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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 computationTue, 02 Dec 2008 12:57:19 -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/02/t1228247908o4gm94wzaaks618.htm/, Retrieved Sun, 19 May 2024 11:14:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28303, Retrieved Sun, 19 May 2024 11:14:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [Non stat time ser...] [2008-12-02 19:57:19] [c5d6d05aee6be5527ac4a30a8c3b8fe5] [Current]
Feedback Forum
2008-12-08 13:50:10 [Katja van Hek] [reply] 
De optimale lambda is hier -0.301472301665314, om na te gaan met welke waarden van d en D je de tijdreeks stationair maakt moet je gebruik maken van VRM en ACF om dit te bevestigen. in dit geval wordt de tijdreeks stationair bij de waarden d=2 en D=0
2008-12-08 16:54:47 [Jonas Janssens] [reply] 
Uit de grafieken die je weergeeft kom je de meest optimale waarde voor Lambda niet te weten. Hiervoor moet je kijken naar de 'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)'-tabel, waar je de waarde voor Lambda kan aflezen: -0.3015. Deze heb je nodig om je tijdreeks stationair te maken.
2008-12-09 22:48:42 [Gert-Jan Geudens] [reply] 
Je bent de lambda vergeten te vermelden. De optimale lamda om de transformatie uit te voeren, is hier gelijk aan -0.3. We zullen yt tot de -0.3de macht zetten.
we krijgen dan nabla nabla12 yt^(-0.3) = et
2008-12-09 22:50:24 [Gert-Jan Geudens] [reply] 
Correctie: de tweede nabla kunnen we weglaten aangezien later zal blijken dat we hier niet seizonaal moeten differentiëren.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,4
107,1
110,7
117,1
118,7
126,5
127,5
134,6
131,8
135,9
142,7
141,7
153,4
145
137,7
148,3
152,2
169,4
168,6
161,1
174,1
179
190,6
190
181,6
174,8
180,5
196,8
193,8
197
216,3
221,4
217,9
229,7
227,4
204,2
196,6
198,8
207,5
190,7
201,6
210,5
223,5
223,8
231,2
244
234,7
250,2
265,7
287,6
283,3
295,4
312,3
333,8
347,7
383,2
407,1
413,6
362,7
321,9
239,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28303&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28303&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1124.97513.035066342196137.3
2164.11666666666717.372697144099652.9
3203.4518.981450275083254.9
4217.75833333333319.62491266145459.5
5334.52549.1788225856322147.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 124.975 & 13.0350663421961 & 37.3 \tabularnewline
2 & 164.116666666667 & 17.3726971440996 & 52.9 \tabularnewline
3 & 203.45 & 18.9814502750832 & 54.9 \tabularnewline
4 & 217.758333333333 & 19.624912661454 & 59.5 \tabularnewline
5 & 334.525 & 49.1788225856322 & 147.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28303&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]124.975[/C][C]13.0350663421961[/C][C]37.3[/C][/ROW]
[ROW][C]2[/C][C]164.116666666667[/C][C]17.3726971440996[/C][C]52.9[/C][/ROW]
[ROW][C]3[/C][C]203.45[/C][C]18.9814502750832[/C][C]54.9[/C][/ROW]
[ROW][C]4[/C][C]217.758333333333[/C][C]19.624912661454[/C][C]59.5[/C][/ROW]
[ROW][C]5[/C][C]334.525[/C][C]49.1788225856322[/C][C]147.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28303&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
1124.97513.035066342196137.3
2164.11666666666717.372697144099652.9
3203.4518.981450275083254.9
4217.75833333333319.62491266145459.5
5334.52549.1788225856322147.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-12.9683819042061
beta0.175182311420090
S.D.0.0319676420393318
T-STAT5.47998852103487
p-value0.0119501420959294

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -12.9683819042061 \tabularnewline
beta & 0.175182311420090 \tabularnewline
S.D. & 0.0319676420393318 \tabularnewline
T-STAT & 5.47998852103487 \tabularnewline
p-value & 0.0119501420959294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28303&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.9683819042061[/C][/ROW]
[ROW][C]beta[/C][C]0.175182311420090[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0319676420393318[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.47998852103487[/C][/ROW]
[ROW][C]p-value[/C][C]0.0119501420959294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28303&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-12.9683819042061
beta0.175182311420090
S.D.0.0319676420393318
T-STAT5.47998852103487
p-value0.0119501420959294






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.8345863273532
beta1.30147230166531
S.D.0.252170374226715
T-STAT5.16108327814598
p-value0.0141077911383081
Lambda-0.301472301665314

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.8345863273532 \tabularnewline
beta & 1.30147230166531 \tabularnewline
S.D. & 0.252170374226715 \tabularnewline
T-STAT & 5.16108327814598 \tabularnewline
p-value & 0.0141077911383081 \tabularnewline
Lambda & -0.301472301665314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28303&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.8345863273532[/C][/ROW]
[ROW][C]beta[/C][C]1.30147230166531[/C][/ROW]
[ROW][C]S.D.[/C][C]0.252170374226715[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.16108327814598[/C][/ROW]
[ROW][C]p-value[/C][C]0.0141077911383081[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.301472301665314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28303&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28303&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-3.8345863273532
beta1.30147230166531
S.D.0.252170374226715
T-STAT5.16108327814598
p-value0.0141077911383081
Lambda-0.301472301665314


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')