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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 computationSun, 07 Dec 2008 07:42:05 -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/07/t12286611487l4e7dcxtbhloap.htm/, Retrieved Wed, 15 May 2024 17:59:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30022, Retrieved Wed, 15 May 2024 17:59:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact214

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [spectrum] [2007-12-20 15:13:34] [74be16979710d4c4e7c6647856088456]
- RMPD  [Histogram] [Histogram] [2007-12-21 10:46:00] [74be16979710d4c4e7c6647856088456]
- RMPD    [Standard Deviation-Mean Plot] [SD-Mean plot] [2007-12-21 10:58:39] [74be16979710d4c4e7c6647856088456]
- R PD        [Standard Deviation-Mean Plot] [invoer] [2008-12-07 14:42:05] [5925747fb2a6bb4cfcd8015825ee5e92] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11554,5
13182,1
14800,1
12150,7
14478,2
13253,9
12036,8
12653,2
14035,4
14571,4
15400,9
14283,2
14485,3
14196,3
15559,1
13767,4
14634
14381,1
12509,9
12122,3
13122,3
13908,7
13456,5
12441,6
12953
13057,2
14350,1
13830,2
13755,5
13574,4
12802,6
11737,3
13850,2
15081,8
13653,3
14019,1
13962
13768,7
14747,1
13858,1
13188
13693,1
12970
11392,8
13985,2
14994,7
13584,7
14257,8
13553,4
14007,3
16535,8
14721,4
13664,6
16805,9
13829,4
13735,6
15870,5
15962,4
15744,1
16083,7
14863,9
15533,1
17473,1
15925,5
15573,7
17495
14155,8
14913,9
17250,4
15879,8
17647,8
17749,9
17111,8
16934,8
20280
16238,2
17896,1
18089,3
15660
16162,4
17850,1
18520,4
18524,7
16843,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30022&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]0 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=30022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30022&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
113533.36666666671240.248517862693846.4
213715.3751026.151369416103436.8
313555.3916666667845.9612439632673344.5
413700.1833333333924.1734792218243601.9
515042.84166666671240.162516812243252.5
616205.15833333331262.465119920213594.1
717509.29166666671283.217649970954620

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 13533.3666666667 & 1240.24851786269 & 3846.4 \tabularnewline
2 & 13715.375 & 1026.15136941610 & 3436.8 \tabularnewline
3 & 13555.3916666667 & 845.961243963267 & 3344.5 \tabularnewline
4 & 13700.1833333333 & 924.173479221824 & 3601.9 \tabularnewline
5 & 15042.8416666667 & 1240.16251681224 & 3252.5 \tabularnewline
6 & 16205.1583333333 & 1262.46511992021 & 3594.1 \tabularnewline
7 & 17509.2916666667 & 1283.21764997095 & 4620 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30022&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]13533.3666666667[/C][C]1240.24851786269[/C][C]3846.4[/C][/ROW]
[ROW][C]2[/C][C]13715.375[/C][C]1026.15136941610[/C][C]3436.8[/C][/ROW]
[ROW][C]3[/C][C]13555.3916666667[/C][C]845.961243963267[/C][C]3344.5[/C][/ROW]
[ROW][C]4[/C][C]13700.1833333333[/C][C]924.173479221824[/C][C]3601.9[/C][/ROW]
[ROW][C]5[/C][C]15042.8416666667[/C][C]1240.16251681224[/C][C]3252.5[/C][/ROW]
[ROW][C]6[/C][C]16205.1583333333[/C][C]1262.46511992021[/C][C]3594.1[/C][/ROW]
[ROW][C]7[/C][C]17509.2916666667[/C][C]1283.21764997095[/C][C]4620[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30022&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
113533.36666666671240.248517862693846.4
213715.3751026.151369416103436.8
313555.3916666667845.9612439632673344.5
413700.1833333333924.1734792218243601.9
515042.84166666671240.162516812243252.5
616205.15833333331262.465119920213594.1
717509.29166666671283.217649970954620






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-47.6987863803736
beta0.0789864842652951
S.D.0.0375647053416026
T-STAT2.10267812690169
p-value0.0894487706588063

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -47.6987863803736 \tabularnewline
beta & 0.0789864842652951 \tabularnewline
S.D. & 0.0375647053416026 \tabularnewline
T-STAT & 2.10267812690169 \tabularnewline
p-value & 0.0894487706588063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30022&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-47.6987863803736[/C][/ROW]
[ROW][C]beta[/C][C]0.0789864842652951[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0375647053416026[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.10267812690169[/C][/ROW]
[ROW][C]p-value[/C][C]0.0894487706588063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30022&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30022&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-47.6987863803736
beta0.0789864842652951
S.D.0.0375647053416026
T-STAT2.10267812690169
p-value0.0894487706588063






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.76539471999389
beta1.12274362701619
S.D.0.546102334114645
T-STAT2.05592167782329
p-value0.0949245899559484
Lambda-0.122743627016194

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.76539471999389 \tabularnewline
beta & 1.12274362701619 \tabularnewline
S.D. & 0.546102334114645 \tabularnewline
T-STAT & 2.05592167782329 \tabularnewline
p-value & 0.0949245899559484 \tabularnewline
Lambda & -0.122743627016194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30022&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.76539471999389[/C][/ROW]
[ROW][C]beta[/C][C]1.12274362701619[/C][/ROW]
[ROW][C]S.D.[/C][C]0.546102334114645[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.05592167782329[/C][/ROW]
[ROW][C]p-value[/C][C]0.0949245899559484[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.122743627016194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30022&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30022&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-3.76539471999389
beta1.12274362701619
S.D.0.546102334114645
T-STAT2.05592167782329
p-value0.0949245899559484
Lambda-0.122743627016194


Figures (Output of Computation)

Input Parameters & R Code

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')