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Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Tue, 20 Dec 2011 10:27:08 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t13243948389ev5kr716mrlor7.htm/, Retrieved Mon, 06 May 2024 06:23:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157993, Retrieved Mon, 06 May 2024 06:23:24 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

136

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [(Partial) Autocorrelation Function] [] [2011-12-05 11:42:22] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMPD  [Variance Reduction Matrix] [Variance Reductio...] [2011-12-20 13:59:28] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMP     [Standard Deviation-Mean Plot] [] [2011-12-20 14:38:17] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM        [ARIMA Backward Selection] [] [2011-12-20 14:48:06] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM D        [(Partial) Autocorrelation Function] [] [2011-12-20 15:23:33] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM            [Spectral Analysis] [] [2011-12-20 15:26:09] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RM                [Variance Reduction Matrix] [] [2011-12-20 15:27:08] [3627de22d386f4cb93d383ef7c1ade7f] [Current]
- R                   [Variance Reduction Matrix] [VRM CV] [2011-12-20 15:27:35] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM                  [Standard Deviation-Mean Plot] [] [2011-12-20 15:29:15] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R                     [Standard Deviation-Mean Plot] [Standard Deviatio...] [2011-12-20 15:29:48] [aba4febe8a2e49e81bdc61a6c01f5c21] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157993&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157993&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157993&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Variance Reduction Matrix
V(Y[t],d=0,D=0)	82310.3850201845	Range	1568	Trim Var.	45743.0908084164
V(Y[t],d=1,D=0)	128477.015376984	Range	2872	Trim Var.	60277.0218833891
V(Y[t],d=2,D=0)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=3,D=0)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=0,D=1)	128477.015376984	Range	2872	Trim Var.	60277.0218833891
V(Y[t],d=1,D=1)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=2,D=1)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=3,D=1)	4507068.42952805	Range	15284	Trim Var.	2182705.08701559
V(Y[t],d=0,D=2)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=1,D=2)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=2,D=2)	4507068.42952805	Range	15284	Trim Var.	2182705.08701559
V(Y[t],d=3,D=2)	16095092.8335614	Range	29683	Trim Var.	8114355.04522113

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 82310.3850201845 & Range & 1568 & Trim Var. & 45743.0908084164 \tabularnewline
V(Y[t],d=1,D=0) & 128477.015376984 & Range & 2872 & Trim Var. & 60277.0218833891 \tabularnewline
V(Y[t],d=2,D=0) & 390330.869691284 & Range & 4587 & Trim Var. & 187514.886399562 \tabularnewline
V(Y[t],d=3,D=0) & 1297161.99764446 & Range & 9005 & Trim Var. & 633633.192509191 \tabularnewline
V(Y[t],d=0,D=1) & 128477.015376984 & Range & 2872 & Trim Var. & 60277.0218833891 \tabularnewline
V(Y[t],d=1,D=1) & 390330.869691284 & Range & 4587 & Trim Var. & 187514.886399562 \tabularnewline
V(Y[t],d=2,D=1) & 1297161.99764446 & Range & 9005 & Trim Var. & 633633.192509191 \tabularnewline
V(Y[t],d=3,D=1) & 4507068.42952805 & Range & 15284 & Trim Var. & 2182705.08701559 \tabularnewline
V(Y[t],d=0,D=2) & 390330.869691284 & Range & 4587 & Trim Var. & 187514.886399562 \tabularnewline
V(Y[t],d=1,D=2) & 1297161.99764446 & Range & 9005 & Trim Var. & 633633.192509191 \tabularnewline
V(Y[t],d=2,D=2) & 4507068.42952805 & Range & 15284 & Trim Var. & 2182705.08701559 \tabularnewline
V(Y[t],d=3,D=2) & 16095092.8335614 & Range & 29683 & Trim Var. & 8114355.04522113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157993&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]82310.3850201845[/C][C]Range[/C][C]1568[/C][C]Trim Var.[/C][C]45743.0908084164[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]128477.015376984[/C][C]Range[/C][C]2872[/C][C]Trim Var.[/C][C]60277.0218833891[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]390330.869691284[/C][C]Range[/C][C]4587[/C][C]Trim Var.[/C][C]187514.886399562[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1297161.99764446[/C][C]Range[/C][C]9005[/C][C]Trim Var.[/C][C]633633.192509191[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]128477.015376984[/C][C]Range[/C][C]2872[/C][C]Trim Var.[/C][C]60277.0218833891[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]390330.869691284[/C][C]Range[/C][C]4587[/C][C]Trim Var.[/C][C]187514.886399562[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1297161.99764446[/C][C]Range[/C][C]9005[/C][C]Trim Var.[/C][C]633633.192509191[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4507068.42952805[/C][C]Range[/C][C]15284[/C][C]Trim Var.[/C][C]2182705.08701559[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]390330.869691284[/C][C]Range[/C][C]4587[/C][C]Trim Var.[/C][C]187514.886399562[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1297161.99764446[/C][C]Range[/C][C]9005[/C][C]Trim Var.[/C][C]633633.192509191[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4507068.42952805[/C][C]Range[/C][C]15284[/C][C]Trim Var.[/C][C]2182705.08701559[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]16095092.8335614[/C][C]Range[/C][C]29683[/C][C]Trim Var.[/C][C]8114355.04522113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157993&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157993&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	82310.3850201845	Range	1568	Trim Var.	45743.0908084164
V(Y[t],d=1,D=0)	128477.015376984	Range	2872	Trim Var.	60277.0218833891
V(Y[t],d=2,D=0)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=3,D=0)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=0,D=1)	128477.015376984	Range	2872	Trim Var.	60277.0218833891
V(Y[t],d=1,D=1)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=2,D=1)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=3,D=1)	4507068.42952805	Range	15284	Trim Var.	2182705.08701559
V(Y[t],d=0,D=2)	390330.869691284	Range	4587	Trim Var.	187514.886399562
V(Y[t],d=1,D=2)	1297161.99764446	Range	9005	Trim Var.	633633.192509191
V(Y[t],d=2,D=2)	4507068.42952805	Range	15284	Trim Var.	2182705.08701559
V(Y[t],d=3,D=2)	16095092.8335614	Range	29683	Trim Var.	8114355.04522113

Figure 1

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Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 1 ;

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()

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Input Parameters & R Code