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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationTue, 21 Dec 2010 00:13:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292890337149pqswsgov504n.htm/, Retrieved Wed, 30 Apr 2025 18:01:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113177, Retrieved Wed, 30 Apr 2025 18:01:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact203

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:09:37] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [] [2010-12-19 15:37:21] [f3d662049ef6875ba0c96bb458434b66]
-   P       [(Partial) Autocorrelation Function] [Paper ACF Verkeer...] [2010-12-20 23:54:09] [abf4ff90b26c6b37be4a30063b404639]
- RMP           [Variance Reduction Matrix] [Paper VRM Verkeer...] [2010-12-21 00:13:28] [33ba4313a043c7c916d0d88da7cd101b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5124
4742
5434
5684
6332
6334
5636
5940
6195
6022
4535
4320
4872
4662
4663
5491
6018
6393
5610
5777
6094
6478
5216
5201
4784
4205
4681
4896
5752
6452
5995
5601
6119
6569
5798
5492
5018
4773
5502
5908
5902
6125
5419
5559
5962
6023
5346
5379
4859
5156
5010
5508
6426
6043
5499
5191
5790
5949
5219
4729

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'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=113177&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=113177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113177&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)354025.168361582Range2364Trim Var.261338.295248078
V(Y[t],d=1,D=0)290314.801870251Range2405Trim Var.195337.625544267
V(Y[t],d=2,D=0)539530.120992135Range2918Trim Var.397890.298642534
V(Y[t],d=3,D=0)1414658.30827068Range4614Trim Var.1017973.45254902
V(Y[t],d=0,D=1)171857.233599291Range1783Trim Var.102129.719512195
V(Y[t],d=1,D=1)190603.77613321Range1893Trim Var.120597.319512195
V(Y[t],d=2,D=1)475617.654589372Range2799Trim Var.314452.686538462
V(Y[t],d=3,D=1)1470509.29090909Range4746Trim Var.940101.956815115
V(Y[t],d=0,D=2)403605.844444444Range3019Trim Var.218545.458669355
V(Y[t],d=1,D=2)512370.322689076Range2977Trim Var.333206.866666667
V(Y[t],d=2,D=2)1317264.79946524Range4242Trim Var.947027.481609195
V(Y[t],d=3,D=2)4157848.49621212Range8062Trim Var.2822179.43349754

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 354025.168361582 & Range & 2364 & Trim Var. & 261338.295248078 \tabularnewline
V(Y[t],d=1,D=0) & 290314.801870251 & Range & 2405 & Trim Var. & 195337.625544267 \tabularnewline
V(Y[t],d=2,D=0) & 539530.120992135 & Range & 2918 & Trim Var. & 397890.298642534 \tabularnewline
V(Y[t],d=3,D=0) & 1414658.30827068 & Range & 4614 & Trim Var. & 1017973.45254902 \tabularnewline
V(Y[t],d=0,D=1) & 171857.233599291 & Range & 1783 & Trim Var. & 102129.719512195 \tabularnewline
V(Y[t],d=1,D=1) & 190603.77613321 & Range & 1893 & Trim Var. & 120597.319512195 \tabularnewline
V(Y[t],d=2,D=1) & 475617.654589372 & Range & 2799 & Trim Var. & 314452.686538462 \tabularnewline
V(Y[t],d=3,D=1) & 1470509.29090909 & Range & 4746 & Trim Var. & 940101.956815115 \tabularnewline
V(Y[t],d=0,D=2) & 403605.844444444 & Range & 3019 & Trim Var. & 218545.458669355 \tabularnewline
V(Y[t],d=1,D=2) & 512370.322689076 & Range & 2977 & Trim Var. & 333206.866666667 \tabularnewline
V(Y[t],d=2,D=2) & 1317264.79946524 & Range & 4242 & Trim Var. & 947027.481609195 \tabularnewline
V(Y[t],d=3,D=2) & 4157848.49621212 & Range & 8062 & Trim Var. & 2822179.43349754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113177&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]354025.168361582[/C][C]Range[/C][C]2364[/C][C]Trim Var.[/C][C]261338.295248078[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]290314.801870251[/C][C]Range[/C][C]2405[/C][C]Trim Var.[/C][C]195337.625544267[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]539530.120992135[/C][C]Range[/C][C]2918[/C][C]Trim Var.[/C][C]397890.298642534[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1414658.30827068[/C][C]Range[/C][C]4614[/C][C]Trim Var.[/C][C]1017973.45254902[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]171857.233599291[/C][C]Range[/C][C]1783[/C][C]Trim Var.[/C][C]102129.719512195[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]190603.77613321[/C][C]Range[/C][C]1893[/C][C]Trim Var.[/C][C]120597.319512195[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]475617.654589372[/C][C]Range[/C][C]2799[/C][C]Trim Var.[/C][C]314452.686538462[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1470509.29090909[/C][C]Range[/C][C]4746[/C][C]Trim Var.[/C][C]940101.956815115[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]403605.844444444[/C][C]Range[/C][C]3019[/C][C]Trim Var.[/C][C]218545.458669355[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]512370.322689076[/C][C]Range[/C][C]2977[/C][C]Trim Var.[/C][C]333206.866666667[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1317264.79946524[/C][C]Range[/C][C]4242[/C][C]Trim Var.[/C][C]947027.481609195[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4157848.49621212[/C][C]Range[/C][C]8062[/C][C]Trim Var.[/C][C]2822179.43349754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113177&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:

Variance Reduction Matrix
V(Y[t],d=0,D=0)354025.168361582Range2364Trim Var.261338.295248078
V(Y[t],d=1,D=0)290314.801870251Range2405Trim Var.195337.625544267
V(Y[t],d=2,D=0)539530.120992135Range2918Trim Var.397890.298642534
V(Y[t],d=3,D=0)1414658.30827068Range4614Trim Var.1017973.45254902
V(Y[t],d=0,D=1)171857.233599291Range1783Trim Var.102129.719512195
V(Y[t],d=1,D=1)190603.77613321Range1893Trim Var.120597.319512195
V(Y[t],d=2,D=1)475617.654589372Range2799Trim Var.314452.686538462
V(Y[t],d=3,D=1)1470509.29090909Range4746Trim Var.940101.956815115
V(Y[t],d=0,D=2)403605.844444444Range3019Trim Var.218545.458669355
V(Y[t],d=1,D=2)512370.322689076Range2977Trim Var.333206.866666667
V(Y[t],d=2,D=2)1317264.79946524Range4242Trim Var.947027.481609195
V(Y[t],d=3,D=2)4157848.49621212Range8062Trim Var.2822179.43349754


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)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()