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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

Fri, 12 Dec 2008 05:35:28 -0700

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/2008/Dec/12/t1229085380kh91dzp2b7xikid.htm/, Retrieved Sun, 19 May 2024 07:22:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32629, Retrieved Sun, 19 May 2024 07:22:12 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

165

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

F     [Univariate Data Series] [Paper - werkloosh...] [2008-12-11 13:38:22] [46c5a5fbda57fdfa1d4ef48658f82a0c]
- RMP     [Standard Deviation-Mean Plot] [Paper - werkloosh...] [2008-12-12 12:35:28] [b23db733701c4d62df5e228d507c1c6a] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32629&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32629&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	49.39725	0.97517486776848	3.872
2	47.5561666666667	1.42974713805899	4.525
3	46.4003333333333	1.68473905901469	5.146
4	51.2165	2.73529501483511	7.692
5	57.1995833333333	2.55670186900422	7.488
6	65.67825	3.45698102987406	8.248
7	71.37625	1.56938517926897	4.563
8	74.5939166666667	1.72209599871432	5.20699999999999
9	76.7360833333333	1.44294764337281	4.84899999999999
10	77.33575	1.20786597126728	4.277
11	77.1799166666667	1.96883327048526	6.783
12	73.0998333333333	1.41382446083685	4.47
13	70.0399166666667	2.66317890903243	9.142
14	70.7145	2.51830836078507	7.22
15	77.52575	3.27953566904607	9.748
16	84.25925	2.65020617122517	7.786
17	90.3215833333333	3.03395207184333	10.2000000000000
18	94.075	2.96675169779401	9.783
19	97.09925	1.90866617515526	6.25699999999999
20	93.6713333333333	1.72127570731886	4.93199999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 49.39725 & 0.97517486776848 & 3.872 \tabularnewline
2 & 47.5561666666667 & 1.42974713805899 & 4.525 \tabularnewline
3 & 46.4003333333333 & 1.68473905901469 & 5.146 \tabularnewline
4 & 51.2165 & 2.73529501483511 & 7.692 \tabularnewline
5 & 57.1995833333333 & 2.55670186900422 & 7.488 \tabularnewline
6 & 65.67825 & 3.45698102987406 & 8.248 \tabularnewline
7 & 71.37625 & 1.56938517926897 & 4.563 \tabularnewline
8 & 74.5939166666667 & 1.72209599871432 & 5.20699999999999 \tabularnewline
9 & 76.7360833333333 & 1.44294764337281 & 4.84899999999999 \tabularnewline
10 & 77.33575 & 1.20786597126728 & 4.277 \tabularnewline
11 & 77.1799166666667 & 1.96883327048526 & 6.783 \tabularnewline
12 & 73.0998333333333 & 1.41382446083685 & 4.47 \tabularnewline
13 & 70.0399166666667 & 2.66317890903243 & 9.142 \tabularnewline
14 & 70.7145 & 2.51830836078507 & 7.22 \tabularnewline
15 & 77.52575 & 3.27953566904607 & 9.748 \tabularnewline
16 & 84.25925 & 2.65020617122517 & 7.786 \tabularnewline
17 & 90.3215833333333 & 3.03395207184333 & 10.2000000000000 \tabularnewline
18 & 94.075 & 2.96675169779401 & 9.783 \tabularnewline
19 & 97.09925 & 1.90866617515526 & 6.25699999999999 \tabularnewline
20 & 93.6713333333333 & 1.72127570731886 & 4.93199999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32629&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]49.39725[/C][C]0.97517486776848[/C][C]3.872[/C][/ROW]
[ROW][C]2[/C][C]47.5561666666667[/C][C]1.42974713805899[/C][C]4.525[/C][/ROW]
[ROW][C]3[/C][C]46.4003333333333[/C][C]1.68473905901469[/C][C]5.146[/C][/ROW]
[ROW][C]4[/C][C]51.2165[/C][C]2.73529501483511[/C][C]7.692[/C][/ROW]
[ROW][C]5[/C][C]57.1995833333333[/C][C]2.55670186900422[/C][C]7.488[/C][/ROW]
[ROW][C]6[/C][C]65.67825[/C][C]3.45698102987406[/C][C]8.248[/C][/ROW]
[ROW][C]7[/C][C]71.37625[/C][C]1.56938517926897[/C][C]4.563[/C][/ROW]
[ROW][C]8[/C][C]74.5939166666667[/C][C]1.72209599871432[/C][C]5.20699999999999[/C][/ROW]
[ROW][C]9[/C][C]76.7360833333333[/C][C]1.44294764337281[/C][C]4.84899999999999[/C][/ROW]
[ROW][C]10[/C][C]77.33575[/C][C]1.20786597126728[/C][C]4.277[/C][/ROW]
[ROW][C]11[/C][C]77.1799166666667[/C][C]1.96883327048526[/C][C]6.783[/C][/ROW]
[ROW][C]12[/C][C]73.0998333333333[/C][C]1.41382446083685[/C][C]4.47[/C][/ROW]
[ROW][C]13[/C][C]70.0399166666667[/C][C]2.66317890903243[/C][C]9.142[/C][/ROW]
[ROW][C]14[/C][C]70.7145[/C][C]2.51830836078507[/C][C]7.22[/C][/ROW]
[ROW][C]15[/C][C]77.52575[/C][C]3.27953566904607[/C][C]9.748[/C][/ROW]
[ROW][C]16[/C][C]84.25925[/C][C]2.65020617122517[/C][C]7.786[/C][/ROW]
[ROW][C]17[/C][C]90.3215833333333[/C][C]3.03395207184333[/C][C]10.2000000000000[/C][/ROW]
[ROW][C]18[/C][C]94.075[/C][C]2.96675169779401[/C][C]9.783[/C][/ROW]
[ROW][C]19[/C][C]97.09925[/C][C]1.90866617515526[/C][C]6.25699999999999[/C][/ROW]
[ROW][C]20[/C][C]93.6713333333333[/C][C]1.72127570731886[/C][C]4.93199999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32629&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	49.39725	0.97517486776848	3.872
2	47.5561666666667	1.42974713805899	4.525
3	46.4003333333333	1.68473905901469	5.146
4	51.2165	2.73529501483511	7.692
5	57.1995833333333	2.55670186900422	7.488
6	65.67825	3.45698102987406	8.248
7	71.37625	1.56938517926897	4.563
8	74.5939166666667	1.72209599871432	5.20699999999999
9	76.7360833333333	1.44294764337281	4.84899999999999
10	77.33575	1.20786597126728	4.277
11	77.1799166666667	1.96883327048526	6.783
12	73.0998333333333	1.41382446083685	4.47
13	70.0399166666667	2.66317890903243	9.142
14	70.7145	2.51830836078507	7.22
15	77.52575	3.27953566904607	9.748
16	84.25925	2.65020617122517	7.786
17	90.3215833333333	3.03395207184333	10.2000000000000
18	94.075	2.96675169779401	9.783
19	97.09925	1.90866617515526	6.25699999999999
20	93.6713333333333	1.72127570731886	4.93199999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.39037925243276
beta	0.0104449170128022
S.D.	0.0108899406466698
T-STAT	0.959134429809435
p-value	0.350198212511188

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.39037925243276 \tabularnewline
beta & 0.0104449170128022 \tabularnewline
S.D. & 0.0108899406466698 \tabularnewline
T-STAT & 0.959134429809435 \tabularnewline
p-value & 0.350198212511188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32629&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.39037925243276[/C][/ROW]
[ROW][C]beta[/C][C]0.0104449170128022[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0108899406466698[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.959134429809435[/C][/ROW]
[ROW][C]p-value[/C][C]0.350198212511188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32629&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	1.39037925243276
beta	0.0104449170128022
S.D.	0.0108899406466698
T-STAT	0.959134429809435
p-value	0.350198212511188

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.09611346750219
beta	0.422742889698852
S.D.	0.357379990784711
T-STAT	1.18289467961153
p-value	0.252240088332874
Lambda	0.577257110301148

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.09611346750219 \tabularnewline
beta & 0.422742889698852 \tabularnewline
S.D. & 0.357379990784711 \tabularnewline
T-STAT & 1.18289467961153 \tabularnewline
p-value & 0.252240088332874 \tabularnewline
Lambda & 0.577257110301148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32629&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.09611346750219[/C][/ROW]
[ROW][C]beta[/C][C]0.422742889698852[/C][/ROW]
[ROW][C]S.D.[/C][C]0.357379990784711[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.18289467961153[/C][/ROW]
[ROW][C]p-value[/C][C]0.252240088332874[/C][/ROW]
[ROW][C]Lambda[/C][C]0.577257110301148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32629&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32629&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	-1.09611346750219
beta	0.422742889698852
S.D.	0.357379990784711
T-STAT	1.18289467961153
p-value	0.252240088332874
Lambda	0.577257110301148

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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