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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

Wed, 22 Dec 2010 13:46:55 +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/22/t12930254783zr8zsfzw63y5am.htm/, Retrieved Mon, 06 May 2024 08:24:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114207, Retrieved Mon, 06 May 2024 08:24:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

136

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Standard Deviation-Mean Plot] [] [2010-12-16 01:48:45] [bcc4ad4a6c0f95d5b548de29638ac6c2]
-   PD      [Standard Deviation-Mean Plot] [] [2010-12-22 13:46:55] [29eeba0e6ce2cd83aa315a4a7ff8c4aa] [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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114207&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114207&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	361.666666666667	11.211465992321	33
2	356.166666666667	11.2236222749029	33
3	369.916666666667	10.4137874808818	27
4	405.666666666667	12.8793939251344	29
5	439.833333333333	15.1647517938704	39
6	463.083333333333	6.15642064445853	17
7	461.833333333333	11.2074109680185	34
8	421.916666666667	13.1249819624696	40
9	401.5	9.18991542151207	28
10	437.75	13.6056472232539	40

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 361.666666666667 & 11.211465992321 & 33 \tabularnewline
2 & 356.166666666667 & 11.2236222749029 & 33 \tabularnewline
3 & 369.916666666667 & 10.4137874808818 & 27 \tabularnewline
4 & 405.666666666667 & 12.8793939251344 & 29 \tabularnewline
5 & 439.833333333333 & 15.1647517938704 & 39 \tabularnewline
6 & 463.083333333333 & 6.15642064445853 & 17 \tabularnewline
7 & 461.833333333333 & 11.2074109680185 & 34 \tabularnewline
8 & 421.916666666667 & 13.1249819624696 & 40 \tabularnewline
9 & 401.5 & 9.18991542151207 & 28 \tabularnewline
10 & 437.75 & 13.6056472232539 & 40 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114207&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]361.666666666667[/C][C]11.211465992321[/C][C]33[/C][/ROW]
[ROW][C]2[/C][C]356.166666666667[/C][C]11.2236222749029[/C][C]33[/C][/ROW]
[ROW][C]3[/C][C]369.916666666667[/C][C]10.4137874808818[/C][C]27[/C][/ROW]
[ROW][C]4[/C][C]405.666666666667[/C][C]12.8793939251344[/C][C]29[/C][/ROW]
[ROW][C]5[/C][C]439.833333333333[/C][C]15.1647517938704[/C][C]39[/C][/ROW]
[ROW][C]6[/C][C]463.083333333333[/C][C]6.15642064445853[/C][C]17[/C][/ROW]
[ROW][C]7[/C][C]461.833333333333[/C][C]11.2074109680185[/C][C]34[/C][/ROW]
[ROW][C]8[/C][C]421.916666666667[/C][C]13.1249819624696[/C][C]40[/C][/ROW]
[ROW][C]9[/C][C]401.5[/C][C]9.18991542151207[/C][C]28[/C][/ROW]
[ROW][C]10[/C][C]437.75[/C][C]13.6056472232539[/C][C]40[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114207&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	361.666666666667	11.211465992321	33
2	356.166666666667	11.2236222749029	33
3	369.916666666667	10.4137874808818	27
4	405.666666666667	12.8793939251344	29
5	439.833333333333	15.1647517938704	39
6	463.083333333333	6.15642064445853	17
7	461.833333333333	11.2074109680185	34
8	421.916666666667	13.1249819624696	40
9	401.5	9.18991542151207	28
10	437.75	13.6056472232539	40

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	12.1162655546075
beta	-0.00169572532592287
S.D.	0.0225195417527183
T-STAT	-0.0753001701607975
p-value	0.941824837991559

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 12.1162655546075 \tabularnewline
beta & -0.00169572532592287 \tabularnewline
S.D. & 0.0225195417527183 \tabularnewline
T-STAT & -0.0753001701607975 \tabularnewline
p-value & 0.941824837991559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114207&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.1162655546075[/C][/ROW]
[ROW][C]beta[/C][C]-0.00169572532592287[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0225195417527183[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0753001701607975[/C][/ROW]
[ROW][C]p-value[/C][C]0.941824837991559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114207&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	12.1162655546075
beta	-0.00169572532592287
S.D.	0.0225195417527183
T-STAT	-0.0753001701607975
p-value	0.941824837991559

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.12523409451918
beta	-0.285251492080307
S.D.	0.911270843300049
T-STAT	-0.313026027528002
p-value	0.762265873921722
Lambda	1.28525149208031

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.12523409451918 \tabularnewline
beta & -0.285251492080307 \tabularnewline
S.D. & 0.911270843300049 \tabularnewline
T-STAT & -0.313026027528002 \tabularnewline
p-value & 0.762265873921722 \tabularnewline
Lambda & 1.28525149208031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114207&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.12523409451918[/C][/ROW]
[ROW][C]beta[/C][C]-0.285251492080307[/C][/ROW]
[ROW][C]S.D.[/C][C]0.911270843300049[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.313026027528002[/C][/ROW]
[ROW][C]p-value[/C][C]0.762265873921722[/C][/ROW]
[ROW][C]Lambda[/C][C]1.28525149208031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114207&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114207&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	4.12523409451918
beta	-0.285251492080307
S.D.	0.911270843300049
T-STAT	-0.313026027528002
p-value	0.762265873921722
Lambda	1.28525149208031

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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