimate
Residual
0.7484
Fit Statistics
-2 Res Log
Likelihood 1391.5
AIC (smaller
is better) 1393.5
AICC (smaller
is better) 1393.5
BIC (smaller
is better) 1397.7
Solution for Fixed Effects
Standard
Effect
Estimate
Error DF
t Value Pr > |t|
Intercept
312.28 0.3637
514 858.72
<.0001
time
0.8051 0.01244
514 64.70
<.0001
time*time
0.01178 0.000266
514 44.25
<.0001
mo
-0.04612 0.3342
514 -0.14
0.8903
mo*mo
0.6626 0.09890
514
6.70 <.0001
mo*mo*mo
-0.1346 0.01121
514 -12.00
<.0001
mo*mo*mo*mo
0.006711
0.000429 514
15.66
<.0001
Type 1 Tests of Fixed Effects
Num Den
Effect
DF
DF
F Value Pr > F
time
1 514
197913 <.0001
time*time
1
514 1963.89 <.0001
mo
1 514
615.64 <.0001
mo*mo
1 514
269.43 <.0001
mo*mo*mo
1
514 1076.47 <.0001
mo*mo*mo*mo
1
514 245.26 <.0001
Type 3 Tests of Fixed Effects
Num Den
Effect
DF DF
F Value Pr > F
time
1 514
4186.59 <.0001
time*time
1
514 1958.27 <.0001
mo
1 514
0.02 0.8903
mo*mo
1 514
44.89 <.0001
mo*mo*mo
1
514 144.04 <.0001
mo*mo*mo*mo
1
514 245.26 <.0001
88
PROC UNIVARIATE DATA=ResidDataP PLOT NORMAL; VAR resid;
91
RUN;
NOTE: The
PROCEDURE UNIVARIATE printed pages
8-9.
NOTE:
PROCEDURE UNIVARIATE used:
real time
3.66 seconds
cpu
time
0.32 seconds
Trend analysis
of carbon dioxide levels
Fit of a
simplified Response Surface
The UNIVARIATE
Procedure
Variable:
Resid
Moments
N
521 Sum
Weights
521
Mean
0 Sum
Observations
0
Std
Deviation 0.86007223
Variance
0.73972425
Skewness
0.29861691
Kurtosis
-0.1936156
Uncorrected
SS 384.65661 Corrected
SS 384.65661
Coeff
Variation
. Std Error Mean
0.03768045
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std
Deviation
0.86007
Median
-0.05525
Variance
0.73972
Mode
.
Range
5.03599
Interquartile
Range 1.22765
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t
0 Pr > |t| 1.0000
Sign
M -9.5
Pr >= |M| 0.4304
Signed
Rank S
-2031.5 Pr >= |S| 0.5551
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.992105 Pr < W
0.0073
Kolmogorov-Smirnov
D
0.041427 Pr > D
0.0284
Cramer-von
Mises W-Sq
0.175167 Pr > W-Sq 0.0113
Anderson-Darling
A-Sq
1.092857 Pr > A-Sq 0.0076
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max 2.7313413
99%
2.0879960
95%
1.5156392
90%
1.1414107
75%
Q3 0.6015282
50%
Median
-0.0552539
25%
Q1
-0.6261222
10%
-1.0483464
5%
-1.2992655
1%
-1.6967417
0%
Min
-2.3046472
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-2.30465
392
2.17174 32
-1.99443
388
2.37034 210
-1.98929
103
2.37386 473
-1.84170
396
2.41438 472
-1.69762
371
2.73134 471
Missing Values
-----Percent Of-----
Missing
Missing
Value Count
All Obs Obs
.
7
1.33 100.00
Stem
Leaf
#
Boxplot
26
3
1 0
24
1
1 |
22
77
2 |
20 1397
4
|
18
013669
6 |
16
301478
6 |
14
014602278999
12 |
12
0027990144589
13 |
10
00112267891246667999
20 |
8
001111233557900223455567888899
30 |
6
0000111123456667990111111122333345568
37
+-----+
4
0000112333334445668999990000000122233889
40
| |
2
000012455556666777791122222346667789
36 | |
0
1111223455555566777770112222234556666788999
43
| + |
-0
8876665554433332222108877666544333222
37 *-----*
-2 98766665544332222211100998887555555444433211000
47
| |
-4
888887777644322221110009999888876655443111000
45
| |
-6
97776333222110009999876664433333222211000
41
+-----+
-8
997776666555531110887776666665322111100
39 |
-10
743211076665554432100
21 |
-12
42100008876544321000
20 |
-14
2009432100
10
|
-16
007200
6 |
-18
994
3 |
-20
|
-22
0
1
|
----+----+----+----+----+----+----+----+----+--
Multiply Stem.Leaf by 10**-1
Normal Probability Plot
2.7+
*
|
*
|
*
|
***+
|
**++
1.7+
**+
|
****
|
**+
|
***
|
****
0.7+
***
|
***
|
***
|
****
|
+**
-0.3+
****
|
***
|
****
|
****
| ***
-1.3+ *****
| ****+
| *** ++
|* +++
|++
-2.3+*
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
Modified: August 16, 2004
James P. Geaghan
