1
**EXAMPLE
1******************************************************;
2
*** The 1994 salaries of
all American league baseball players ***;
3
*** as reported in USA
Today on April 5,
1994.
***;
4
*** Salaries include
pro-rated signing
bonuses.
***;
5
*****************************************************************;
6
OPTIONS PS=256 LS=132
NOCENTER NODATE PAGENO=1;
7
dm
'log;clear;output;clear';
8
filename input
'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\07b-AnovaRBD_baseball.DAT';
9
10
DATA salaries; length
team player $ 20; INFILE input MISSOVER;
11
INPUT Team $ 1-20
Player $ 24-43 Position $ 47-48 read $ 50-51 Salary 60-68;
12
TITLE1 'EXST7015: Salaries of all American
league baseball players (1994)';
13
TITLE2 'Salaries
in thousands of dollars';
14
DH = 'No '; if read eq
'dh' then DH = 'Yes'; drop read;
15
salary = salary /
1000;
16
lsalary = log(salary);
17
CARDS;
NOTE: The
infile INPUT is:
File
Name=C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\07b-AnovaRBD_baseball.DAT,
RECFM=V,LRECL=256
NOTE: 374
records were read from the infile INPUT.
The minimum record length was
68.
The maximum record length was
68.
NOTE: The data
set WORK.SALARIES has 374 observations and 6 variables.
NOTE: DATA
statement used:
real time
0.11 seconds
cpu
time
0.09 seconds
17
! RUN;
18
;
19
PROC PRINT
data=salaries; TITLE3 'RAW DATA LISTING'; RUN;
NOTE: There
were 374 observations read from the data set WORK.SALARIES.
NOTE: The
PROCEDURE PRINT printed pages 1-2.
NOTE:
PROCEDURE PRINT used:
real time
0.06 seconds
cpu
time
0.06 seconds
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
RAW
DATA LISTING
Obs
team
player
Position Salary
DH lsalary
1
Baltimore Orioles Rafael
Palmeiro
1b 5406.60
No
8.59538
2 Baltimore Orioles Cal
Ripken
ss 5400.00
No
8.59415
3 Baltimore Orioles Mike
Devereaux
of 3375.00
No
8.12415
4 Baltimore Orioles Sid
Fernandez
p 3333.33
No
8.11173
5 Baltimore Orioles Brady
Anderson
of 3083.33
No
8.03377
6 Baltimore Orioles Ben
McDonald
p 2675.00
No 7.89170
. . .
373
Toronto Blue Jays Paul
Spoljaric
p
109.00 No
4.69135
374
Toronto Blue Jays Paul
Menhart
p
109.00 No
4.69135
21
PROC MIXED DATA=salaries cl covtest;
CLASSES team position dh;
22
TITLE3 'Analysis of Variance - PROC
MIXED';
23
MODEL salary = position DH / htype=3
DDFM=Satterthwaite outp=ResidData;
24
random team;
25
lsmeans position / pdiff
adjust=tukey;
26
ods output diffs=ppp;
27
ods output lsmeans=mmm;
28
*ods listing exclude diffs;
29
*ods listing exclude lsmeans;
30
run;
WARNING:
Length of CLASS variable team truncated to 16.
NOTE:
Convergence criteria met.
NOTE:
The data set WORK.MMM has 8 observations and 7 variables.
NOTE:
The data set WORK.PPP has 28 observations and 10 variables.
NOTE:
The data set WORK.RESIDDATA has 374 observations and 13 variables.
NOTE:
The PROCEDURE MIXED printed page 3.
NOTE:
PROCEDURE MIXED used:
real time
0.27 seconds
cpu
time
0.27 seconds
31
%include
'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\pdmix800.sas';
647
%pdmix800(ppp,mmm,alpha=.05,sort=yes);
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED
The
Mixed Procedure
Model Information
Data
Set
WORK.SALARIES
Dependent
Variable
Salary
Covariance
Structure Variance
Components
Estimation
Method
REML
Residual
Variance Method Profile
Fixed
Effects SE Method Model-Based
Degrees
of Freedom Method Satterthwaite
Class Level Information
Class
Levels
Values
team
14 Baltimore Oriole Boston Red
Sox California Angel
Chicago
White So Cleveland Indian
Detroit Tigers Kansas
City
Roya Milwaukee Brewer
Minnesota Twins New York
Yankees Oakland Athletic
Seattle Mariners Texas
Rangers
Toronto Blue Jay
Position
8
1b 2b 3b c if of p ss
DH
2 No Yes
Dimensions
Covariance
Parameters
2
Columns
in
X
11
Columns
in
Z
14
Subjects
1
Max
Obs Per
Subject
374
Observations
Used
374
Observations
Not
Used
0
Total
Observations
374
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 6346.82951099
1
2
6346.81578713 0.00000000
Convergence criteria met.
Covariance
Parameter Estimates
Standard Z
Cov
Parm
Estimate
Error
Value Pr
Z
Alpha
Lower Upper
team
3466.41
30458 0.11
0.4547 0.05
513.45
3.81E125
Residual
1924296 145057
13.27
<.0001 0.05
1668871 2243534
Fit Statistics
-2
Res Log
Likelihood 6346.8
AIC
(smaller is better) 6350.8
AICC
(smaller is better) 6350.8
BIC
(smaller is better) 6352.1
Type
3 Tests of Fixed Effects
Num Den
Effect
DF
DF F Value Pr > F
Position
7
359 2.75 0.0085
DH
1 364
4.45 0.0356
Least
Squares Means
Standard
Effect
Position Estimate
Error DF
t Value Pr > |t|
Position
1b
2853.96 423.51
363
6.74 <.0001
Position
2b
2065.92 475.36
361
4.35 <.0001
Position
3b
1921.43 516.99
364
3.72 0.0002
Position
c
1615.79 437.88
364
3.69 0.0003
Position
if
1231.97 500.13
363
2.46 0.0142
Position
of
2296.24 383.25
361
5.99 <.0001
Position
p
1958.94 375.99
356
5.21 <.0001
Position
ss
1751.07 437.93
363
4.00 <.0001
Differences of Least Squares Means
Standard
Effect
Position _Position
Estimate
Error DF
t Value Pr > |t|
Adjustment Adj P
Position
1b
2b
788.04 474.63
362
1.66 0.0977
Tukey-Kramer 0.7128
Position
1b
3b
932.53 488.80
357
1.91 0.0572
Tukey-Kramer 0.5464
Position
1b
c
1238.18 404.34
355
3.06 0.0024
Tukey-Kramer 0.0481
Position
1b
if
1621.99 471.06
363
3.44 0.0006
Tukey-Kramer 0.0147
Position
1b
of
557.73 351.72
356
1.59 0.1137
Tukey-Kramer 0.7587
Position
1b
p
895.02 336.27
356
2.66 0.0081
Tukey-Kramer 0.1380
Position
1b
ss
1102.89 404.37
356
2.73 0.0067
Tukey-Kramer 0.1178
Position
2b
3b
144.49
517.94 362
0.28
0.7804 Tukey-Kramer 1.0000
Position
2b
c
450.13 439.15
363
1.03 0.3060
Tukey-Kramer 0.9705
Position
2b
if
833.94 501.29
365
1.66 0.0971
Tukey-Kramer 0.7108
Position
2b
of
-230.32 391.74
363 -0.59
0.5569
Tukey-Kramer 0.9990
Position
2b
p
106.98 377.39
364
0.28 0.7770
Tukey-Kramer 1.0000
Position
2b
ss
314.85 439.12
362
0.72 0.4738
Tukey-Kramer 0.9965
Position
3b
c
305.64 446.79
358
0.68 0.4944
Tukey-Kramer 0.9974
Position
3b
if
689.46 508.05
365
1.36 0.1756
Tukey-Kramer 0.8758
Position
3b
of
-374.81 401.41
362 -0.93
0.3511
Tukey-Kramer 0.9826
Position
3b
p
-37.5081 386.28
360 -0.10
0.9227
Tukey-Kramer 1.0000
Position
3b
ss
170.36 446.80
359
0.38 0.7032
Tukey-Kramer 0.9999
Position
c
if
383.81 427.29
364
0.90 0.3696
Tukey-Kramer 0.9861
Position
c
of
-680.45 292.64
355 -2.33
0.0206
Tukey-Kramer 0.2828
Position
c
p
-343.15 271.57
354 -1.26
0.2072
Tukey-Kramer 0.9116
Position
c
ss
-135.29 352.39
355 -0.38
0.7013
Tukey-Kramer 0.9999
Position
if
of
-1064.26 379.47
364 -2.80
0.0053
Tukey-Kramer 0.0971
Position
if
p
-726.96 363.50
365 -2.00
0.0463
Tukey-Kramer 0.4834
Position
if
ss
-519.10 427.38
365 -1.21
0.2253
Tukey-Kramer 0.9273
Position
of
p
337.30 187.67
357
1.80 0.0731
Tukey-Kramer 0.6223
Position
of
ss
545.16 292.68
358
1.86 0.0633
Tukey-Kramer 0.5775
Position
p
ss
207.87 271.59
357
0.77 0.4446
Tukey-Kramer 0.9947
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED
Effect=Position
Method=Tukey-Kramer(P<.05) Comparison Group=1
Standard Letter
MinSig
MaxSig AvgSig
Obs
Position Estimate
Error
Group
Diff
Diff Diff
1
1b
2853.96
423.51
A
572.129 1579.01 1203.47
2
of
2296.24
383.25 AB
572.129 1579.01 1203.47
3
2b
2065.92
475.36 AB
572.129 1579.01 1203.47
4
p
1958.94
375.99 AB
572.129 1579.01 1203.47
5
3b
1921.43
516.99 AB
572.129 1579.01 1203.47
6
ss
1751.07
437.93 AB
572.129 1579.01 1203.47
7
c
1615.79
437.88
B
572.129 1579.01 1203.47
8
if
1231.97
500.13
B
572.129 1579.01 1203.47
650
proc sort data=salaries; by position;
run;
NOTE:
There were 374 observations read from the data set WORK.SALARIES.
NOTE:
The data set WORK.SALARIES has 374 observations and 6 variables.
NOTE:
PROCEDURE SORT used:
real time
0.04 seconds
cpu
time
0.04 seconds
651
proc means data=salaries noprint; by
position; var salary;
652
output out = next n=m mean=mean
var=var std=std stderr=stderr;
653
run;
NOTE:
There were 374 observations read from the data set WORK.SALARIES.
NOTE:
The data set WORK.NEXT has 8 observations and 8 variables.
NOTE:
PROCEDURE MEANS used:
real time
0.03 seconds
cpu time
0.03
seconds
654
proc sort data=next; by descending
mean; run;
NOTE:
There were 8 observations read from the data set WORK.NEXT.
NOTE:
The data set WORK.NEXT has 8 observations and 8 variables.
NOTE:
PROCEDURE SORT used:
real time
0.04 seconds
cpu
time
0.04 seconds
655
proc print data=next;
656
TITLE3 'Listing of means by
position';
657
run;
NOTE:
There were 8 observations read from the data set WORK.NEXT.
NOTE:
The PROCEDURE PRINT printed page 5.
NOTE:
PROCEDURE PRINT used:
The SAS
System
real time
0.01 seconds
cpu
time
0.01 seconds
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Listing
of means by position
Obs
Position _TYPE_
_FREQ_ m
mean
var
std stderr
1
1b
0
20
20 2246.55
3361252.63 1833.37
409.954
2
of
0
82
82 1555.90
2630761.85 1621.96
179.116
3
2b
0
15
15 1411.89
1998451.89 1413.67
365.007
4
p
0 165
165 1199.79
1890770.20 1375.05
107.048
5
3b
0
14
14 1165.40
1542338.81 1241.91
331.914
6
ss
0
31
31 992.22
1434743.33 1197.81
215.133
7
c
0
31
31 857.87
797114.46 892.81
160.354
8
if
0 16
16 468.84
671899.22 819.69 204.924
659
OPTIONS PS=52 ls=111;
660
proc plot data=ResidData; plot
resid*pred;
661
TITLE3 'Analysis of Variance - PROC
MIXED';
662
TITLE4 'Residual plot';
663
run;
663
!
OPTIONS PS=256 ls=80;
664
NOTE:
There were 374 observations read from the data set WORK.RESIDDATA.
NOTE:
The PROCEDURE PLOT printed page 6.
NOTE:
PROCEDURE PLOT used:
real time
0.02 seconds
cpu
time
0.02 seconds
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED
Residual
plot
Plot of
Resid*Pred. Legend: A = 1 obs, B = 2
obs, etc.
Resid
|
|
5000
+
|
|
|
A
|
4000
+
C A A
|
A
|
A
|
A
A
A
|
A B
3000
+
A
B A
|
B B
|
AB
|
C
A
|
AF
B
A
2000
+
A B
AE
A
A
|
A
F A
|
B
A
B A
|
A B
E A AA
|
A A
BD B
1000
+
A C AB
A B
|
A B
|
A
A C
|
A A
AB
B
A
A
|
A A AA
E A AC
0
+
B
B
E B
|
D BA
AE
|
GA CC AB
ABH A AA
|
BB AC EL
B
BA
A
|
EC BJ JK
AD
-1000
+
KZ CA BD
|
A A F
|
CW B
|
C
|
B
A
-2000
+
B
|
---+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+--
0
500
1000
1500
2000
2500
3000
3500 4000
Pred
NOTE: 25 obs
hidden.
665
PROC UNIVARIATE DATA=ResidData PLOT
NORMAL; VAR resid;
666
TITLE4 'Residual analysis with PROC
UNIVARIATE';
667
RUN;
NOTE:
The PROCEDURE UNIVARIATE printed page 7.
NOTE:
PROCEDURE UNIVARIATE used:
real time
0.02 seconds
cpu
time
0.02 seconds
667
!
QUIT;
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED
Residual
analysis with PROC UNIVARIATE
The
UNIVARIATE Procedure
Variable:
Resid
Moments
N
374 Sum
Weights
374
Mean
0
Sum
Observations
0
Std
Deviation 1371.12189
Variance
1879975.25
Skewness
1.14864767
Kurtosis
0.44981134
Uncorrected
SS 701230767 Corrected
SS 701230767
Coeff
Variation
.
Std Error Mean 70.8990253
Basic Statistical Measures
Location
Variability
Mean
0.00 Std
Deviation
1371
Median
-580.87
Variance
1879975
Mode
-1082.71
Range
6394
Interquartile Range 1919
NOTE:
The mode displayed is the smallest of 2 modes with a count of 3.
Tests for Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t
0
Pr > |t| 1.0000
Sign
M -54
Pr >= |M| <.0001
Signed
Rank S -3878.5
Pr >= |S| 0.0637
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.864381 Pr < W <0.0001
Kolmogorov-Smirnov
D
0.187785 Pr > D <0.0100
Cramer-von
Mises W-Sq
3.64595
Pr > W-Sq <0.0050
Anderson-Darling
A-Sq
19.53307 Pr > A-Sq <0.0050
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max 4400.707
99%
4017.597
95%
2878.646
90%
2118.449
75%
Q3 904.436
50%
Median -580.868
25%
Q1 -1014.244
10%
-1277.183
5%
-1415.098
1%
-1848.584
0%
Min -1992.824
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-1992.82
183
3953.94 347
-1940.49
76
4017.60 348
-1849.27
306
4029.02 240
-1848.58
202
4093.31 80
-1831.02
92
4400.71 2
Histogram
# Boxplot
4250+**
4 0
.**
4
0
.***
8 |
.***
9 |
.*******
19 |
.*******
20 |
1250+*********
26
|
.*****
13 +-----+
.**********
30 |
+ |
.****************
48 | |
.********************************* 98
*-----*
.*****************************
87
+-----+
-1750+***
8 |
----+----+----+----+----+----+---
* may represent up to 3 counts
Normal Probability Plot
4250+
*
*
|
***
|
****
++++
|
*** +++
|
****+++
|
***++
1250+
***+
|
++**
|
++++***
|
+++*****
|
********
|
**************
-1750+* **** ++++
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
669
OPTIONS PS=52 ls=111;
670
PROC CHART DATA=salaries;
671
TITLE3 'Histogram of baseball player
salaries';
672
VBAR position / SUMVAR=salary
TYPE=MEAN; RUN;
NOTE:
The PROCEDURE CHART printed page 8.
NOTE:
PROCEDURE CHART used:
real time
0.01 seconds
cpu
time
0.01 seconds
673
run; quit; OPTIONS PS=256 ls=80;
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Histogram
of baseball player salaries
Salary Mean
| *****
| *****
2100
+
*****
| *****
| *****
| *****
1800
+
*****
| *****
| *****
|
*****
*****
1500
+
*****
*****
|
*****
*****
*****
|
*****
*****
*****
|
*****
*****
*****
1200
+
*****
*****
*****
***** *****
|
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
|
*****
*****
*****
*****
***** *****
900
+
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
***** *****
600
+
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
*****
***** *****
300
+
*****
*****
***** *****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
*****
***** *****
|
*****
*****
*****
*****
*****
*****
***** *****
--------------------------------------------------------------------------------------------------------
1b
2b
3b
c
if
of
p ss
Position
675
PROC MIXED DATA=salaries cl; CLASSES team position dh;
676
TITLE3 'Analysis of Variance - PROC MIXED with logarithmic
transformation';
677
MODEL lsalary = position DH / htype=3 DDFM=Satterthwaite
outp=ResidData2;
678
random team;
679
run;
WARNING:
Length of CLASS variable team
truncated to 16.
NOTE:
Convergence criteria met.
NOTE: The data
set WORK.RESIDDATA2 has 374
observations and 13 variables.
NOTE: The
PROCEDURE MIXED printed page 9.
NOTE:
PROCEDURE MIXED used:
real time
0.17 seconds
cpu
time
0.16 seconds
679
! quit;
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED with logarithmic transformation
The
Mixed Procedure
Model Information
Data
Set
WORK.SALARIES
Dependent
Variable
lsalary
Covariance
Structure Variance
Components
Estimation
Method
REML
Residual
Variance Method Profile
Fixed
Effects SE Method Model-Based
Degrees
of Freedom Method Satterthwaite
Class Level Information
Class
Levels
Values
team
14 Baltimore Oriole Boston Red
Sox California Angel
Chicago
White So Cleveland Indian
Detroit Tigers Kansas
City
Roya Milwaukee Brewer
Minnesota Twins New York
Yankees Oakland Athletic
Seattle Mariners Texas
Rangers
Toronto Blue Jay
Position
8
1b 2b 3b c if of p ss
DH
2
No Yes
Dimensions
Covariance
Parameters
2
Columns
in
X
11
Columns
in
Z
14
Subjects
1
Max
Obs Per
Subject
374
Observations
Used
374
Observations
Not
Used
0
Total
Observations
374
Iteration History
Iteration
Evaluations -2 Res Log
Like Criterion
0
1 1221.23422138
1
2
1220.79934573 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov
Parm Estimate
Alpha
Lower Upper
team
0.01687 0.05
0.002732 846.73
Residual
1.5200 0.05
1.3181 1.7723
Fit Statistics
-2
Res Log
Likelihood 1220.8
AIC
(smaller is better) 1224.8
AICC
(smaller is better) 1224.8
BIC
(smaller is better) 1226.1
Type 3 Tests of Fixed Effects
Num
Den
Effect
DF
DF F Value Pr > F
Position
7
358 2.18 0.0356
DH
1 362
3.06 0.0811
680
PROC UNIVARIATE DATA=ResidData2 PLOT
NORMAL; VAR resid;
681
TITLE4 'Residual analysis with PROC
UNIVARIATE';
682
RUN;
NOTE:
The PROCEDURE UNIVARIATE printed page 10.
NOTE:
PROCEDURE UNIVARIATE used:
real time
0.03 seconds
cpu
time
0.03 seconds
682
!
QUIT;
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED with logarithmic transformation
Residual
analysis with PROC UNIVARIATE
The
UNIVARIATE Procedure
Variable:
Resid
Moments
N
374 Sum
Weights
374
Mean
0 Sum
Observations
0
Std
Deviation 1.21463657
Variance
1.47534199
Skewness
0.11338944
Kurtosis
-1.2644419
Uncorrected
SS 550.302561 Corrected
SS 550.302561
Coeff
Variation
. Std Error Mean
0.06280736
Basic Statistical Measures
Location
Variability
Mean
0.00000 Std Deviation
1.21464
Median
-0.09396
Variance
1.47534
Mode
-1.63399
Range
4.82406
Interquartile Range 2.19735
NOTE:
The mode displayed is the smallest of 2 modes with a count of 3.
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's
t t
0
Pr > |t| 1.0000
Sign
M -11
Pr >= |M| 0.2775
Signed
Rank S
-32.5
Pr >= |S| 0.9876
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W
0.946761 Pr < W <0.0001
Kolmogorov-Smirnov
D
0.084031 Pr > D <0.0100
Cramer-von
Mises W-Sq
0.874675
Pr > W-Sq <0.0050
Anderson-Darling
A-Sq
6.050037 Pr > A-Sq <0.0050
Quantiles
(Definition 5)
Quantile
Estimate
100%
Max 2.4878558
99%
2.1264322
95%
1.9098152
90%
1.6593573
75%
Q3 1.0782959
50%
Median -0.0939615
25%
Q1 -1.1190570
10%
-1.5963910
5%
-1.6813634
1%
-1.9400166
0%
Min -2.3362008
Extreme Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-2.33620
9
2.11858 247
-2.04187
3
2.12643 190
-1.94872
121
2.14542 213
-1.94002
109
2.30579 344
-1.94002
108
2.48786 85
Stem
Leaf
# Boxplot
24
9
1 |
22
1
1 |
20
23349235
8 |
18
1157790123355889
16 |
16
024556667700245668
18 |
14 0001233566688899000134566667
28
|
12
24455667891245889
17 |
10
001223345589989
15 +-----+
8
23334668888044778
17 | |
6
23346802245666
14 | |
4
135688812478
12 | |
2
1111266133579
13 | |
0
0012223457706899
16 |
+ |
-0 97655544422200099876544222 26
*-----*
-2
988653332222109776640
21
| |
-4
75443100643
11 | |
-6
9888655543199210
16 | |
-8
7655422109876553111
19
| |
-10
98755432221975543210
20
+-----+
-12
9665554200098887776521
22
|
-14 876655543188776544442221
24
|
-16 855540885444333322222110000
27
|
-18
5444987653
10 |
-20
4
1 |
-22
4
1 |
----+----+----+----+----+---
Multiply Stem.Leaf by 10**-1
Normal Probability Plot
2.5+
++ *
|
+ *
|
++*****
*
|
*****
|
****
|
****+
|
***++
|
**
+
|
**++
|
**+
|
**
|
**
0.1+
+**
|
***
|
+**
|
+**
|
++**
|
++***
|
+ **
|
+***
| ****
|
******
|* ***** ++
|*
++
-2.3+*
+
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
684
OPTIONS PS=52 ls=111;
685
proc plot data=ResidData2; plot
resid*pred;
686
TITLE4 'Residual
plot';
687
run;
EXST7015:
Salaries of all American league baseball players (1994)
Salaries
in thousands of dollars
Analysis
of Variance - PROC MIXED with logarithmic transformation
Residual
plot
Plot of Resid*Pred. Legend: A = 1 obs, B = 2 obs, etc.
Resid |
3 +
|
|
| A
|
A
|
ABA
2
+
CC A
CA A
|
A AG
B A
|
B A AC DAA
A
|
A
BBAABBAAAACCA A
|
A CA ABABAAAA A A
|
A A
AA A AA B
1
+
AB AAABAA ABA
A A
|
A
AA
BBAAA
BAA
A
A
|
A
AA AA AB B
|
A
A DC AA
|
B
A AAAA
AA
|
A A
BAB A
A
A
0 +
A
BAABAD AA AABA A
|
A
B A CBC E
A
A
|
A A CEB AAAC
A
|
CA
A A AA
A A A
|
A
AA AAA AA
B
| B A
A A
AC AC AA A A A
-1
+
A B A A AAC
B A
A
A
|
AA AD
BA BAA
|
AD A ABBABA ABA B
|
BABBFCAAAA A
AA
|
CKC B D
|
AACCA A
-2
+
CA A
|
|
A
|
|
|
-3 +
|
---+-------------+-------------+-------------+-------------+-------------+------
5.5
6.0
6.5
7.0
7.5 8.0
Pred
Modified: August 16, 2004
James P. Geaghan