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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 computationFri, 16 Dec 2011 05:18:42 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/16/t1324031065sgohnbtb8hu8tsc.htm/, Retrieved Sun, 05 May 2024 18:44:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155782, Retrieved Sun, 05 May 2024 18:44:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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   [Spectral Analysis] [Unemployment] [2010-11-29 09:21:38] [b98453cac15ba1066b407e146608df68]
-    D    [Spectral Analysis] [Workshop 9, Cumul...] [2010-12-05 17:58:39] [3635fb7041b1998c5a1332cf9de22bce]
-    D      [Spectral Analysis] [Paper CP] [2010-12-19 15:14:56] [3635fb7041b1998c5a1332cf9de22bce]
-    D        [Spectral Analysis] [Paper CP 2] [2010-12-19 21:32:42] [3635fb7041b1998c5a1332cf9de22bce]
- RMPD            [Variance Reduction Matrix] [Variance Reductio...] [2011-12-16 10:18:42] [274a40ad31da88f12aea425a159a1f93] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9911.00
8915.00
9452.00
9112.00
8472.00
8230.00
8384.00
8625.00
8221.00
8649.00
8625.00
10443.00
10357.00
8586.00
8892.00
8329.00
8101.00
7922.00
8120.00
7838.00
7735.00
8406.00
8209.00
9451.00
10041.00
9411.00
10405.00
8467.00
8464.00
8102.00
7627.00
7513.00
7510.00
8291.00
8064.00
9383.00
9706.00
8579.00
9474.00
8318.00
8213.00
8059.00
9111.00
7708.00
7680.00
8014.00
8007.00
8718.00
9486.00
9113.00
9025.00
8476.00
7952.00
7759.00
7835.00
7600.00
7651.00
8319.00
8812.00
8630.00

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'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155782&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155782&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'AstonUniversity' @ aston.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)570063.371751412Range2933Trim Var.383078.893081761
V(Y[t],d=1,D=0)500085.691408533Range3756Trim Var.261134.113207547
V(Y[t],d=2,D=0)1234338.98124622Range5009Trim Var.770534.34841629
V(Y[t],d=3,D=0)3969511.87593985Range9423Trim Var.2367739.53647059
V(Y[t],d=0,D=1)300168.1875Range2789Trim Var.125295.795586527
V(Y[t],d=1,D=1)385666.279370953Range2902Trim Var.205442.437804878
V(Y[t],d=2,D=1)962542.695652174Range4960Trim Var.471615.938461538
V(Y[t],d=3,D=1)3005794.22525253Range8215Trim Var.1488871.94062078
V(Y[t],d=0,D=2)972000.057142857Range4833Trim Var.381330.931451613
V(Y[t],d=1,D=2)1189289.72605042Range4960Trim Var.688010.855913979
V(Y[t],d=2,D=2)2795162.20053476Range8617Trim Var.1346428.18850575
V(Y[t],d=3,D=2)8766004.77272727Range14529Trim Var.4291607.43596059

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 570063.371751412 & Range & 2933 & Trim Var. & 383078.893081761 \tabularnewline
V(Y[t],d=1,D=0) & 500085.691408533 & Range & 3756 & Trim Var. & 261134.113207547 \tabularnewline
V(Y[t],d=2,D=0) & 1234338.98124622 & Range & 5009 & Trim Var. & 770534.34841629 \tabularnewline
V(Y[t],d=3,D=0) & 3969511.87593985 & Range & 9423 & Trim Var. & 2367739.53647059 \tabularnewline
V(Y[t],d=0,D=1) & 300168.1875 & Range & 2789 & Trim Var. & 125295.795586527 \tabularnewline
V(Y[t],d=1,D=1) & 385666.279370953 & Range & 2902 & Trim Var. & 205442.437804878 \tabularnewline
V(Y[t],d=2,D=1) & 962542.695652174 & Range & 4960 & Trim Var. & 471615.938461538 \tabularnewline
V(Y[t],d=3,D=1) & 3005794.22525253 & Range & 8215 & Trim Var. & 1488871.94062078 \tabularnewline
V(Y[t],d=0,D=2) & 972000.057142857 & Range & 4833 & Trim Var. & 381330.931451613 \tabularnewline
V(Y[t],d=1,D=2) & 1189289.72605042 & Range & 4960 & Trim Var. & 688010.855913979 \tabularnewline
V(Y[t],d=2,D=2) & 2795162.20053476 & Range & 8617 & Trim Var. & 1346428.18850575 \tabularnewline
V(Y[t],d=3,D=2) & 8766004.77272727 & Range & 14529 & Trim Var. & 4291607.43596059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155782&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]570063.371751412[/C][C]Range[/C][C]2933[/C][C]Trim Var.[/C][C]383078.893081761[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]500085.691408533[/C][C]Range[/C][C]3756[/C][C]Trim Var.[/C][C]261134.113207547[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1234338.98124622[/C][C]Range[/C][C]5009[/C][C]Trim Var.[/C][C]770534.34841629[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3969511.87593985[/C][C]Range[/C][C]9423[/C][C]Trim Var.[/C][C]2367739.53647059[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]300168.1875[/C][C]Range[/C][C]2789[/C][C]Trim Var.[/C][C]125295.795586527[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]385666.279370953[/C][C]Range[/C][C]2902[/C][C]Trim Var.[/C][C]205442.437804878[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]962542.695652174[/C][C]Range[/C][C]4960[/C][C]Trim Var.[/C][C]471615.938461538[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3005794.22525253[/C][C]Range[/C][C]8215[/C][C]Trim Var.[/C][C]1488871.94062078[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]972000.057142857[/C][C]Range[/C][C]4833[/C][C]Trim Var.[/C][C]381330.931451613[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1189289.72605042[/C][C]Range[/C][C]4960[/C][C]Trim Var.[/C][C]688010.855913979[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2795162.20053476[/C][C]Range[/C][C]8617[/C][C]Trim Var.[/C][C]1346428.18850575[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]8766004.77272727[/C][C]Range[/C][C]14529[/C][C]Trim Var.[/C][C]4291607.43596059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155782&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)570063.371751412Range2933Trim Var.383078.893081761
V(Y[t],d=1,D=0)500085.691408533Range3756Trim Var.261134.113207547
V(Y[t],d=2,D=0)1234338.98124622Range5009Trim Var.770534.34841629
V(Y[t],d=3,D=0)3969511.87593985Range9423Trim Var.2367739.53647059
V(Y[t],d=0,D=1)300168.1875Range2789Trim Var.125295.795586527
V(Y[t],d=1,D=1)385666.279370953Range2902Trim Var.205442.437804878
V(Y[t],d=2,D=1)962542.695652174Range4960Trim Var.471615.938461538
V(Y[t],d=3,D=1)3005794.22525253Range8215Trim Var.1488871.94062078
V(Y[t],d=0,D=2)972000.057142857Range4833Trim Var.381330.931451613
V(Y[t],d=1,D=2)1189289.72605042Range4960Trim Var.688010.855913979
V(Y[t],d=2,D=2)2795162.20053476Range8617Trim Var.1346428.18850575
V(Y[t],d=3,D=2)8766004.77272727Range14529Trim Var.4291607.43596059


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()