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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 computationFri, 12 Dec 2008 07:44:37 -0700
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/Dec/12/t1229093188rve690tzgq8jri3.htm/, Retrieved Sat, 11 May 2024 06:36:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32806, Retrieved Sat, 11 May 2024 06:36:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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]
F RMP   [Standard Deviation-Mean Plot] [Taak 8 stap 1] [2008-12-12 12:09:36] [491a70d26f8c977398d8a0c1c87d3dd4]
-    D      [Standard Deviation-Mean Plot] [paper standard de...] [2008-12-12 14:44:37] [2ba2a74112fb2c960057a572bf2825d3] [Current]
- RM D        [Variance Reduction Matrix] [paper variance re...] [2008-12-12 14:54:46] [491a70d26f8c977398d8a0c1c87d3dd4]
- RMP           [(Partial) Autocorrelation Function] [Paper autocorrela...] [2008-12-12 15:10:41] [491a70d26f8c977398d8a0c1c87d3dd4]
-   P             [(Partial) Autocorrelation Function] [Paper autocorrela...] [2008-12-12 15:21:21] [491a70d26f8c977398d8a0c1c87d3dd4]
- RMP           [ARIMA Backward Selection] [Paper ARIMA backw...] [2008-12-16 19:22:07] [491a70d26f8c977398d8a0c1c87d3dd4]
- RM              [ARIMA Forecasting] [Paper Arima forec...] [2008-12-16 19:41:13] [491a70d26f8c977398d8a0c1c87d3dd4]
- RM              [ARIMA Forecasting] [Paper Arima forec...] [2008-12-16 19:55:16] [491a70d26f8c977398d8a0c1c87d3dd4]
-  MPD              [ARIMA Forecasting] [Ws 9] [2009-12-04 14:55:47] [74be16979710d4c4e7c6647856088456]
-                     [ARIMA Forecasting] [Workshop 9-1] [2009-12-04 21:41:47] [aba88da643e3763d32ff92bd8f92a385]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,3
101,2
107,7
110,4
101,9
115,9
89,9
88,6
117,2
123,9
100
103,6
94,1
98,7
119,5
112,7
104,4
124,7
89,1
97
121,6
118,8
114
111,5
97,2
102,5
113,4
109,8
104,9
126,1
80
96,8
117,2
112,3
117,3
111,1
102,2
104,3
122,9
107,6
121,3
131,5
89
104,4
128,9
135,9
133,3
121,3
120,5
120,4
137,9
126,1
133,2
151,1
105
119
140,4
156,6
137,1
122,7

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=32806&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=32806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32806&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
1105.310.492854711659735.3
2108.84166666666711.853074655458835.6
3107.38333333333312.137907063361046.1
4116.88333333333314.947899416630346.9
5130.83333333333314.686316038676251.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 105.3 & 10.4928547116597 & 35.3 \tabularnewline
2 & 108.841666666667 & 11.8530746554588 & 35.6 \tabularnewline
3 & 107.383333333333 & 12.1379070633610 & 46.1 \tabularnewline
4 & 116.883333333333 & 14.9478994166303 & 46.9 \tabularnewline
5 & 130.833333333333 & 14.6863160386762 & 51.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32806&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]105.3[/C][C]10.4928547116597[/C][C]35.3[/C][/ROW]
[ROW][C]2[/C][C]108.841666666667[/C][C]11.8530746554588[/C][C]35.6[/C][/ROW]
[ROW][C]3[/C][C]107.383333333333[/C][C]12.1379070633610[/C][C]46.1[/C][/ROW]
[ROW][C]4[/C][C]116.883333333333[/C][C]14.9478994166303[/C][C]46.9[/C][/ROW]
[ROW][C]5[/C][C]130.833333333333[/C][C]14.6863160386762[/C][C]51.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32806&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
1105.310.492854711659735.3
2108.84166666666711.853074655458835.6
3107.38333333333312.137907063361046.1
4116.88333333333314.947899416630346.9
5130.83333333333314.686316038676251.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.68438657023004
beta0.153783515619206
S.D.0.0583946453126364
T-STAT2.63352084417795
p-value0.078088713779677

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.68438657023004 \tabularnewline
beta & 0.153783515619206 \tabularnewline
S.D. & 0.0583946453126364 \tabularnewline
T-STAT & 2.63352084417795 \tabularnewline
p-value & 0.078088713779677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32806&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.68438657023004[/C][/ROW]
[ROW][C]beta[/C][C]0.153783515619206[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0583946453126364[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.63352084417795[/C][/ROW]
[ROW][C]p-value[/C][C]0.078088713779677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32806&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32806&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-4.68438657023004
beta0.153783515619206
S.D.0.0583946453126364
T-STAT2.63352084417795
p-value0.078088713779677






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.23856159126345
beta1.43307146098910
S.D.0.526657968225191
T-STAT2.72106670258589
p-value0.0724841590839985
Lambda-0.433071460989104

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.23856159126345 \tabularnewline
beta & 1.43307146098910 \tabularnewline
S.D. & 0.526657968225191 \tabularnewline
T-STAT & 2.72106670258589 \tabularnewline
p-value & 0.0724841590839985 \tabularnewline
Lambda & -0.433071460989104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32806&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.23856159126345[/C][/ROW]
[ROW][C]beta[/C][C]1.43307146098910[/C][/ROW]
[ROW][C]S.D.[/C][C]0.526657968225191[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.72106670258589[/C][/ROW]
[ROW][C]p-value[/C][C]0.0724841590839985[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.433071460989104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32806&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32806&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-4.23856159126345
beta1.43307146098910
S.D.0.526657968225191
T-STAT2.72106670258589
p-value0.0724841590839985
Lambda-0.433071460989104


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')