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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 computationThu, 16 Dec 2010 20:01:05 +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/16/t1292529616f8hunxmjpc0fvzz.htm/, Retrieved Fri, 03 May 2024 04:58:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111247, Retrieved Fri, 03 May 2024 04:58:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

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] [] [2010-12-16 20:01:05] [40b262140b988d7b8204c4955f8b7651] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-2.0
2.6
0.2
0.1
-0.1
0.1
-1.6
2.3
-0.3
0.0
0.1
0.4
-1.9
2.4
0.0
0.4
0.1
0.2
-1.3
2.1
-0.1
0.3
0.3
0.2
-1.9
2.7
0.0
-0.2
0.2
0.1
-1.5
2.1
-0.3
-0.2
0.2
0.3
-2.0
2.6
0.0
0.5
-0.1
0.2
-1.6
2.1
-0.2
0.0
0.2
0.2
-2.2
2.7
-0.3
0.4
-0.1
0.0
-1.6
2.2
-0.3
0.0
0.1
0.1
-1.9
2.5
0.1
-0.1
0.3
0.1
-1.9
2.5
-0.3
0.2
0.2
0.1
-2.4
3.1
-0.3
0.2
0.1
0.2
-1.8
2.4
-0.4
0.0
0.0
0.2
-2.4
3.2
0.0
0.1
0.1
0.1
-1.8
2.5
-0.6
0.0
0.0
0.4
-2.5
3.1
0.2
-0.3
0.3
0.4
-1.8
2.6
-0.3
0.3
0.0
0.4
-2.9
3.6
-0.1
0.3
0.0
0.3
-2.1
2.6
-0.2
0.0
-0.2
0.3
-3.1
3.4
-0.1
0.1
0.3
0.1
-2.5
3.1
-0.1
0.1
0.0

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111247&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111247&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.96571697005285Range6.7Trim Var.1.14764017991005
V(Y[t],d=1,D=0)6.15107930828861Range10.2Trim Var.4.16032608695652
V(Y[t],d=2,D=0)20.8393653100775Range20.1Trim Var.13.8309687261632
V(Y[t],d=3,D=0)73.7462936761811Range34.3Trim Var.52.6575725818972
V(Y[t],d=0,D=1)0.058810710724968Range1.3Trim Var.0.0306758775205377
V(Y[t],d=1,D=1)0.154785600463567Range2.1Trim Var.0.0732851008215086
V(Y[t],d=2,D=1)0.520333038608901Range3.9Trim Var.0.253098394324122
V(Y[t],d=3,D=1)1.8532143928036Range7.5Trim Var.0.919319454817028
V(Y[t],d=0,D=2)0.171232586845354Range2.2Trim Var.0.0931514527568062
V(Y[t],d=1,D=2)0.454548966756514Range3.3Trim Var.0.227495222169135
V(Y[t],d=2,D=2)1.55246703296703Range6.4Trim Var.0.813964469378214
V(Y[t],d=3,D=2)5.581821321882Range12.6Trim Var.2.83182513139035

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.96571697005285 & Range & 6.7 & Trim Var. & 1.14764017991005 \tabularnewline
V(Y[t],d=1,D=0) & 6.15107930828861 & Range & 10.2 & Trim Var. & 4.16032608695652 \tabularnewline
V(Y[t],d=2,D=0) & 20.8393653100775 & Range & 20.1 & Trim Var. & 13.8309687261632 \tabularnewline
V(Y[t],d=3,D=0) & 73.7462936761811 & Range & 34.3 & Trim Var. & 52.6575725818972 \tabularnewline
V(Y[t],d=0,D=1) & 0.058810710724968 & Range & 1.3 & Trim Var. & 0.0306758775205377 \tabularnewline
V(Y[t],d=1,D=1) & 0.154785600463567 & Range & 2.1 & Trim Var. & 0.0732851008215086 \tabularnewline
V(Y[t],d=2,D=1) & 0.520333038608901 & Range & 3.9 & Trim Var. & 0.253098394324122 \tabularnewline
V(Y[t],d=3,D=1) & 1.8532143928036 & Range & 7.5 & Trim Var. & 0.919319454817028 \tabularnewline
V(Y[t],d=0,D=2) & 0.171232586845354 & Range & 2.2 & Trim Var. & 0.0931514527568062 \tabularnewline
V(Y[t],d=1,D=2) & 0.454548966756514 & Range & 3.3 & Trim Var. & 0.227495222169135 \tabularnewline
V(Y[t],d=2,D=2) & 1.55246703296703 & Range & 6.4 & Trim Var. & 0.813964469378214 \tabularnewline
V(Y[t],d=3,D=2) & 5.581821321882 & Range & 12.6 & Trim Var. & 2.83182513139035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111247&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.96571697005285[/C][C]Range[/C][C]6.7[/C][C]Trim Var.[/C][C]1.14764017991005[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]6.15107930828861[/C][C]Range[/C][C]10.2[/C][C]Trim Var.[/C][C]4.16032608695652[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]20.8393653100775[/C][C]Range[/C][C]20.1[/C][C]Trim Var.[/C][C]13.8309687261632[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]73.7462936761811[/C][C]Range[/C][C]34.3[/C][C]Trim Var.[/C][C]52.6575725818972[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.058810710724968[/C][C]Range[/C][C]1.3[/C][C]Trim Var.[/C][C]0.0306758775205377[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.154785600463567[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.0732851008215086[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.520333038608901[/C][C]Range[/C][C]3.9[/C][C]Trim Var.[/C][C]0.253098394324122[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.8532143928036[/C][C]Range[/C][C]7.5[/C][C]Trim Var.[/C][C]0.919319454817028[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.171232586845354[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.0931514527568062[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.454548966756514[/C][C]Range[/C][C]3.3[/C][C]Trim Var.[/C][C]0.227495222169135[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1.55246703296703[/C][C]Range[/C][C]6.4[/C][C]Trim Var.[/C][C]0.813964469378214[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]5.581821321882[/C][C]Range[/C][C]12.6[/C][C]Trim Var.[/C][C]2.83182513139035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111247&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)1.96571697005285Range6.7Trim Var.1.14764017991005
V(Y[t],d=1,D=0)6.15107930828861Range10.2Trim Var.4.16032608695652
V(Y[t],d=2,D=0)20.8393653100775Range20.1Trim Var.13.8309687261632
V(Y[t],d=3,D=0)73.7462936761811Range34.3Trim Var.52.6575725818972
V(Y[t],d=0,D=1)0.058810710724968Range1.3Trim Var.0.0306758775205377
V(Y[t],d=1,D=1)0.154785600463567Range2.1Trim Var.0.0732851008215086
V(Y[t],d=2,D=1)0.520333038608901Range3.9Trim Var.0.253098394324122
V(Y[t],d=3,D=1)1.8532143928036Range7.5Trim Var.0.919319454817028
V(Y[t],d=0,D=2)0.171232586845354Range2.2Trim Var.0.0931514527568062
V(Y[t],d=1,D=2)0.454548966756514Range3.3Trim Var.0.227495222169135
V(Y[t],d=2,D=2)1.55246703296703Range6.4Trim Var.0.813964469378214
V(Y[t],d=3,D=2)5.581821321882Range12.6Trim Var.2.83182513139035


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()