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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

Mon, 20 Dec 2010 14:52:44 +0000

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/2010/Dec/20/t1292856652d6xl66wmy10c1ke.htm/, Retrieved Fri, 03 May 2024 23:59:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112980, Retrieved Fri, 03 May 2024 23:59:34 +0000

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No (this computation is public)

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Estimated Impact

112

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

-       [Variance Reduction Matrix] [] [2010-12-20 14:52:44] [40b262140b988d7b8204c4955f8b7651] [Current]

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Dataseries X:

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Boxplots

9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.0
9.0
8.9
8.8
8.7
8.5
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.0
7.0
6.8
6.8
6.7
6.8
6.7
6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7.0
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8.0
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8.0
8.0
8.0
8.0
7.9
7.9
7.8
7.8
8.0
7.8
7.4
7.2
7.0
7.0
7.2
7.2
7.2
7.0
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.0
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=112980&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=112980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112980&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.644453357100416	Range	3.2	Trim Var.	0.435886646629455
V(Y[t],d=1,D=0)	0.0184520123839009	Range	0.9	Trim Var.	0.0070241159734453
V(Y[t],d=2,D=0)	0.0189403973509934	Range	0.700000000000001	Trim Var.	0.00909236305477805
V(Y[t],d=3,D=0)	0.0441333333333333	Range	1.3	Trim Var.	0.0250945545682387
V(Y[t],d=0,D=1)	0.674768254919588	Range	3.4	Trim Var.	0.455655071304811
V(Y[t],d=1,D=1)	0.0363961499493415	Range	1	Trim Var.	0.0182258064516129
V(Y[t],d=2,D=1)	0.0381274409044194	Range	0.800000000000002	Trim Var.	0.0233383010432191
V(Y[t],d=3,D=1)	0.085070378479825	Range	1.5	Trim Var.	0.0512477052189877
V(Y[t],d=0,D=2)	0.826822301729278	Range	3.6	Trim Var.	0.590275862068965
V(Y[t],d=1,D=2)	0.107283187984496	Range	2	Trim Var.	0.0497854217854218
V(Y[t],d=2,D=2)	0.118818282480315	Range	1.5	Trim Var.	0.0765170670037928
V(Y[t],d=3,D=2)	0.265629296337958	Range	2.8	Trim Var.	0.146972972972973

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.644453357100416 & Range & 3.2 & Trim Var. & 0.435886646629455 \tabularnewline
V(Y[t],d=1,D=0) & 0.0184520123839009 & Range & 0.9 & Trim Var. & 0.0070241159734453 \tabularnewline
V(Y[t],d=2,D=0) & 0.0189403973509934 & Range & 0.700000000000001 & Trim Var. & 0.00909236305477805 \tabularnewline
V(Y[t],d=3,D=0) & 0.0441333333333333 & Range & 1.3 & Trim Var. & 0.0250945545682387 \tabularnewline
V(Y[t],d=0,D=1) & 0.674768254919588 & Range & 3.4 & Trim Var. & 0.455655071304811 \tabularnewline
V(Y[t],d=1,D=1) & 0.0363961499493415 & Range & 1 & Trim Var. & 0.0182258064516129 \tabularnewline
V(Y[t],d=2,D=1) & 0.0381274409044194 & Range & 0.800000000000002 & Trim Var. & 0.0233383010432191 \tabularnewline
V(Y[t],d=3,D=1) & 0.085070378479825 & Range & 1.5 & Trim Var. & 0.0512477052189877 \tabularnewline
V(Y[t],d=0,D=2) & 0.826822301729278 & Range & 3.6 & Trim Var. & 0.590275862068965 \tabularnewline
V(Y[t],d=1,D=2) & 0.107283187984496 & Range & 2 & Trim Var. & 0.0497854217854218 \tabularnewline
V(Y[t],d=2,D=2) & 0.118818282480315 & Range & 1.5 & Trim Var. & 0.0765170670037928 \tabularnewline
V(Y[t],d=3,D=2) & 0.265629296337958 & Range & 2.8 & Trim Var. & 0.146972972972973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112980&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.644453357100416[/C][C]Range[/C][C]3.2[/C][C]Trim Var.[/C][C]0.435886646629455[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0184520123839009[/C][C]Range[/C][C]0.9[/C][C]Trim Var.[/C][C]0.0070241159734453[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0189403973509934[/C][C]Range[/C][C]0.700000000000001[/C][C]Trim Var.[/C][C]0.00909236305477805[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0441333333333333[/C][C]Range[/C][C]1.3[/C][C]Trim Var.[/C][C]0.0250945545682387[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.674768254919588[/C][C]Range[/C][C]3.4[/C][C]Trim Var.[/C][C]0.455655071304811[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0363961499493415[/C][C]Range[/C][C]1[/C][C]Trim Var.[/C][C]0.0182258064516129[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0381274409044194[/C][C]Range[/C][C]0.800000000000002[/C][C]Trim Var.[/C][C]0.0233383010432191[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.085070378479825[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0512477052189877[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.826822301729278[/C][C]Range[/C][C]3.6[/C][C]Trim Var.[/C][C]0.590275862068965[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.107283187984496[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]0.0497854217854218[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.118818282480315[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0765170670037928[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.265629296337958[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.146972972972973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112980&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)	0.644453357100416	Range	3.2	Trim Var.	0.435886646629455
V(Y[t],d=1,D=0)	0.0184520123839009	Range	0.9	Trim Var.	0.0070241159734453
V(Y[t],d=2,D=0)	0.0189403973509934	Range	0.700000000000001	Trim Var.	0.00909236305477805
V(Y[t],d=3,D=0)	0.0441333333333333	Range	1.3	Trim Var.	0.0250945545682387
V(Y[t],d=0,D=1)	0.674768254919588	Range	3.4	Trim Var.	0.455655071304811
V(Y[t],d=1,D=1)	0.0363961499493415	Range	1	Trim Var.	0.0182258064516129
V(Y[t],d=2,D=1)	0.0381274409044194	Range	0.800000000000002	Trim Var.	0.0233383010432191
V(Y[t],d=3,D=1)	0.085070378479825	Range	1.5	Trim Var.	0.0512477052189877
V(Y[t],d=0,D=2)	0.826822301729278	Range	3.6	Trim Var.	0.590275862068965
V(Y[t],d=1,D=2)	0.107283187984496	Range	2	Trim Var.	0.0497854217854218
V(Y[t],d=2,D=2)	0.118818282480315	Range	1.5	Trim Var.	0.0765170670037928
V(Y[t],d=3,D=2)	0.265629296337958	Range	2.8	Trim Var.	0.146972972972973

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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()

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code