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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 07 Dec 2010 10:34:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291717981ftewnnt69gs0ego.htm/, Retrieved Sat, 04 May 2024 05:04:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106156, Retrieved Sat, 04 May 2024 05:04:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- R PD      [Standard Deviation-Mean Plot] [Workshop 9; Coffe...] [2010-12-07 10:34:12] [50e0b5177c9c80b42996aa89930b928a] [Current]
-    D        [Standard Deviation-Mean Plot] [Paper; SMP Coffee] [2010-12-21 15:30:39] [8ffb4cfa64b4677df0d2c448735a40bb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
168.67
164.83
184.38
180.81
190.54
181.41
155.67
135.99
125.88
126.09
114.86
127.98
127.98
125.11
125.93
128.2
125.93
111.94
120.01
124.09
126.02
136.41
143.79
141.67
143.9
155
144.83
141.4
137
141.02
131.11
132.83
136.73
141.18
137.86
133.79
128.53
125.87
124.27
123.96
128.15
126.4
127.86
129.31
132.56
141.28
145.55
146.54
143.14
145.72
148.21
150.4
149.94
146.66
143.37
145.29
140.24
136.12
140.25
140.64
145.58
143.73
141.27
140.66
141.94
141.16
134.31
132.93
133.07
140.48
154.85
196.77
235.3
226.52
237.62
224.07
208.74
174.54
170.63
172.23
198.36
175.91
154.63
134.31
121.75
119.6
102.04
106.3
116.38
103.72
98.56
100.9
110
118.26
124.77
125.22
126.38
137.14
134.74
134.3
136.39
141.83
139.24
128.89
134.83
130.43
132.09
144.95
149.5
137.57
139.38
143.06
138.65
123.21
85.91
77.4
77.84
67.76
70.72
72.55
75.83
84.01
93.96
93.73
92.02
88.26
86.48
94.42
94.92
91.41
84.84
89.89
86.32
89.57
93.72
92.27
87.59
85.5
82.81
81.62
87.45
79.86
78.52
75.1
72.99
67.88
70.14
65.43
60.26
58.38
57.68
52.42
52.73
61.4
67.13
77.46
68.66
67.46
62.77
56.88
61.48
61.99
71.56
76.56
79.82
75.05
77.07
80
77.21
82.16
85.57
89.23
121.98
142.56
217.67
198.07
220.1
198.68
181.64
167.47
172.33
168.71
178.22
172.81
168.83
152.25
143.83
151.41
131.87
125.38
123.23
103.99
109.38
123.79
119.05
122.01
128.56
127.91
120.47
122.49
114.05
120.62
119.61
115.01
131.83
167.2
193.82
204.43
264.5
212.55
186.52
185.17
184.38
161.45
154.15
174.25
175.04
175.87
154.82
147.08
134.35
121.56
113.86
119.89
108.07
107.07
115.14
116.03
111.48
103.24
103.23
99.69
108.91
104.21
90.85
87.64
81.06
92.2
114.02
123.56
109.17
101.65
97.95
92.56
91.76
84.1
84.67
74.52
73.83
75.37
70.47
64.5
64.98
66.94
65.93
65.51
68.94
63.67
58.47
59.68
57.71
56.53
58.96
55.6
57.34
60.51
66.38
65.78
58.43
55.16
53.09
52.02
57.58
64.05
70.18
63.86
65.22
67.6
61.66
65.32
66.18
61.34
62.29
63.6
65.51
62.58
62.36
64.88
73.73
77.51
77.47
74.34
75.81
82.16
73.96
73.17
80.99
79.81
89.51
102.57
107.11
122.23
134.69
128.79
126.16
119.98
108.45
108.43
98.17
106.09
108.81
103.03
124.36
118.52
112.2
114.71
107.96
101.21
102.77
112.13
109.36
110.91
123.57
129.95
124.46
122.34
116.61
114.59
112.52
118.67
116.8
123.63
128.04
134.57
130.33
136.47
139.05
158.21
148.07
137.74
139.74
144.08
145.35
145.77
140.56
121.41
120.44
116.97
128.03
128.51
127.76
134.58
147.64
144.46
137.6
146.87
145.67
151.95
150.23
155.86
154.4
156.36
162.13
171.06
174.01
193.52
205.26
212.8
222.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106156&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106156&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1154.75916666666727.235694312739175.68
2128.098.8664761884302131.85
3139.7208333333336.468624215582823.89
4131.698.1176765596611922.58
5144.1654.3490824528649914.28
6145.562517.201696071238863.84
7192.73833333333333.87979790466103.31
8112.2916666666679.7984626190525226.66
9135.1008333333335.3222918138256218.57
10106.962533.801700905293381.74
1189.14755.6359997499838619.09
1285.02755.6174292486542618.62
1363.65833333333337.8541845631176225.04
1469.94166666666677.9013874884367123.12
15148.52833333333355.6281065050154142.89
16149.40523.9871024056374.23
17120.2458333333335.5141775259669319.18
18185.02083333333333.4433913728131132.67
19132.39833333333324.948950363540868.8
20101.67416666666712.150513987133042.5
2185.045833333333313.789211499860344.67
2261.914.5554582645437613.34
2360.3655.704541253167618.16
2464.0452.007139529506886.25999999999999
2580.08583333333338.4749604003723129.4
26114.32833333333311.546817612212336.52
27113.9708333333338.7294407384471428.74
28123.25257.8347409599227323.95
29138.11583333333312.423012706142241.24
30141.5966666666679.937371459050528.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 154.759166666667 & 27.2356943127391 & 75.68 \tabularnewline
2 & 128.09 & 8.86647618843021 & 31.85 \tabularnewline
3 & 139.720833333333 & 6.4686242155828 & 23.89 \tabularnewline
4 & 131.69 & 8.11767655966119 & 22.58 \tabularnewline
5 & 144.165 & 4.34908245286499 & 14.28 \tabularnewline
6 & 145.5625 & 17.2016960712388 & 63.84 \tabularnewline
7 & 192.738333333333 & 33.87979790466 & 103.31 \tabularnewline
8 & 112.291666666667 & 9.79846261905252 & 26.66 \tabularnewline
9 & 135.100833333333 & 5.32229181382562 & 18.57 \tabularnewline
10 & 106.9625 & 33.8017009052933 & 81.74 \tabularnewline
11 & 89.1475 & 5.63599974998386 & 19.09 \tabularnewline
12 & 85.0275 & 5.61742924865426 & 18.62 \tabularnewline
13 & 63.6583333333333 & 7.85418456311762 & 25.04 \tabularnewline
14 & 69.9416666666667 & 7.90138748843671 & 23.12 \tabularnewline
15 & 148.528333333333 & 55.6281065050154 & 142.89 \tabularnewline
16 & 149.405 & 23.98710240563 & 74.23 \tabularnewline
17 & 120.245833333333 & 5.51417752596693 & 19.18 \tabularnewline
18 & 185.020833333333 & 33.4433913728131 & 132.67 \tabularnewline
19 & 132.398333333333 & 24.9489503635408 & 68.8 \tabularnewline
20 & 101.674166666667 & 12.1505139871330 & 42.5 \tabularnewline
21 & 85.0458333333333 & 13.7892114998603 & 44.67 \tabularnewline
22 & 61.91 & 4.55545826454376 & 13.34 \tabularnewline
23 & 60.365 & 5.7045412531676 & 18.16 \tabularnewline
24 & 64.045 & 2.00713952950688 & 6.25999999999999 \tabularnewline
25 & 80.0858333333333 & 8.47496040037231 & 29.4 \tabularnewline
26 & 114.328333333333 & 11.5468176122123 & 36.52 \tabularnewline
27 & 113.970833333333 & 8.72944073844714 & 28.74 \tabularnewline
28 & 123.2525 & 7.83474095992273 & 23.95 \tabularnewline
29 & 138.115833333333 & 12.4230127061422 & 41.24 \tabularnewline
30 & 141.596666666667 & 9.9373714590505 & 28.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106156&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]154.759166666667[/C][C]27.2356943127391[/C][C]75.68[/C][/ROW]
[ROW][C]2[/C][C]128.09[/C][C]8.86647618843021[/C][C]31.85[/C][/ROW]
[ROW][C]3[/C][C]139.720833333333[/C][C]6.4686242155828[/C][C]23.89[/C][/ROW]
[ROW][C]4[/C][C]131.69[/C][C]8.11767655966119[/C][C]22.58[/C][/ROW]
[ROW][C]5[/C][C]144.165[/C][C]4.34908245286499[/C][C]14.28[/C][/ROW]
[ROW][C]6[/C][C]145.5625[/C][C]17.2016960712388[/C][C]63.84[/C][/ROW]
[ROW][C]7[/C][C]192.738333333333[/C][C]33.87979790466[/C][C]103.31[/C][/ROW]
[ROW][C]8[/C][C]112.291666666667[/C][C]9.79846261905252[/C][C]26.66[/C][/ROW]
[ROW][C]9[/C][C]135.100833333333[/C][C]5.32229181382562[/C][C]18.57[/C][/ROW]
[ROW][C]10[/C][C]106.9625[/C][C]33.8017009052933[/C][C]81.74[/C][/ROW]
[ROW][C]11[/C][C]89.1475[/C][C]5.63599974998386[/C][C]19.09[/C][/ROW]
[ROW][C]12[/C][C]85.0275[/C][C]5.61742924865426[/C][C]18.62[/C][/ROW]
[ROW][C]13[/C][C]63.6583333333333[/C][C]7.85418456311762[/C][C]25.04[/C][/ROW]
[ROW][C]14[/C][C]69.9416666666667[/C][C]7.90138748843671[/C][C]23.12[/C][/ROW]
[ROW][C]15[/C][C]148.528333333333[/C][C]55.6281065050154[/C][C]142.89[/C][/ROW]
[ROW][C]16[/C][C]149.405[/C][C]23.98710240563[/C][C]74.23[/C][/ROW]
[ROW][C]17[/C][C]120.245833333333[/C][C]5.51417752596693[/C][C]19.18[/C][/ROW]
[ROW][C]18[/C][C]185.020833333333[/C][C]33.4433913728131[/C][C]132.67[/C][/ROW]
[ROW][C]19[/C][C]132.398333333333[/C][C]24.9489503635408[/C][C]68.8[/C][/ROW]
[ROW][C]20[/C][C]101.674166666667[/C][C]12.1505139871330[/C][C]42.5[/C][/ROW]
[ROW][C]21[/C][C]85.0458333333333[/C][C]13.7892114998603[/C][C]44.67[/C][/ROW]
[ROW][C]22[/C][C]61.91[/C][C]4.55545826454376[/C][C]13.34[/C][/ROW]
[ROW][C]23[/C][C]60.365[/C][C]5.7045412531676[/C][C]18.16[/C][/ROW]
[ROW][C]24[/C][C]64.045[/C][C]2.00713952950688[/C][C]6.25999999999999[/C][/ROW]
[ROW][C]25[/C][C]80.0858333333333[/C][C]8.47496040037231[/C][C]29.4[/C][/ROW]
[ROW][C]26[/C][C]114.328333333333[/C][C]11.5468176122123[/C][C]36.52[/C][/ROW]
[ROW][C]27[/C][C]113.970833333333[/C][C]8.72944073844714[/C][C]28.74[/C][/ROW]
[ROW][C]28[/C][C]123.2525[/C][C]7.83474095992273[/C][C]23.95[/C][/ROW]
[ROW][C]29[/C][C]138.115833333333[/C][C]12.4230127061422[/C][C]41.24[/C][/ROW]
[ROW][C]30[/C][C]141.596666666667[/C][C]9.9373714590505[/C][C]28.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106156&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1154.75916666666727.235694312739175.68
2128.098.8664761884302131.85
3139.7208333333336.468624215582823.89
4131.698.1176765596611922.58
5144.1654.3490824528649914.28
6145.562517.201696071238863.84
7192.73833333333333.87979790466103.31
8112.2916666666679.7984626190525226.66
9135.1008333333335.3222918138256218.57
10106.962533.801700905293381.74
1189.14755.6359997499838619.09
1285.02755.6174292486542618.62
1363.65833333333337.8541845631176225.04
1469.94166666666677.9013874884367123.12
15148.52833333333355.6281065050154142.89
16149.40523.9871024056374.23
17120.2458333333335.5141775259669319.18
18185.02083333333333.4433913728131132.67
19132.39833333333324.948950363540868.8
20101.67416666666712.150513987133042.5
2185.045833333333313.789211499860344.67
2261.914.5554582645437613.34
2360.3655.704541253167618.16
2464.0452.007139529506886.25999999999999
2580.08583333333338.4749604003723129.4
26114.32833333333311.546817612212336.52
27113.9708333333338.7294407384471428.74
28123.25257.8347409599227323.95
29138.11583333333312.423012706142241.24
30141.5966666666679.937371459050528.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.72822094162036
beta0.194544582397338
S.D.0.0535559900492489
T-STAT3.6325457193199
p-value0.00111490606017126

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8.72822094162036 \tabularnewline
beta & 0.194544582397338 \tabularnewline
S.D. & 0.0535559900492489 \tabularnewline
T-STAT & 3.6325457193199 \tabularnewline
p-value & 0.00111490606017126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106156&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.72822094162036[/C][/ROW]
[ROW][C]beta[/C][C]0.194544582397338[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0535559900492489[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.6325457193199[/C][/ROW]
[ROW][C]p-value[/C][C]0.00111490606017126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106156&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.72822094162036
beta0.194544582397338
S.D.0.0535559900492489
T-STAT3.6325457193199
p-value0.00111490606017126






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.07980738365565
beta1.36473746744364
S.D.0.348610760261346
T-STAT3.91478870709707
p-value0.000527823774142492
Lambda-0.364737467443641

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.07980738365565 \tabularnewline
beta & 1.36473746744364 \tabularnewline
S.D. & 0.348610760261346 \tabularnewline
T-STAT & 3.91478870709707 \tabularnewline
p-value & 0.000527823774142492 \tabularnewline
Lambda & -0.364737467443641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106156&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.07980738365565[/C][/ROW]
[ROW][C]beta[/C][C]1.36473746744364[/C][/ROW]
[ROW][C]S.D.[/C][C]0.348610760261346[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.91478870709707[/C][/ROW]
[ROW][C]p-value[/C][C]0.000527823774142492[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.364737467443641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106156&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106156&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.07980738365565
beta1.36473746744364
S.D.0.348610760261346
T-STAT3.91478870709707
p-value0.000527823774142492
Lambda-0.364737467443641


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')