1
********************************************;
2 *** Data from
Freund & Wilson (1993) ***;
3 *** TABLE 8.24
: ESTIMATING TREE WEIGHTS ***;
4
********************************************;
5 options ps=256
ls=80 nocenter nodate nonumber;
6
7 ODS HTML
7 !
file='C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\01-Slr-Trees.html';
NOTE: Writing HTML Body file:
C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\01-Slr-Trees.html
8
9 data one;
infile cards missover;
10 TITLE1
'EXST7015: Estimating tree weights from morphometric variables';
11 input
ObsNo Dbh Height Age Grav Weight ObsID $;
12 ******** label
ObsNo = 'Original observation number'
13
Dbh = 'Diameter at breast height (inches)'
14
Height = 'Height of the tree (feet)'
15
Age = 'Age of the tree (years)'
16
Grav = 'Specific gravity of the wood'
17
Weight = 'Harvest weight of the tree (lbs)'
18
ObsId = 'Identification letter added to dataset';
19
lweight = log(weight);
20
ldbh = log(DBH);
21 cards;
NOTE: The data set WORK.ONE has 47 observations and 9 variables.
NOTE: DATA statement used:
real
time 1.24
seconds
cpu
time
0.20 seconds
21
! run;
69 ;
70 proc print data=one;
TITLE2 'Raw data print'; run;
NOTE: There were 47 observations read from the data set WORK.ONE.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
real
time 0.97
seconds
cpu
time
0.17 seconds
EXST7015: Estimating tree weights from other morphometric variables
Raw data print
Obs
Obs
Obs No Dbh
Height Age Grav
Weight ID lweight
ldbh
1 1
5.7 34
10 0.409
174 a 5.15906
1.74047
2 2
8.1 68
17 0.501
745 b 6.61338
2.09186
3 3
8.3 70
17 0.445
814 c 6.70196
2.11626
4 4
7.0 54
17 0.442
408 d 6.01127
1.94591
5 5
6.2 37
12 0.353
226 e 5.42053
1.82455
6 6
11.4 79
27 0.429 1675
f 7.42357 2.43361
7 7
11.6 70
26 0.497 1491
g 7.30720 2.45101
8 8
4.5 37
12 0.380
121 h 4.79579
1.50408
...
44 44
4.0 38
13 0.407
76 R 4.33073
1.38629
45 45
8.0 61
13 0.508
614 S 6.41999
2.07944
46 46
5.2 47
13 0.432
194 T 5.26786
1.64866
47 47
3.7 33
13 0.389
66 U 4.18965
1.30833
72 options ls=111
ps=61; proc plot data=one; plot weight*Dbh=obsid;
73 TITLE2
'Scatter plot'; run;
74 options ps=256
ls=132;
NOTE: There were 47 observations read from the data set WORK.ONE.
NOTE: The PROCEDURE PLOT printed page 2.
NOTE: PROCEDURE PLOT used:
real
time 0.22
seconds
cpu
time
0.02 seconds
EXST7015: Estimating tree weights from other morphometric variables
Scatter plot
Plot of Weight*Dbh. Symbol is value of ObsID.
Weight |
|
1800 +
|
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|
f q
|
1600 +
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g
|
1400 +
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1200 +
|
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1000 +
|
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800
+
c z
|
b t
|
N
|
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600
+
S
|
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y s
|
D
|
400
+
d
|
l u
|
o
|
B COj
|
F k Je
200
+
A L m
|
a
|
w h
| I Kn H r
| i
0 +
|
--+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-
3
4
5
6
7
8
9
10
11
12 13
Dbh
NOTE: 11 obs hidden.
76 proc means data=one
n mean max min var std stderr;
77
TITLE2 'Raw data means';
78
var Dbh Height Age Grav Weight; run;
NOTE: There were 47 observations read from the data set WORK.ONE.
NOTE: The PROCEDURE MEANS printed page 3.
NOTE: PROCEDURE MEANS used:
real
time 0.25
seconds
cpu
time
0.04 seconds
EXST7015: Estimating tree weights from other morphometric variables
Raw data means
The MEANS Procedure
Variable
N
Mean
Maximum
Minimum
Variance Std
Dev Std Error
--------------------------------------------------------------------------------------------------------------
Dbh
47
6.1531915
12.1000000
3.5000000
4.4016744
2.0980168 0.3060272
Height 47
49.5957447
79.0000000
27.0000000
167.6808511
12.9491641 1.8888297
Age
47
16.9574468
27.0000000
10.0000000
26.9111933
5.1876000 0.7566892
Grav
47
0.4452979
0.5080000
0.3530000
0.0014853
0.0385402 0.0056217
Weight 47
369.3404255
1692.00
58.0000000
154916.75
393.5946534 57.4116808
--------------------------------------------------------------------------------------------------------------
80 proc univariate
data=one normal plot;
81
TITLE2 'Raw data Univariate analysis';
82
var Weight Dbh; run;
NOTE: The PROCEDURE UNIVARIATE printed pages 4-5.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.53
seconds
cpu
time
0.06 seconds
EXST7015: Estimating tree weights from other morphometric variables
Raw data Univariate analysis
The UNIVARIATE Procedure
Variable: Weight
Moments
N
47 Sum
Weights
47
Mean
369.340426 Sum
Observations 17359
Std Deviation
393.594653
Variance
154916.751
Skewness
2.20870748
Kurtosis
4.83581557
Uncorrected SS
13537551 Corrected
SS 7126170.55
Coeff Variation 106.566903 Std
Error Mean 57.4116808
Basic Statistical Measures
Location
Variability
Mean 369.3404 Std
Deviation
393.59465
Median 224.0000
Variance
154917
Mode 84.0000
Range
1634
Interquartile Range 341.00000
NOTE: The mode displayed is the smallest of 3 modes with a count of 2.
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t t 6.433193 Pr
> |t| <.0001
Sign
M 23.5 Pr >=
|M| <.0001
Signed Rank S
564 Pr >= |S| <.0001
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.710878 Pr <
W <0.0001
Kolmogorov-Smirnov D
0.24806 Pr > D <0.0100
Cramer-von Mises W-Sq
0.77793 Pr > W-Sq <0.0050
Anderson-Darling A-Sq
4.435579 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 1692
99%
1692
95%
1491
90%
814
75%
Q3
462
50% Median 224
25%
Q1
121
10%
74
5%
66
1%
58
0%
Min
58
Extreme Observations
----Lowest---- ----Highest---
Value
Obs
Value Obs
58
9
814 3
60
16
815 26
66
47
1491 7
70
35
1675 6
74
18
1692 17
Stem
Leaf
#
Boxplot
Normal Probability Plot
16
89
2 *
1650+
* *
15
|
14
9
1
*
|
*
13
|
++
12
|
++
11
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+++
10
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++
9
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+++
8
12
2
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850+
++**
7
147
3
|
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+***
6
1
1
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+++*
5
24
2
|
|
++ *
4
16
2 +-----+
|
+++ **
3
00144
5 | +
|
|
++ ***
2
001112233488
12 *-----*
|
+********
1
00222799
8 +-----+
|
*****
0
667778889
9
| 50+
* * * **** **+
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
Multiply Stem.Leaf by
10**+2
-2
-1
0
+1 +2
EXST7015: Estimating tree weights from other morphometric variables
Raw data Univariate analysis
The UNIVARIATE Procedure
Variable: Dbh
Moments
N
47 Sum
Weights
47
Mean
6.15319149 Sum
Observations 289.2
Std Deviation
2.09801677
Variance
4.40167438
Skewness
1.17285986
Kurtosis
1.18369068
Uncorrected SS
1981.98 Corrected
SS 202.477021
Coeff Variation 34.0963998 Std
Error Mean 0.3060272
Basic Statistical Measures
Location
Variability
Mean 6.153191 Std
Deviation
2.09802
Median 5.700000
Variance
4.40167
Mode 4.000000
Range
8.60000
Interquartile Range 2.90000
NOTE: The mode displayed is the smallest of 2 modes with a count of 4.
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t t 20.10668 Pr
> |t| <.0001
Sign
M 23.5 Pr >=
|M| <.0001
Signed Rank S
564 Pr >= |S| <.0001
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.89407 Pr <
W 0.0005
Kolmogorov-Smirnov D
0.171951 Pr > D <0.0100
Cramer-von Mises W-Sq
0.214712 Pr > W-Sq <0.0050
Anderson-Darling A-Sq
1.387777 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 12.1
99%
12.1
95%
11.4
90%
8.8
75%
Q3
7.4
50% Median 5.7
25%
Q1
4.5
10%
4.0
5%
3.7
1%
3.5
0%
Min
3.5
Extreme Observations
----Lowest---- ----Highest---
Value
Obs
Value Obs
3.5
9
8.8 26
3.7
47
9.3 20
3.7
35
11.4 6
3.9
37
11.6 7
4.0
44
12.1 17
Stem
Leaf
#
Boxplot
Normal Probability Plot
12
1
1 0
12.25+
*
11
6
1
|
|
*
11
4
1
|
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* ++
10
|
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+++
10
|
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++
9
|
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+++
9
3
1
|
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*+
8
68
2
|
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**
8
013
3
|
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***
7
78
2
|
|
+*
7
04
2 +-----+
|
+**
6
57
2 |
|
|
+++**
6
0011122
7 | +
|
|
+****
5
5666677
7 *-----*
|
****
5
0224
4 |
|
|
***
4
555
3 +-----+
|
**
4
0000233
7
|
|
******
3
5779
4 |
3.75+ * * * ++
----+----+----+----+
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
84 proc reg data=one
LINEPRINTER; ID ObsID DBH;
85
TITLE2 'Simple linear regression';
86
model Weight = Dbh / p xpx i influence clb alpha=0.01; *** CLI CLM;
87
Slope:Test DBH = 200;
88
Joint:TEST intercept = 0, DBH = 200;
89
run;
NOTE: 47 observations read.
NOTE: 47 observations used in computations.
89
!
options ls=78 ps=45;
90
plot residual.*predicted.=obsid; run;
91
OUTPUT OUT=NEXT1 P=YHat R=E STUDENT=student rstudent=rstudent
92
lcl=lcl lclm=lclm ucl=ucl uclm=uclm;
93 run;
94 options ps=61 ls=132;
NOTE: The data set WORK.NEXT1 has 47 observations and 17 variables.
NOTE: The PROCEDURE REG printed pages 6-11.
NOTE: PROCEDURE REG used:
real
time 1.09
seconds
cpu
time
0.17 seconds
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
The REG Procedure
Model: MODEL1
Model Crossproducts X'X X'Y Y'Y
Variable
Intercept
Dbh
Weight
Intercept
47
289.2
17359
Dbh
289.2
1981.98 142968.3
Weight
17359
142968.3 13537551
X'X Inverse, Parameter
Estimates, and SSE
Variable
Intercept
Dbh
Weight
Intercept
0.2082694963
-0.030389579 -729.3963003
Dbh
-0.030389579
0.004938832 178.56371409
Weight
-729.3963003
178.56371409 670190.7322
Analysis of Variance
Sum of Mean
Source
DF
Squares
Square F Value Pr > F
Model
1
6455980
6455980 433.49 <.0001
Error
45
670191 14893
Corrected Total
46 7126171
Root
MSE
122.03740 R-Square 0.9060
Dependent Mean
369.34043 Adj R-Sq 0.9039
Coeff
Var
33.04198
Parameter Estimates
Parameter Standard
Variable DF
Estimate
Error t Value Pr >
|t| 99% Confidence Limits
Intercept 1
-729.39630 55.69366
-13.10 <.0001
-879.18914 -579.60346
Dbh
1 178.56371
8.57640
20.82
<.0001
155.49675 201.63067
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
The REG Procedure
Model: MODEL1
Test Slope Results for Dependent Variable Weight
Mean
Source
DF
Square F Value Pr > F
Numerator
1
93041 6.25 0.0162
Denominator
45
14893
Test Joint Results for Dependent Variable Weight
Mean
Source
DF
Square F Value Pr > F
Numerator
2 17479620
1173.67 <.0001
Denominator
45 14893
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
The REG Procedure
Model: MODEL1
Dependent Variable: Weight
Output Statistics
Dep Var
Predicted
Hat Diag
Cov
------DFBETAS------
Obs ObsID
Dbh Weight
Value Residual
RStudent
H Ratio DFFITS
Intercept Dbh
1
a
5.7 174.0000 288.4169
-114.4169 -0.9471
0.0223 1.0275 -0.1430
-0.0736 0.0305
2
b
8.1 745.0000 716.9698
28.0302 0.2319
0.0400 1.0869
0.0473 -0.0197 0.0324
3
c
8.3 814.0000 752.6825
61.3175 0.5096
0.0440 1.0814
0.1094 -0.0502 0.0786
4
d
7 408.0000 520.5497
-112.5497 -0.9326
0.0248 1.0314
-0.1488 0.0092 -0.0562
5
e
6.2 226.0000 377.6987
-151.6987 -1.2648
0.0213 0.9950 -0.1865
-0.0556 -0.0042
6
f
11.4
1675 1306
368.7700 3.7355
0.1572 0.7154
1.6135 -1.2320 1.5004
7
g
11.6
1491 1342
149.0572 1.3511
0.1678 1.1587
0.6067 -0.4681 0.5669
8
h
4.5 121.0000 74.1404
46.8596 0.3871
0.0348 1.0763
0.0735 0.0617 -0.0458
9
i
3.5 58.0000 -104.4233
162.4233 1.3837
0.0560 1.0176
0.3372 0.3180 -0.2656
10
j
6.2 278.0000 377.6987
-99.6987 -0.8228
0.0213 1.0366 -0.1213
-0.0362 -0.0027
11
k
5.7 220.0000 288.4169
-68.4169 -0.5627
0.0223 1.0546 -0.0850
-0.0437 0.0181
12
l
6 342.0000 341.9860
0.0140 0.000115 0.0214
1.0688 0.0000
0.0000 -0.0000
13
m
5.6 209.0000 270.5605
-61.5605 -0.5061
0.0228 1.0580 -0.0773
-0.0427 0.0199
14
n
4 84.0000 -15.1414
99.1414 0.8280
0.0442 1.0610
0.1780 0.1609 -0.1282
15
o
6.7 313.0000 466.9806
-153.9806 -1.2856
0.0228 0.9942 -0.1962
-0.0133 -0.0500
16
p
4 60.0000 -15.1414
75.1414 0.6255
0.0442 1.0751
0.1345 0.1216 -0.0968
17
q
12.1
1692 1431
260.7754 2.5208
0.1959 0.9932
1.2444 -0.9822 1.1749
18
r
4.5 74.0000
74.1404 -0.1404 -0.001158
0.0348 1.0837 -0.0002
-0.0002 0.0001
19
s
8.6 515.0000 806.2516
-291.2516 -2.6020
0.0508 0.8277
-0.6022 0.3106 -0.4592
20
t
9.3 766.0000 931.2462
-165.2462 -1.4200
0.0702 1.0285
-0.3901 0.2399 -0.3257
21
u
6.5 345.0000 431.2678
-86.2678 -0.7108
0.0219 1.0452 -0.1063
-0.0169 -0.0175
22
v
5.6 210.0000 270.5605
-60.5605 -0.4978
0.0228 1.0584 -0.0760
-0.0420 0.0196
23
w
4.3 100.0000 38.4277
61.5723 0.5102
0.0382 1.0748
0.1017 0.0885 -0.0678
24
x
4.5 122.0000 74.1404
47.8596 0.3954
0.0348 1.0760
0.0751 0.0631 -0.0468
25
y
7.7 539.0000 645.5443
-106.5443 -0.8857
0.0331 1.0442
-0.1639 0.0508 -0.0979
26
z
8.8 815.0000 841.9644
-26.9644 -0.2250
0.0559 1.1053
-0.0547 0.0300 -0.0431
27
A
5 194.0000 163.4223
30.5777 0.2515
0.0278 1.0728
0.0426 0.0315 -0.0207
28
B
5.4 280.0000 234.8478
45.1522 0.3709
0.0241 1.0651
0.0583 0.0363 -0.0199
29
C
6 296.0000 341.9860
-45.9860 -0.3773
0.0214 1.0620 -0.0558
-0.0217 0.0041
30
D
7.4 462.0000 591.9752
-129.9752 -1.0829
0.0290 1.0220
-0.1870 0.0400 -0.0963
31
E
5.6 200.0000 270.5605
-70.5605 -0.5806
0.0228 1.0542 -0.0887
-0.0490 0.0228
32
F
5.5 229.0000 252.7041
-23.7041 -0.1944
0.0234 1.0692 -0.0301
-0.0177 0.0090
33
G
4.3 125.0000 38.4277
86.5723 0.7195
0.0382 1.0624
0.1435 0.1247 -0.0955
34
H
4.2 84.0000
20.5713 63.4287
0.5262 0.0401
1.0761 0.1076
0.0949 -0.0737
35
I
3.7 70.0000 -68.7106
138.7106 1.1716
0.0510 1.0365
0.2716 0.2525 -0.2073
36
J
6.1 224.0000 359.8424
-135.8424 -1.1286
0.0213 1.0094 -0.1665
-0.0572 0.0043
37
K
3.9 99.0000 -32.9978
131.9978 1.1105
0.0464 1.0378
0.2448 0.2236 -0.1801
38
L
5.2 200.0000 199.1350
0.8650 0.007101 0.0258
1.0736 0.0012
0.0008 -0.0005
39
M
5.6 214.0000 270.5605
-56.5605 -0.4647
0.0228 1.0599 -0.0710
-0.0392 0.0183
40
N
7.8 712.0000 663.4007
48.5993 0.4015
0.0347 1.0756
0.0761 -0.0258 0.0473
41
O
6.1 297.0000 359.8424
-62.8424 -0.5163
0.0213 1.0559 -0.0761
-0.0262 0.0020
42
P
6.1 238.0000 359.8424
-121.8424 -1.0094
0.0213 1.0209 -0.1489
-0.0512 0.0038
43
Q
4 89.0000 -15.1414
104.1414 0.8705
0.0442 1.0576
0.1871 0.1692 -0.1347
44
R
4 76.0000 -15.1414
91.1414 0.7603
0.0442 1.0661
0.1634 0.1478 -0.1177
45
S
8 614.0000 699.1134
-85.1134 -0.7072
0.0381 1.0631
-0.1408 0.0551 -0.0936
46
T
5.2 194.0000 199.1350
-5.1350 -0.0422
0.0258 1.0735 -0.0069
-0.0047 0.0029
47
U
3.7 66.0000 -68.7106
134.7106 1.1368
0.0510 1.0402
0.2635 0.2450 -0.2012
Sum of
Residuals
0
Sum of Squared
Residuals
670191
Predicted Residual SS
(PRESS) 810382
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
The REG Procedure
Model: MODEL1
Dependent Variable: Weight
-+------+------+------+------+------+------+------+------+------+--
RESIDUAL
|
|
400
+
+
|
f |
|
|
|
|
|
|
|
q |
|
|
200
+
+
|
i
|
|
?K
g |
R
|
Q
|
e
| ?
G
|
s
| ? ?
B
N
c
|
i
|
A
b
|
d 0
+ r
?
l
+
u
|
F
z
|
a
|
?k
CO
|
l
|
j u
S
|
|
a P d
y
|
|
? o
D
|
|
t
|
-200
+
+
|
|
|
|
|
s
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|
|
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|
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-400
+
+
|
|
-+------+------+------+------+------+------+------+------+------+--
-200 0
200 400 600
800 1000 1200 1400 1600
Predicted Value of Weight PRED
95 proc print
data=next1;
96
TITLE3 'Listing of observation diagnostics';
97
var ObsId DBH Weight YHat E student rstudent lcl lclm ucl uclm; run;
NOTE: There were 47 observations read from the data set WORK.NEXT1.
NOTE: The PROCEDURE PRINT printed page 12.
NOTE: PROCEDURE PRINT used:
real
time 0.21
seconds
cpu
time
0.04 seconds
98 options ps=256 ls=80;
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
Listing of observation diagnostics
Obs
Obs ID
Dbh Weight
YHat
E student
rstudent
lcl
lclm
ucl uclm
1 a
5.7
174 288.42
-114.417 -0.94818
-0.94710
-43.45 239.41
620.28 337.42
2 b
8.1
745
716.97 28.030
0.23442 0.23194
382.24 651.33
1051.70 782.61
3 c
8.3
814
752.68 61.317
0.51389 0.50965
417.30 683.80
1088.06 821.56
4 d
7.0
408 520.55
-112.550 -0.93392
-0.93256
188.27 468.84
852.83 572.26
5 e
6.2
226 377.70
-151.699 -1.25650
-1.26484
45.99 329.81
709.40 425.59
6 f
11.4 1675
1306.23 368.770
3.29162 3.73546
953.14 1176.08
1659.32 1436.38
7 g
11.6 1491
1341.94 149.057
1.33889 1.35112
987.24 1207.49
1696.64 1476.40
8 h
4.5
121
74.14 46.860
0.39083 0.38712
-259.75
12.93 408.03
135.35
9 i
3.5
58 -104.42
162.423 1.36987
1.38372 -441.73
-182.13 232.88
-26.72
10 j
6.2
278 377.70
-99.699 -0.82579
-0.82282
45.99 329.81
709.40 425.59
11 k
5.7
220 288.42
-68.417 -0.56698
-0.56266
-43.45 239.41
620.28 337.42
12 l
6.0
342
341.99
0.014 0.00012
0.00011
10.26 293.98
673.71 389.99
13 m
5.6
209 270.56
-61.560 -0.51029
-0.50605
-61.39 221.01
602.51 320.11
14 n
4.0
84
-15.14 99.141
0.83095 0.82804
-350.54 -84.13
320.26 53.84
15 o
6.7
313 466.98
-153.981 -1.27635
-1.28558
135.04 417.47
798.92 516.49
16 p
4.0
60
-15.14 75.141
0.62979 0.62552
-350.54 -84.13
320.26 53.84
17 q
12.1 1692
1431.22 260.775
2.38302 2.52082
1072.28 1285.93
1790.17 1576.51
18 r
4.5
74
74.14 -0.140
-0.00117 -0.00116
-259.75
12.93 408.03
135.35
19 s
8.6
515 806.25
-291.252 -2.44967
-2.60199
469.78 732.24
1142.72 880.26
20 t
9.3
766 931.25
-165.246 -1.40424
-1.42001
591.69 844.29
1270.80 1018.20
21 u
6.5
345 431.27
-86.268 -0.71476
-0.71082
99.47 382.73
763.07 479.81
22 v
5.6
210 270.56
-60.560 -0.50200
-0.49778
-61.39 221.01
602.51 320.11
23 w
4.3
100
38.43 61.572
0.51447 0.51022
-296.02 -25.76
372.87 102.61
24 x
4.5
122
74.14 47.860
0.39917 0.39541
-259.75
12.93 408.03
135.35
25 y
7.7
539 645.54
-106.544 -0.88786
-0.88573
311.93 585.83
979.16 705.25
26 z
8.8
815 841.96
-26.964 -0.22740
-0.22498
504.69 764.38
1179.24 919.55
27 A
5.0
194
163.42 30.578
0.25412 0.25146
-169.35 108.65
496.19 218.19
28 B
5.4
280
234.85 45.152
0.37452 0.37092
-97.31 183.92
567.01 285.78
29 C
6.0
296 341.99
-45.986 -0.38092
-0.37727
10.26 293.98
673.71 389.99
30 D
7.4
462 591.98
-129.975 -1.08081
-1.08288
259.03 536.12
924.92 647.83
31 E
5.6
200 270.56
-70.560 -0.58489
-0.58057
-61.39 221.01
602.51 320.11
32 F
5.5
229 252.70
-23.704 -0.19655
-0.19444
-79.34 202.51
584.75 302.90
33 G
4.3
125
38.43 86.572
0.72336 0.71947
-296.02 -25.76
372.87 102.61
34 H
4.2
84
20.57 63.429
0.53050 0.52622
-314.18 -45.17
355.32 86.31
35 I
3.7
70 -68.71
138.711 1.16676
1.17159 -405.21
-142.83
267.79 5.41
36 J
6.1
224 359.84
-135.842 -1.12516
-1.12858
28.14 311.95
691.55 407.74
37 K
3.9
99 -33.00
131.998 1.10759
1.11046 -368.75
-103.66
302.75 37.67
38 L
5.2
200
199.14
0.865 0.00718
0.00710 -133.30
146.45 531.57
251.82
39 M
5.6
214 270.56
-56.560 -0.46884
-0.46474
-61.39 221.01
602.51 320.11
40 N
7.8
712
663.40 48.599
0.40532 0.40153
329.53 602.28
997.27 724.52
41 O
6.1
297 359.84
-62.842 -0.52051
-0.51625
28.14 311.95
691.55 407.74
42 P
6.1
238 359.84
-121.842 -1.00920
-1.00941
28.14 311.95
691.55 407.74
43 Q
4.0
89 -15.14
104.141 0.87285
0.87050 -350.54
-84.13
320.26 53.84
44 R
4.0
76
-15.14 91.141
0.76389 0.76031
-350.54 -84.13
320.26 53.84
45 S
8.0
614 699.11
-85.113 -0.71112
-0.70716
364.69 635.03
1033.54 763.20
46 T
5.2
194
199.14 -5.135
-0.04263 -0.04215
-133.30 146.45
531.57 251.82
47 U
3.7
66 -68.71
134.711 1.13312
1.13679 -405.21
-142.83
267.79 5.41
100 proc univariate
data=next1 normal plot; var e;
101
TITLE3 'Residual analysis'; run;
NOTE: The PROCEDURE UNIVARIATE printed page 13.
NOTE: PROCEDURE UNIVARIATE used:
real
time 0.11
seconds
cpu
time
0.03 seconds
EXST7015: Estimating tree weights from other morphometric variables
Simple linear regression
Residual analysis
The UNIVARIATE Procedure
Variable: E (Residual)
Moments
N
47 Sum
Weights
47
Mean
0 Sum
Observations
0
Std Deviation
120.703619
Variance
14569.3637
Skewness
0.47869472
Kurtosis
1.04153074
Uncorrected SS 670190.732
Corrected SS 670190.732
Coeff
Variation
. Std Error Mean
17.6064324
Basic Statistical Measures
Location
Variability
Mean 0.00000 Std
Deviation
120.70362
Median -0.14041
Variance
14569
Mode
.
Range
660.02160
Interquartile Range 161.40929
Tests for
Location: Mu0=0
Test
-Statistic- -----p Value------
Student's t
t 0
Pr > |t| 1.0000
Sign
M -0.5 Pr >=
|M| 1.0000
Signed Rank S
-25 Pr >= |S| 0.7946
Tests for Normality
Test
--Statistic--- -----p Value------
Shapiro-Wilk
W 0.973389 Pr <
W 0.3544
Kolmogorov-Smirnov D
0.084574 Pr > D >0.1500
Cramer-von Mises W-Sq
0.044081 Pr > W-Sq >0.2500
Anderson-Darling A-Sq
0.354877 Pr > A-Sq >0.2500
Quantiles (Definition 5)
Quantile Estimate
100% Max 368.769960
99%
368.769960
95%
162.423301
90%
138.710558
75% Q3 75.141444
50% Median -0.140413
25% Q1 -86.267841
10%
-135.842356
5%
-153.980584
1%
-291.251641
0% Min -291.251641
Extreme
Observations
------Lowest-----
-----Highest-----
Value
Obs
Value Obs
-291.252
19
138.711 35
-165.246
20
149.057 7
-153.981
15
162.423 9
-151.699
5
260.775 17
-135.842
36
368.770 6
Stem
Leaf
# Boxplot
3
7
1 0
3
2
6
1 |
2
|
1
56
2 |
1
00334
5 |
0
5555666899
10 +-----+
0
0033
4 | + |
-0
3210
4 *-----*
-0
997766665
9 +-----+
-1
4321110
7 |
-1
755
3 |
-2
|
-2
9
1 |
----+----+----+----+
Multiply Stem.Leaf by 10**+2
Normal Probability Plot
375+
*
|
+
|
* ++++
|
++++
|
+++*
|
+*****
|
*****
|
+****
|
++***
|
******
|
******
| * *+*+
|
++++
-275+ ++*+
+----+----+----+----+----+----+----+----+----+----+
-2
-1
0
+1 +2
6 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2----+----
7 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1-
8 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+--
9 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+-
10 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+--
11 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----+----
12 font fixed courier new
----+----1----+----2----+----3----+----4----+----5----+----6----
110 GOPTIONS DEVICE=CGMflwa
GSFMODE=REPLACE GSFNAME=OUT NOPROMPT noROTATE
111
ftext='TimesRoman' ftitle='TimesRoman' htext=1 htitle=1 ctitle=black
ctext=black;
112
113 GOPTIONS GSFNAME=OUT1;
114 FILENAME
OUT1'C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\SLR-Trees1.CGM';
NOTE: There were 47 observations read from the data set WORK.ONE.
NOTE: The PROCEDURE PLOT printed page 14.
NOTE: PROCEDURE PLOT used:
real
time 0.09
seconds
cpu
time
0.04 seconds
115 PROC GPLOT DATA=ONE;
116 TITLE1
font='TimesRoman' H=1 'Simple Linear Regression Example';
117 TITLE2
font='TimesRoman' H=1 'Wood harvest from trees';
118 PLOT weight*Dbh=1
weight*Dbh=2 / overlay HAXIS=AXIS1 VAXIS=AXIS2;
119 AXIS1
LABEL=(font='TimesRoman' H=1 'Diameter at breast height (inches)')
WIDTH=1 MINOR=(N=1)
120
VALUE=(font='TimesRoman' H=1) color=black ORDER=3 TO 13 BY 1;
121 AXIS2
LABEL=(ANGLE=90 font='TimesRoman' H=1 'Weight of wood harvested (lbs)')
WIDTH=1
122
VALUE=(font='TimesRoman' H=1) MINOR=(N=5) color=black ORDER=0 TO 1800
BY 200;
123
SYMBOL1 color=red V=None I=RLcli99 L=1 MODE=INCLUDE;
124
SYMBOL2 color=blue V=dot I=None L=1
MODE=INCLUDE; RUN;
NOTE: Regression equation : Weight = -729.3963 + 178.5637*Dbh.
NOTE: Foreground color BLACK same as background. Part of your graph may
not be visible.
NOTE: 52 RECORDS WRITTEN TO
C:\Geaghan\EXST\EXST7015New\Fall2002\SAS\SLR-Trees1.CGM
125 **** V = "dot" would
place a dot for each point;
126 **** I = for regression:
R requests fitted regression line, L, Q or C requests Linear,
127
Quadraatic or cubic, CLM or CLI requests corresponding confidence
interval and
128
95 specifies alpha level for CI (any value from 50 to 99);
129 **** I = for categories"
requests STD (std dev) 1 (1 width, 2 or 3) M (of mean=std err)
130
J (join means of bars) t (add top & bottom hash) p (use pooled
variance);
131 **** Other options for
categories: omit M=std dev, use B to get bar for min/max;
132 RUN:
NOTE: There were 47 observations read from the data set WORK.ONE.
NOTE: PROCEDURE GPLOT used:
real
time 0.22
seconds
cpu
time
0.10 seconds
Modified: August 16, 2004
James P. Geaghan