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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 computationWed, 22 Dec 2010 14:17:17 +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/22/t1293027492ejkmyiks6pku2fh.htm/, Retrieved Mon, 06 May 2024 09:51:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114240, Retrieved Mon, 06 May 2024 09:51:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD          [Variance Reduction Matrix] [] [2010-12-22 14:17:17] [5a59313293e5c9f616ad36f6edd018c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.769
9.321
9.939
9.336
10.195
9.464
10.010
10.213
9.563
9.890
9.305
9.391
9.928
8.686
9.843
9.627
10.074
9.503
10.119
10.000
9.313
9.866
9.172
9.241
9.659
8.904
9.755
9.080
9.435
8.971
10.063
9.793
9.454
9.759
8.820
9.403
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114240&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114240&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114240&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.263028810087719Range2.541Trim Var.0.163350332147743
V(Y[t],d=1,D=0)0.371533678163494Range2.491Trim Var.0.279013314285714
V(Y[t],d=2,D=0)1.22138691191947Range4.365Trim Var.0.944696792885829
V(Y[t],d=3,D=0)4.2748025514259Range8.326Trim Var.3.26242393417573
V(Y[t],d=0,D=1)0.0964175058806655Range1.432Trim Var.0.0617117654572381
V(Y[t],d=1,D=1)0.150008806935057Range1.737Trim Var.0.100983426940639
V(Y[t],d=2,D=1)0.421283723727793Range2.887Trim Var.0.280544758802817
V(Y[t],d=3,D=1)1.32394706944444Range5.371Trim Var.0.867719323541248
V(Y[t],d=0,D=2)0.202272956964006Range1.915Trim Var.0.133451271577381
V(Y[t],d=1,D=2)0.332658507847083Range2.774Trim Var.0.183615142857143
V(Y[t],d=2,D=2)0.83584584699793Range4.266Trim Var.0.50158972421999
V(Y[t],d=3,D=2)2.46716989428815Range7.011Trim Var.1.4804350874317

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.263028810087719 & Range & 2.541 & Trim Var. & 0.163350332147743 \tabularnewline
V(Y[t],d=1,D=0) & 0.371533678163494 & Range & 2.491 & Trim Var. & 0.279013314285714 \tabularnewline
V(Y[t],d=2,D=0) & 1.22138691191947 & Range & 4.365 & Trim Var. & 0.944696792885829 \tabularnewline
V(Y[t],d=3,D=0) & 4.2748025514259 & Range & 8.326 & Trim Var. & 3.26242393417573 \tabularnewline
V(Y[t],d=0,D=1) & 0.0964175058806655 & Range & 1.432 & Trim Var. & 0.0617117654572381 \tabularnewline
V(Y[t],d=1,D=1) & 0.150008806935057 & Range & 1.737 & Trim Var. & 0.100983426940639 \tabularnewline
V(Y[t],d=2,D=1) & 0.421283723727793 & Range & 2.887 & Trim Var. & 0.280544758802817 \tabularnewline
V(Y[t],d=3,D=1) & 1.32394706944444 & Range & 5.371 & Trim Var. & 0.867719323541248 \tabularnewline
V(Y[t],d=0,D=2) & 0.202272956964006 & Range & 1.915 & Trim Var. & 0.133451271577381 \tabularnewline
V(Y[t],d=1,D=2) & 0.332658507847083 & Range & 2.774 & Trim Var. & 0.183615142857143 \tabularnewline
V(Y[t],d=2,D=2) & 0.83584584699793 & Range & 4.266 & Trim Var. & 0.50158972421999 \tabularnewline
V(Y[t],d=3,D=2) & 2.46716989428815 & Range & 7.011 & Trim Var. & 1.4804350874317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114240&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.263028810087719[/C][C]Range[/C][C]2.541[/C][C]Trim Var.[/C][C]0.163350332147743[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.371533678163494[/C][C]Range[/C][C]2.491[/C][C]Trim Var.[/C][C]0.279013314285714[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.22138691191947[/C][C]Range[/C][C]4.365[/C][C]Trim Var.[/C][C]0.944696792885829[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4.2748025514259[/C][C]Range[/C][C]8.326[/C][C]Trim Var.[/C][C]3.26242393417573[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.0964175058806655[/C][C]Range[/C][C]1.432[/C][C]Trim Var.[/C][C]0.0617117654572381[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.150008806935057[/C][C]Range[/C][C]1.737[/C][C]Trim Var.[/C][C]0.100983426940639[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.421283723727793[/C][C]Range[/C][C]2.887[/C][C]Trim Var.[/C][C]0.280544758802817[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.32394706944444[/C][C]Range[/C][C]5.371[/C][C]Trim Var.[/C][C]0.867719323541248[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.202272956964006[/C][C]Range[/C][C]1.915[/C][C]Trim Var.[/C][C]0.133451271577381[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.332658507847083[/C][C]Range[/C][C]2.774[/C][C]Trim Var.[/C][C]0.183615142857143[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.83584584699793[/C][C]Range[/C][C]4.266[/C][C]Trim Var.[/C][C]0.50158972421999[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2.46716989428815[/C][C]Range[/C][C]7.011[/C][C]Trim Var.[/C][C]1.4804350874317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114240&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114240&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)0.263028810087719Range2.541Trim Var.0.163350332147743
V(Y[t],d=1,D=0)0.371533678163494Range2.491Trim Var.0.279013314285714
V(Y[t],d=2,D=0)1.22138691191947Range4.365Trim Var.0.944696792885829
V(Y[t],d=3,D=0)4.2748025514259Range8.326Trim Var.3.26242393417573
V(Y[t],d=0,D=1)0.0964175058806655Range1.432Trim Var.0.0617117654572381
V(Y[t],d=1,D=1)0.150008806935057Range1.737Trim Var.0.100983426940639
V(Y[t],d=2,D=1)0.421283723727793Range2.887Trim Var.0.280544758802817
V(Y[t],d=3,D=1)1.32394706944444Range5.371Trim Var.0.867719323541248
V(Y[t],d=0,D=2)0.202272956964006Range1.915Trim Var.0.133451271577381
V(Y[t],d=1,D=2)0.332658507847083Range2.774Trim Var.0.183615142857143
V(Y[t],d=2,D=2)0.83584584699793Range4.266Trim Var.0.50158972421999
V(Y[t],d=3,D=2)2.46716989428815Range7.011Trim Var.1.4804350874317


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()