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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 computationMon, 01 Dec 2008 13:56:57 -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/01/t12281650535nx6yvbaqliuz29.htm/, Retrieved Sun, 05 May 2024 17:24:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27397, Retrieved Sun, 05 May 2024 17:24:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

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] [lambda werkloosheid] [2008-12-01 20:56:57] [357d3e8a0ea9b107f483347f947dfe8f] [Current]
-    D    [Standard Deviation-Mean Plot] [lambda inflatie] [2008-12-01 20:59:22] [2a0ad3a9bcadca2da0acb91636601c6c]
Feedback Forum
2008-12-04 16:09:18 [Matthieu Blondeau] [reply] 
De student had geen SMP moeten gebruiken maar een analyse doen met ACF, VRM en spectral.

ACF
Men moet de 'd' en 'D' veranderen om zo de reeks stationair te maken.
Naarmate we d en D aanpassen van 0 naar 1 kunnen we zien dat de autocorrelatie zo goed als verdwijnt. De lange termijntrend kan verwijderd worden door d op 1 te zetten. De Seizoenaliteit kunnen we verwijderen door D op 1 te zetten.

VRM
Met de VRM moet men de kleinste waarde kiezen om op deze manier te weten welke waarde we aan 'd' en 'D' moeten toekennen om zo de reeks stationair te maken.
Om dit na te gaan moet men in de tabel de kleinste variantie zoeken. De kleinste waarde bedraagt 1139.35152171772, deze komt twee keer voor. Hieruit kunnen we concluderen dat we ofwel één keer gewoon moeten differentiëren (d=1) ofwel één keer seizoenaal moeten differentiëren (D=1) om de variantie in de tijdreeks zo klein mogelijk te maken.

Spectral
Men moet de 'd' en 'D' aanpassen om zo de trend en de seizoenaliteit er uit te halen en zo de lijn tussen de stippellijnen te krijgen.
Naarmate we d en D aanpassen van 0 naar 1 kunnen we in het Raw Periodogram zien dat de dalende lange termijntrendlijn en de seizoenaliteit verdwijnt. De lange termijntrend kan verwijderd worden d op 1 te zetten. De seizoenaliteit kunnen we verwijderen door D op 1 te zetten.
Ook in het Cumulative Periodogram zien we dat de curve, door aanpassing van d en D van 0 naar 1, steeds beter naar het betrouwbaarheidsinterval komt te liggen. De geschikte graad van seasonal en non-seasonal differencing die het gemiddelde stationair maken bedraagt dus in beide gevallen 1.
  2008-12-04 16:10:49 [Matthieu Blondeau] [reply] 
Deze comment is niet helemaal correct. Deze was voor een andere student bedoeld.
ACF
Men moet de 'd' en 'D' veranderen om zo de reeks stationair te maken.

VRM
Met de VRM moet men de kleinste waarde kiezen om op deze manier te weten welke waarde we aan 'd' en 'D' moeten toekennen om zo de reeks stationair te maken.

Spectral
Men moet de 'd' en 'D' aanpassen om zo de trend en de seizoenaliteit er uit te halen en zo de lijn tussen de stippellijnen te krijgen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27397&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27397&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1534594.66666666730815.993204041278857
2573223.2529138.899421173675951
3596256.83333333321872.512296293661428
4591583.41666666720492.339275749560067
5536043.522048.403836270665929

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 534594.666666667 & 30815.9932040412 & 78857 \tabularnewline
2 & 573223.25 & 29138.8994211736 & 75951 \tabularnewline
3 & 596256.833333333 & 21872.5122962936 & 61428 \tabularnewline
4 & 591583.416666667 & 20492.3392757495 & 60067 \tabularnewline
5 & 536043.5 & 22048.4038362706 & 65929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27397&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]534594.666666667[/C][C]30815.9932040412[/C][C]78857[/C][/ROW]
[ROW][C]2[/C][C]573223.25[/C][C]29138.8994211736[/C][C]75951[/C][/ROW]
[ROW][C]3[/C][C]596256.833333333[/C][C]21872.5122962936[/C][C]61428[/C][/ROW]
[ROW][C]4[/C][C]591583.416666667[/C][C]20492.3392757495[/C][C]60067[/C][/ROW]
[ROW][C]5[/C][C]536043.5[/C][C]22048.4038362706[/C][C]65929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27397&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
1534594.66666666730815.993204041278857
2573223.2529138.899421173675951
3596256.83333333321872.512296293661428
4591583.41666666720492.339275749560067
5536043.522048.403836270665929






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha69154.8959199306
beta-0.0781884384829114
S.D.0.0805674296448632
T-STAT-0.970472048414126
p-value0.403393059536814

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 69154.8959199306 \tabularnewline
beta & -0.0781884384829114 \tabularnewline
S.D. & 0.0805674296448632 \tabularnewline
T-STAT & -0.970472048414126 \tabularnewline
p-value & 0.403393059536814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27397&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]69154.8959199306[/C][/ROW]
[ROW][C]beta[/C][C]-0.0781884384829114[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0805674296448632[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.970472048414126[/C][/ROW]
[ROW][C]p-value[/C][C]0.403393059536814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27397&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)
alpha69154.8959199306
beta-0.0781884384829114
S.D.0.0805674296448632
T-STAT-0.970472048414126
p-value0.403393059536814






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha32.8552753262795
beta-1.71735253475433
S.D.1.78879432478498
T-STAT-0.960061484408363
p-value0.407848570685357
Lambda2.71735253475433

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 32.8552753262795 \tabularnewline
beta & -1.71735253475433 \tabularnewline
S.D. & 1.78879432478498 \tabularnewline
T-STAT & -0.960061484408363 \tabularnewline
p-value & 0.407848570685357 \tabularnewline
Lambda & 2.71735253475433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27397&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]32.8552753262795[/C][/ROW]
[ROW][C]beta[/C][C]-1.71735253475433[/C][/ROW]
[ROW][C]S.D.[/C][C]1.78879432478498[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.960061484408363[/C][/ROW]
[ROW][C]p-value[/C][C]0.407848570685357[/C][/ROW]
[ROW][C]Lambda[/C][C]2.71735253475433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27397&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)
alpha32.8552753262795
beta-1.71735253475433
S.D.1.78879432478498
T-STAT-0.960061484408363
p-value0.407848570685357
Lambda2.71735253475433


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')