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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 computationSat, 04 Dec 2010 11:49:41 +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/04/t12914633557tg25koe05kh7qo.htm/, Retrieved Sun, 05 May 2024 07:03:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105107, Retrieved Sun, 05 May 2024 07:03:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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]
-   PD      [Standard Deviation-Mean Plot] [SMP CPI] [2010-12-04 11:49:41] [b6992a7b26e556359948e164e4227eba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
115,65
116,00
115,92
116,10
116,44
116,65
117,45
117,58
117,43
117,24
117,25
117,29
117,83
118,22
118,11
118,23
118,15
118,23
119,03
119,38
118,97
118,78
118,97
118,94
119,86
120,09
120,13
120,15
119,90
120,00
120,84
121,17
120,81
121,00
121,12
121,29
122,09
121,88
121,31
121,33
121,45
121,67
122,78
122,84
122,34
122,37
122,72
122,68
122,78
123,08
122,92
123,51
124,18
124,05
124,36
123,87
123,84
123,85
123,83
123,84
124,27
124,56
124,57
124,87
125,08
124,86
124,89
124,58
124,83
124,97
125,19
125,42
125,74
126,07
126,35
126,69
126,85
127,12
127,43
127,49
128,05
127,85
128,35
128,29
128,38
128,80
129,18
130,14
130,77
131,19
131,32
131,41
131,61
131,69
131,94
131,70
132,54
132,74
133,02
132,76
133,05
132,74
133,16
133,10
133,37
133,15
133,18
133,29
133,76
134,51
134,82
134,71
134,52
134,86
135,11
135,28
135,61
135,22
135,47
135,42
135,85
136,27
136,30
136,85
137,05
137,03
137,45
137,49
137,55
138,04
138,03
137,75
138,27
138,99
139,74
139,70
139,97
140,21
140,78
140,80
140,64
140,42
140,85
140,96
141,04
141,71
141,60
142,11
142,59
142,56
143,00
143,18
143,15
143,10
143,45
143,59
143,92
144,66
144,34
144,82
144,49
144,41
144,99
144,95
145,00
145,66
146,68
147,38
147,94
149,12
149,95
150,19
151,16
151,74
152,56
152,09
152,46
152,66
152,38
152,59
152,88
153,29
152,35
152,49
152,20
151,57
151,55
151,79
151,52
151,76
151,92
152,20
152,75
153,49
153,78
154,10
154,62
154,65
154,81
154,92
155,40
155,63
155,76

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105107&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]1 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=105107&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105107&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1116.750.7014919166254941.92999999999999
2118.570.4915652180905011.55000000000000
3120.530.5523009719676081.43000000000001
4122.1216666666670.5822032343268171.53
5123.6758333333330.5012975587654931.58000000000000
6124.8408333333330.3134981030342311.15000000000001
7127.190.8692420941152242.61
8130.67751.246435827761413.56
9133.0083333333330.2554793474426010.830000000000013
10134.9408333333330.5231453532299251.85000000000002
11137.1383333333330.7129813631802882.1900
12140.1108333333330.8282891275320922.69
13142.590.8100392807534932.55000000000001
14145.1083333333331.006450408237993.46000000000001
15151.2366666666671.581111998409714.72
16152.1266666666670.5571409701377731.76999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 116.75 & 0.701491916625494 & 1.92999999999999 \tabularnewline
2 & 118.57 & 0.491565218090501 & 1.55000000000000 \tabularnewline
3 & 120.53 & 0.552300971967608 & 1.43000000000001 \tabularnewline
4 & 122.121666666667 & 0.582203234326817 & 1.53 \tabularnewline
5 & 123.675833333333 & 0.501297558765493 & 1.58000000000000 \tabularnewline
6 & 124.840833333333 & 0.313498103034231 & 1.15000000000001 \tabularnewline
7 & 127.19 & 0.869242094115224 & 2.61 \tabularnewline
8 & 130.6775 & 1.24643582776141 & 3.56 \tabularnewline
9 & 133.008333333333 & 0.255479347442601 & 0.830000000000013 \tabularnewline
10 & 134.940833333333 & 0.523145353229925 & 1.85000000000002 \tabularnewline
11 & 137.138333333333 & 0.712981363180288 & 2.1900 \tabularnewline
12 & 140.110833333333 & 0.828289127532092 & 2.69 \tabularnewline
13 & 142.59 & 0.810039280753493 & 2.55000000000001 \tabularnewline
14 & 145.108333333333 & 1.00645040823799 & 3.46000000000001 \tabularnewline
15 & 151.236666666667 & 1.58111199840971 & 4.72 \tabularnewline
16 & 152.126666666667 & 0.557140970137773 & 1.76999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105107&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]116.75[/C][C]0.701491916625494[/C][C]1.92999999999999[/C][/ROW]
[ROW][C]2[/C][C]118.57[/C][C]0.491565218090501[/C][C]1.55000000000000[/C][/ROW]
[ROW][C]3[/C][C]120.53[/C][C]0.552300971967608[/C][C]1.43000000000001[/C][/ROW]
[ROW][C]4[/C][C]122.121666666667[/C][C]0.582203234326817[/C][C]1.53[/C][/ROW]
[ROW][C]5[/C][C]123.675833333333[/C][C]0.501297558765493[/C][C]1.58000000000000[/C][/ROW]
[ROW][C]6[/C][C]124.840833333333[/C][C]0.313498103034231[/C][C]1.15000000000001[/C][/ROW]
[ROW][C]7[/C][C]127.19[/C][C]0.869242094115224[/C][C]2.61[/C][/ROW]
[ROW][C]8[/C][C]130.6775[/C][C]1.24643582776141[/C][C]3.56[/C][/ROW]
[ROW][C]9[/C][C]133.008333333333[/C][C]0.255479347442601[/C][C]0.830000000000013[/C][/ROW]
[ROW][C]10[/C][C]134.940833333333[/C][C]0.523145353229925[/C][C]1.85000000000002[/C][/ROW]
[ROW][C]11[/C][C]137.138333333333[/C][C]0.712981363180288[/C][C]2.1900[/C][/ROW]
[ROW][C]12[/C][C]140.110833333333[/C][C]0.828289127532092[/C][C]2.69[/C][/ROW]
[ROW][C]13[/C][C]142.59[/C][C]0.810039280753493[/C][C]2.55000000000001[/C][/ROW]
[ROW][C]14[/C][C]145.108333333333[/C][C]1.00645040823799[/C][C]3.46000000000001[/C][/ROW]
[ROW][C]15[/C][C]151.236666666667[/C][C]1.58111199840971[/C][C]4.72[/C][/ROW]
[ROW][C]16[/C][C]152.126666666667[/C][C]0.557140970137773[/C][C]1.76999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105107&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105107&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
1116.750.7014919166254941.92999999999999
2118.570.4915652180905011.55000000000000
3120.530.5523009719676081.43000000000001
4122.1216666666670.5822032343268171.53
5123.6758333333330.5012975587654931.58000000000000
6124.8408333333330.3134981030342311.15000000000001
7127.190.8692420941152242.61
8130.67751.246435827761413.56
9133.0083333333330.2554793474426010.830000000000013
10134.9408333333330.5231453532299251.85000000000002
11137.1383333333330.7129813631802882.1900
12140.1108333333330.8282891275320922.69
13142.590.8100392807534932.55000000000001
14145.1083333333331.006450408237993.46000000000001
15151.2366666666671.581111998409714.72
16152.1266666666670.5571409701377731.76999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.17031332914840
beta0.0142683486392837
S.D.0.00701943858202299
T-STAT2.03269085875691
p-value0.0615015956615179

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.17031332914840 \tabularnewline
beta & 0.0142683486392837 \tabularnewline
S.D. & 0.00701943858202299 \tabularnewline
T-STAT & 2.03269085875691 \tabularnewline
p-value & 0.0615015956615179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105107&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.17031332914840[/C][/ROW]
[ROW][C]beta[/C][C]0.0142683486392837[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00701943858202299[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.03269085875691[/C][/ROW]
[ROW][C]p-value[/C][C]0.0615015956615179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105107&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105107&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-1.17031332914840
beta0.0142683486392837
S.D.0.00701943858202299
T-STAT2.03269085875691
p-value0.0615015956615179






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.5417475643500
beta2.27590006532594
S.D.1.33260277460470
T-STAT1.70786081846562
p-value0.109730502197262
Lambda-1.27590006532594

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.5417475643500 \tabularnewline
beta & 2.27590006532594 \tabularnewline
S.D. & 1.33260277460470 \tabularnewline
T-STAT & 1.70786081846562 \tabularnewline
p-value & 0.109730502197262 \tabularnewline
Lambda & -1.27590006532594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105107&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.5417475643500[/C][/ROW]
[ROW][C]beta[/C][C]2.27590006532594[/C][/ROW]
[ROW][C]S.D.[/C][C]1.33260277460470[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.70786081846562[/C][/ROW]
[ROW][C]p-value[/C][C]0.109730502197262[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.27590006532594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105107&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105107&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-11.5417475643500
beta2.27590006532594
S.D.1.33260277460470
T-STAT1.70786081846562
p-value0.109730502197262
Lambda-1.27590006532594


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')