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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 21 Dec 2010 16:43:27 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292949662aox5iw0zop2og4w.htm/, Retrieved Sun, 19 May 2024 19:48:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113743, Retrieved Sun, 19 May 2024 19:48:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

150

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   [(Partial) Autocorrelation Function] [WS8 Autocorolation] [2010-12-01 09:55:45] [b84bdc9bd81e1f02ca0dcc4710c1b790]
- RMPD      [Standard Deviation-Mean Plot] [SMP] [2010-12-21 16:43:27] [a8abc7260f3c847aeac0a796e7895a2e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=113743&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=113743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113743&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	151581.666666667	4633.96863749997	12866
2	167107.416666667	5156.04893584108	12458
3	186230.416666667	4700.66230262644	12855
4	202430	4442.40078417884	12363
5	216129.416666667	3518.38068275562	8659
6	226791.333333333	3115.56139208952	7810
7	241100.666666667	5598.6645214946	14120
8	259736.916666667	5607.00718190005	15288
9	283407	5495.16516419827	16037

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 151581.666666667 & 4633.96863749997 & 12866 \tabularnewline
2 & 167107.416666667 & 5156.04893584108 & 12458 \tabularnewline
3 & 186230.416666667 & 4700.66230262644 & 12855 \tabularnewline
4 & 202430 & 4442.40078417884 & 12363 \tabularnewline
5 & 216129.416666667 & 3518.38068275562 & 8659 \tabularnewline
6 & 226791.333333333 & 3115.56139208952 & 7810 \tabularnewline
7 & 241100.666666667 & 5598.6645214946 & 14120 \tabularnewline
8 & 259736.916666667 & 5607.00718190005 & 15288 \tabularnewline
9 & 283407 & 5495.16516419827 & 16037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113743&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]151581.666666667[/C][C]4633.96863749997[/C][C]12866[/C][/ROW]
[ROW][C]2[/C][C]167107.416666667[/C][C]5156.04893584108[/C][C]12458[/C][/ROW]
[ROW][C]3[/C][C]186230.416666667[/C][C]4700.66230262644[/C][C]12855[/C][/ROW]
[ROW][C]4[/C][C]202430[/C][C]4442.40078417884[/C][C]12363[/C][/ROW]
[ROW][C]5[/C][C]216129.416666667[/C][C]3518.38068275562[/C][C]8659[/C][/ROW]
[ROW][C]6[/C][C]226791.333333333[/C][C]3115.56139208952[/C][C]7810[/C][/ROW]
[ROW][C]7[/C][C]241100.666666667[/C][C]5598.6645214946[/C][C]14120[/C][/ROW]
[ROW][C]8[/C][C]259736.916666667[/C][C]5607.00718190005[/C][C]15288[/C][/ROW]
[ROW][C]9[/C][C]283407[/C][C]5495.16516419827[/C][C]16037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113743&T=1

As an alternative you can also use a QR Code:

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

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	151581.666666667	4633.96863749997	12866
2	167107.416666667	5156.04893584108	12458
3	186230.416666667	4700.66230262644	12855
4	202430	4442.40078417884	12363
5	216129.416666667	3518.38068275562	8659
6	226791.333333333	3115.56139208952	7810
7	241100.666666667	5598.6645214946	14120
8	259736.916666667	5607.00718190005	15288
9	283407	5495.16516419827	16037

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3477.15421941337
beta	0.00567246703865062
S.D.	0.0075911222950943
T-STAT	0.747250119039237
p-value	0.479255871715297

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3477.15421941337 \tabularnewline
beta & 0.00567246703865062 \tabularnewline
S.D. & 0.0075911222950943 \tabularnewline
T-STAT & 0.747250119039237 \tabularnewline
p-value & 0.479255871715297 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113743&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3477.15421941337[/C][/ROW]
[ROW][C]beta[/C][C]0.00567246703865062[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0075911222950943[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.747250119039237[/C][/ROW]
[ROW][C]p-value[/C][C]0.479255871715297[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113743&T=2

As an alternative you can also use a QR Code:

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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3477.15421941337
beta	0.00567246703865062
S.D.	0.0075911222950943
T-STAT	0.747250119039237
p-value	0.479255871715297

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.42547101094867
beta	0.164021139203551
S.D.	0.380155495144109
T-STAT	0.431458025199331
p-value	0.679111809804442
Lambda	0.835978860796449

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.42547101094867 \tabularnewline
beta & 0.164021139203551 \tabularnewline
S.D. & 0.380155495144109 \tabularnewline
T-STAT & 0.431458025199331 \tabularnewline
p-value & 0.679111809804442 \tabularnewline
Lambda & 0.835978860796449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113743&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.42547101094867[/C][/ROW]
[ROW][C]beta[/C][C]0.164021139203551[/C][/ROW]
[ROW][C]S.D.[/C][C]0.380155495144109[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.431458025199331[/C][/ROW]
[ROW][C]p-value[/C][C]0.679111809804442[/C][/ROW]
[ROW][C]Lambda[/C][C]0.835978860796449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113743&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113743&T=3

As an alternative you can also use a QR Code:

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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.42547101094867
beta	0.164021139203551
S.D.	0.380155495144109
T-STAT	0.431458025199331
p-value	0.679111809804442
Lambda	0.835978860796449

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code