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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 computationMon, 27 Dec 2010 09:44:58 +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/27/t1293443462g4j8y1wk116p6fs.htm/, Retrieved Mon, 06 May 2024 11:09:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115869, Retrieved Mon, 06 May 2024 11:09:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [] [2010-12-27 09:44:58] [c984196f1244e05baf3e7c2e52d47a33] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 10 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115869&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]10 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115869&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 time10 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.20647540983607Range7.8Trim Var.0.297728592162554
V(Y[t],d=1,D=0)1.62355649717514Range13.4Trim Var.0.0621383647798742
V(Y[t],d=2,D=0)5.20998831092928Range21.4Trim Var.0.0848981900452488
V(Y[t],d=3,D=0)18.0478917120387Range42Trim Var.0.185230015082956
V(Y[t],d=0,D=1)2.61208333333333Range13.8Trim Var.0.492015503875969
V(Y[t],d=1,D=1)4.06722960992908Range13.8Trim Var.0.0688902439024391
V(Y[t],d=2,D=1)12.9720999074931Range27.3Trim Var.0.0859756097560976
V(Y[t],d=3,D=1)44.6977632850242Range42.3Trim Var.3.01583974358975
V(Y[t],d=0,D=2)7.16803303303303Range19.4Trim Var.1.08564393939394
V(Y[t],d=1,D=2)13.6618730158730Range27.3Trim Var.0.369677419354839
V(Y[t],d=2,D=2)44.0429915966387Range42.3Trim Var.8.27169892473118
V(Y[t],d=3,D=2)152.900436720143Range84.3Trim Var.20.1689195402299

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.20647540983607 & Range & 7.8 & Trim Var. & 0.297728592162554 \tabularnewline
V(Y[t],d=1,D=0) & 1.62355649717514 & Range & 13.4 & Trim Var. & 0.0621383647798742 \tabularnewline
V(Y[t],d=2,D=0) & 5.20998831092928 & Range & 21.4 & Trim Var. & 0.0848981900452488 \tabularnewline
V(Y[t],d=3,D=0) & 18.0478917120387 & Range & 42 & Trim Var. & 0.185230015082956 \tabularnewline
V(Y[t],d=0,D=1) & 2.61208333333333 & Range & 13.8 & Trim Var. & 0.492015503875969 \tabularnewline
V(Y[t],d=1,D=1) & 4.06722960992908 & Range & 13.8 & Trim Var. & 0.0688902439024391 \tabularnewline
V(Y[t],d=2,D=1) & 12.9720999074931 & Range & 27.3 & Trim Var. & 0.0859756097560976 \tabularnewline
V(Y[t],d=3,D=1) & 44.6977632850242 & Range & 42.3 & Trim Var. & 3.01583974358975 \tabularnewline
V(Y[t],d=0,D=2) & 7.16803303303303 & Range & 19.4 & Trim Var. & 1.08564393939394 \tabularnewline
V(Y[t],d=1,D=2) & 13.6618730158730 & Range & 27.3 & Trim Var. & 0.369677419354839 \tabularnewline
V(Y[t],d=2,D=2) & 44.0429915966387 & Range & 42.3 & Trim Var. & 8.27169892473118 \tabularnewline
V(Y[t],d=3,D=2) & 152.900436720143 & Range & 84.3 & Trim Var. & 20.1689195402299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115869&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.20647540983607[/C][C]Range[/C][C]7.8[/C][C]Trim Var.[/C][C]0.297728592162554[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.62355649717514[/C][C]Range[/C][C]13.4[/C][C]Trim Var.[/C][C]0.0621383647798742[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]5.20998831092928[/C][C]Range[/C][C]21.4[/C][C]Trim Var.[/C][C]0.0848981900452488[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]18.0478917120387[/C][C]Range[/C][C]42[/C][C]Trim Var.[/C][C]0.185230015082956[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2.61208333333333[/C][C]Range[/C][C]13.8[/C][C]Trim Var.[/C][C]0.492015503875969[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]4.06722960992908[/C][C]Range[/C][C]13.8[/C][C]Trim Var.[/C][C]0.0688902439024391[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]12.9720999074931[/C][C]Range[/C][C]27.3[/C][C]Trim Var.[/C][C]0.0859756097560976[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]44.6977632850242[/C][C]Range[/C][C]42.3[/C][C]Trim Var.[/C][C]3.01583974358975[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]7.16803303303303[/C][C]Range[/C][C]19.4[/C][C]Trim Var.[/C][C]1.08564393939394[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]13.6618730158730[/C][C]Range[/C][C]27.3[/C][C]Trim Var.[/C][C]0.369677419354839[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]44.0429915966387[/C][C]Range[/C][C]42.3[/C][C]Trim Var.[/C][C]8.27169892473118[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]152.900436720143[/C][C]Range[/C][C]84.3[/C][C]Trim Var.[/C][C]20.1689195402299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115869&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)1.20647540983607Range7.8Trim Var.0.297728592162554
V(Y[t],d=1,D=0)1.62355649717514Range13.4Trim Var.0.0621383647798742
V(Y[t],d=2,D=0)5.20998831092928Range21.4Trim Var.0.0848981900452488
V(Y[t],d=3,D=0)18.0478917120387Range42Trim Var.0.185230015082956
V(Y[t],d=0,D=1)2.61208333333333Range13.8Trim Var.0.492015503875969
V(Y[t],d=1,D=1)4.06722960992908Range13.8Trim Var.0.0688902439024391
V(Y[t],d=2,D=1)12.9720999074931Range27.3Trim Var.0.0859756097560976
V(Y[t],d=3,D=1)44.6977632850242Range42.3Trim Var.3.01583974358975
V(Y[t],d=0,D=2)7.16803303303303Range19.4Trim Var.1.08564393939394
V(Y[t],d=1,D=2)13.6618730158730Range27.3Trim Var.0.369677419354839
V(Y[t],d=2,D=2)44.0429915966387Range42.3Trim Var.8.27169892473118
V(Y[t],d=3,D=2)152.900436720143Range84.3Trim Var.20.1689195402299


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()