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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 computationWed, 15 Dec 2010 14:44:13 +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/15/t1292425132z71c1dqmb1ymobt.htm/, Retrieved Fri, 03 May 2024 05:30:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110441, Retrieved Fri, 03 May 2024 05:30:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

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] [] [2010-12-15 14:44:13] [b7dd4adfab743bef2d672ff51f950617] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
186448
190530
194207
190855
200779
204428
207617
212071
214239
215883
223484
221529
225247
226699
231406
232324
237192
236727
240698
240688
245283
243556
247826
245798
250479
249216
251896
247616
249994
246552
248771
247551
249745
245742
249019
245841
248771
244723
246878
246014
248496
244351
248016
246509
249426
247840
251035
250161
254278
250801
253985
249174
251287
247947
249992
243805
255812
250417
253033
248705
253950
251484
251093
245996
252721
248019
250464
245571
252690
250183
253639
254436
265280
268705
270643
271480

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'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=110441&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=110441&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110441&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)331693227.74386Range85032Trim Var.167625378.021949
V(Y[t],d=1,D=0)15762602.8605405Range18194Trim Var.10031005.7987336
V(Y[t],d=2,D=0)48602879.2789707Range35596Trim Var.32888697.425641
V(Y[t],d=3,D=0)185069455.446728Range62022Trim Var.133361803.222115
V(Y[t],d=0,D=1)39855075.5179969Range26585Trim Var.27531117.7529762
V(Y[t],d=1,D=1)8143331.54044266Range17650Trim Var.2923282.50435228
V(Y[t],d=2,D=1)20312000.5923395Range26832Trim Var.7711714.70121629
V(Y[t],d=3,D=1)66536108.5029838Range45169Trim Var.25316890.3191257
V(Y[t],d=0,D=2)28950522.8996927Range28116Trim Var.14920667.5581921
V(Y[t],d=1,D=2)21432120.1610131Range28554Trim Var.8022593.25774401
V(Y[t],d=2,D=2)59131806.5081585Range43412Trim Var.22540406.4718693
V(Y[t],d=3,D=2)196578533.902885Range73650Trim Var.81202828.8258145

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 331693227.74386 & Range & 85032 & Trim Var. & 167625378.021949 \tabularnewline
V(Y[t],d=1,D=0) & 15762602.8605405 & Range & 18194 & Trim Var. & 10031005.7987336 \tabularnewline
V(Y[t],d=2,D=0) & 48602879.2789707 & Range & 35596 & Trim Var. & 32888697.425641 \tabularnewline
V(Y[t],d=3,D=0) & 185069455.446728 & Range & 62022 & Trim Var. & 133361803.222115 \tabularnewline
V(Y[t],d=0,D=1) & 39855075.5179969 & Range & 26585 & Trim Var. & 27531117.7529762 \tabularnewline
V(Y[t],d=1,D=1) & 8143331.54044266 & Range & 17650 & Trim Var. & 2923282.50435228 \tabularnewline
V(Y[t],d=2,D=1) & 20312000.5923395 & Range & 26832 & Trim Var. & 7711714.70121629 \tabularnewline
V(Y[t],d=3,D=1) & 66536108.5029838 & Range & 45169 & Trim Var. & 25316890.3191257 \tabularnewline
V(Y[t],d=0,D=2) & 28950522.8996927 & Range & 28116 & Trim Var. & 14920667.5581921 \tabularnewline
V(Y[t],d=1,D=2) & 21432120.1610131 & Range & 28554 & Trim Var. & 8022593.25774401 \tabularnewline
V(Y[t],d=2,D=2) & 59131806.5081585 & Range & 43412 & Trim Var. & 22540406.4718693 \tabularnewline
V(Y[t],d=3,D=2) & 196578533.902885 & Range & 73650 & Trim Var. & 81202828.8258145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110441&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]331693227.74386[/C][C]Range[/C][C]85032[/C][C]Trim Var.[/C][C]167625378.021949[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]15762602.8605405[/C][C]Range[/C][C]18194[/C][C]Trim Var.[/C][C]10031005.7987336[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]48602879.2789707[/C][C]Range[/C][C]35596[/C][C]Trim Var.[/C][C]32888697.425641[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]185069455.446728[/C][C]Range[/C][C]62022[/C][C]Trim Var.[/C][C]133361803.222115[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]39855075.5179969[/C][C]Range[/C][C]26585[/C][C]Trim Var.[/C][C]27531117.7529762[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8143331.54044266[/C][C]Range[/C][C]17650[/C][C]Trim Var.[/C][C]2923282.50435228[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]20312000.5923395[/C][C]Range[/C][C]26832[/C][C]Trim Var.[/C][C]7711714.70121629[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]66536108.5029838[/C][C]Range[/C][C]45169[/C][C]Trim Var.[/C][C]25316890.3191257[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28950522.8996927[/C][C]Range[/C][C]28116[/C][C]Trim Var.[/C][C]14920667.5581921[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]21432120.1610131[/C][C]Range[/C][C]28554[/C][C]Trim Var.[/C][C]8022593.25774401[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]59131806.5081585[/C][C]Range[/C][C]43412[/C][C]Trim Var.[/C][C]22540406.4718693[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]196578533.902885[/C][C]Range[/C][C]73650[/C][C]Trim Var.[/C][C]81202828.8258145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110441&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110441&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)331693227.74386Range85032Trim Var.167625378.021949
V(Y[t],d=1,D=0)15762602.8605405Range18194Trim Var.10031005.7987336
V(Y[t],d=2,D=0)48602879.2789707Range35596Trim Var.32888697.425641
V(Y[t],d=3,D=0)185069455.446728Range62022Trim Var.133361803.222115
V(Y[t],d=0,D=1)39855075.5179969Range26585Trim Var.27531117.7529762
V(Y[t],d=1,D=1)8143331.54044266Range17650Trim Var.2923282.50435228
V(Y[t],d=2,D=1)20312000.5923395Range26832Trim Var.7711714.70121629
V(Y[t],d=3,D=1)66536108.5029838Range45169Trim Var.25316890.3191257
V(Y[t],d=0,D=2)28950522.8996927Range28116Trim Var.14920667.5581921
V(Y[t],d=1,D=2)21432120.1610131Range28554Trim Var.8022593.25774401
V(Y[t],d=2,D=2)59131806.5081585Range43412Trim Var.22540406.4718693
V(Y[t],d=3,D=2)196578533.902885Range73650Trim Var.81202828.8258145


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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()