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Description of Statistical Computation

Author's title

Standard Deviation-Mean Plot - Olieprijzen in constante dollar - Bram Op de...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 18 May 2008 04:40:48 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/18/t1211107310y56zx4r5iy351ax.htm/, Retrieved Tue, 14 May 2024 00:30:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12716, Retrieved Tue, 14 May 2024 00:30:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-05-18 10:40:48] [f1ad3272590ff3a9e1233970549442f0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
23.11
18.64
14.94
16.90
15.46
11.15
13.13
12.48
12.95
12.59
10.58
10.58
12.39
15.53
13.06
10.22
16.33
19.72
21.31
18.84
24.84
15.67
15.57
12.73
13.56
15.54
17.22
12.14
11.07
12.02
11.55
6.92
10.33
8.38
12.11
11.46
12.75
13.32
13.00
11.90
11.79
12.55
11.84
11.25
11.15
10.99
11.70
14.01
17.51
17.27
16.90
15.79
15.45
16.24
16.71
16.77
16.64
17.80
16.87
16.13
15.76
15.66
15.54
15.30
15.05
14.69
14.39
14.18
13.70
13.66
13.27
13.56
13.14
14.19
22.57
23.09
23.31
22.91
22.36
43.06
64.67
64.68
56.90
48.79
45.21
41.40
22.17
25.52
20.28
22.87
27.63
22.95
21.35
18.38
17.15
18.27
19.40
20.52

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12716&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12716&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
118.39753.486319692741908.17
213.0551.802710921547514.31
311.6751.272910051810422.37
412.82.186702235483075.31
519.052.081585933849484.98
617.20255.2709352427565812.11
714.6152.227128195681605.08
810.392.345620031747115.1
910.571.634768077332893.73
1012.74250.6081871970591511.42
1111.85750.5333776023294071.3
1211.96251.398460463033073.02
1316.86750.7608931155775661.72000000000000
1416.29250.6096105314050941.32
1516.860.6988085097745551.67000000000000
1615.5650.1982422760159900.459999999999999
1714.57750.3781864619470140.870000000000001
1813.54750.194143417778370.43
1918.24755.312992722248619.95
2027.9110.107505462114120.7
2158.767.5902349546418315.89
2233.57511.424548131107923.04
2323.43253.060853639101357.35
2418.78751.796447884020024.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 18.3975 & 3.48631969274190 & 8.17 \tabularnewline
2 & 13.055 & 1.80271092154751 & 4.31 \tabularnewline
3 & 11.675 & 1.27291005181042 & 2.37 \tabularnewline
4 & 12.8 & 2.18670223548307 & 5.31 \tabularnewline
5 & 19.05 & 2.08158593384948 & 4.98 \tabularnewline
6 & 17.2025 & 5.27093524275658 & 12.11 \tabularnewline
7 & 14.615 & 2.22712819568160 & 5.08 \tabularnewline
8 & 10.39 & 2.34562003174711 & 5.1 \tabularnewline
9 & 10.57 & 1.63476807733289 & 3.73 \tabularnewline
10 & 12.7425 & 0.608187197059151 & 1.42 \tabularnewline
11 & 11.8575 & 0.533377602329407 & 1.3 \tabularnewline
12 & 11.9625 & 1.39846046303307 & 3.02 \tabularnewline
13 & 16.8675 & 0.760893115577566 & 1.72000000000000 \tabularnewline
14 & 16.2925 & 0.609610531405094 & 1.32 \tabularnewline
15 & 16.86 & 0.698808509774555 & 1.67000000000000 \tabularnewline
16 & 15.565 & 0.198242276015990 & 0.459999999999999 \tabularnewline
17 & 14.5775 & 0.378186461947014 & 0.870000000000001 \tabularnewline
18 & 13.5475 & 0.19414341777837 & 0.43 \tabularnewline
19 & 18.2475 & 5.31299272224861 & 9.95 \tabularnewline
20 & 27.91 & 10.1075054621141 & 20.7 \tabularnewline
21 & 58.76 & 7.59023495464183 & 15.89 \tabularnewline
22 & 33.575 & 11.4245481311079 & 23.04 \tabularnewline
23 & 23.4325 & 3.06085363910135 & 7.35 \tabularnewline
24 & 18.7875 & 1.79644788402002 & 4.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12716&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]18.3975[/C][C]3.48631969274190[/C][C]8.17[/C][/ROW]
[ROW][C]2[/C][C]13.055[/C][C]1.80271092154751[/C][C]4.31[/C][/ROW]
[ROW][C]3[/C][C]11.675[/C][C]1.27291005181042[/C][C]2.37[/C][/ROW]
[ROW][C]4[/C][C]12.8[/C][C]2.18670223548307[/C][C]5.31[/C][/ROW]
[ROW][C]5[/C][C]19.05[/C][C]2.08158593384948[/C][C]4.98[/C][/ROW]
[ROW][C]6[/C][C]17.2025[/C][C]5.27093524275658[/C][C]12.11[/C][/ROW]
[ROW][C]7[/C][C]14.615[/C][C]2.22712819568160[/C][C]5.08[/C][/ROW]
[ROW][C]8[/C][C]10.39[/C][C]2.34562003174711[/C][C]5.1[/C][/ROW]
[ROW][C]9[/C][C]10.57[/C][C]1.63476807733289[/C][C]3.73[/C][/ROW]
[ROW][C]10[/C][C]12.7425[/C][C]0.608187197059151[/C][C]1.42[/C][/ROW]
[ROW][C]11[/C][C]11.8575[/C][C]0.533377602329407[/C][C]1.3[/C][/ROW]
[ROW][C]12[/C][C]11.9625[/C][C]1.39846046303307[/C][C]3.02[/C][/ROW]
[ROW][C]13[/C][C]16.8675[/C][C]0.760893115577566[/C][C]1.72000000000000[/C][/ROW]
[ROW][C]14[/C][C]16.2925[/C][C]0.609610531405094[/C][C]1.32[/C][/ROW]
[ROW][C]15[/C][C]16.86[/C][C]0.698808509774555[/C][C]1.67000000000000[/C][/ROW]
[ROW][C]16[/C][C]15.565[/C][C]0.198242276015990[/C][C]0.459999999999999[/C][/ROW]
[ROW][C]17[/C][C]14.5775[/C][C]0.378186461947014[/C][C]0.870000000000001[/C][/ROW]
[ROW][C]18[/C][C]13.5475[/C][C]0.19414341777837[/C][C]0.43[/C][/ROW]
[ROW][C]19[/C][C]18.2475[/C][C]5.31299272224861[/C][C]9.95[/C][/ROW]
[ROW][C]20[/C][C]27.91[/C][C]10.1075054621141[/C][C]20.7[/C][/ROW]
[ROW][C]21[/C][C]58.76[/C][C]7.59023495464183[/C][C]15.89[/C][/ROW]
[ROW][C]22[/C][C]33.575[/C][C]11.4245481311079[/C][C]23.04[/C][/ROW]
[ROW][C]23[/C][C]23.4325[/C][C]3.06085363910135[/C][C]7.35[/C][/ROW]
[ROW][C]24[/C][C]18.7875[/C][C]1.79644788402002[/C][C]4.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12716&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
118.39753.486319692741908.17
213.0551.802710921547514.31
311.6751.272910051810422.37
412.82.186702235483075.31
519.052.081585933849484.98
617.20255.2709352427565812.11
714.6152.227128195681605.08
810.392.345620031747115.1
910.571.634768077332893.73
1012.74250.6081871970591511.42
1111.85750.5333776023294071.3
1211.96251.398460463033073.02
1316.86750.7608931155775661.72000000000000
1416.29250.6096105314050941.32
1516.860.6988085097745551.67000000000000
1615.5650.1982422760159900.459999999999999
1714.57750.3781864619470140.870000000000001
1813.54750.194143417778370.43
1918.24755.312992722248619.95
2027.9110.107505462114120.7
2158.767.5902349546418315.89
2233.57511.424548131107923.04
2323.43253.060853639101357.35
2418.78751.796447884020024.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.03807808305904
beta0.209452173826233
S.D.0.0458150002149106
T-STAT4.57169426702451
p-value0.000149311582365608

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.03807808305904 \tabularnewline
beta & 0.209452173826233 \tabularnewline
S.D. & 0.0458150002149106 \tabularnewline
T-STAT & 4.57169426702451 \tabularnewline
p-value & 0.000149311582365608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12716&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.03807808305904[/C][/ROW]
[ROW][C]beta[/C][C]0.209452173826233[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0458150002149106[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.57169426702451[/C][/ROW]
[ROW][C]p-value[/C][C]0.000149311582365608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12716&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12716&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-1.03807808305904
beta0.209452173826233
S.D.0.0458150002149106
T-STAT4.57169426702451
p-value0.000149311582365608






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.22039941591226
beta1.66856351726294
S.D.0.495449501373472
T-STAT3.36777716525577
p-value0.00277665027818061
Lambda-0.66856351726294

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.22039941591226 \tabularnewline
beta & 1.66856351726294 \tabularnewline
S.D. & 0.495449501373472 \tabularnewline
T-STAT & 3.36777716525577 \tabularnewline
p-value & 0.00277665027818061 \tabularnewline
Lambda & -0.66856351726294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12716&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.22039941591226[/C][/ROW]
[ROW][C]beta[/C][C]1.66856351726294[/C][/ROW]
[ROW][C]S.D.[/C][C]0.495449501373472[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.36777716525577[/C][/ROW]
[ROW][C]p-value[/C][C]0.00277665027818061[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.66856351726294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12716&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12716&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-4.22039941591226
beta1.66856351726294
S.D.0.495449501373472
T-STAT3.36777716525577
p-value0.00277665027818061
Lambda-0.66856351726294


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')