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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, 29 Dec 2010 13:11:37 +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/29/t1293628156z07wt0zqiea8np7.htm/, Retrieved Fri, 03 May 2024 05:14:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116793, Retrieved Fri, 03 May 2024 05:14:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact43

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] [] [2010-12-22 21:18:53] [29e492448d11757ae0fad5ef6e7f8e86]
-    D    [Variance Reduction Matrix] [] [2010-12-29 13:11:37] [e180d4cd19004beeddc12e67012247dc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
09,166456
07,970589
07,104091
06,621064
07,529215
08,170938
08,157450
07,378962
07,921496
08,156740
08,856365
08,817177
08,734347
09,345927
08,992970
10,785120
08,886867
08,818847
08,823744
09,165298
08,652657
08,173054
07,563416
07,595809
08,381467
07,216432
06,540178
06,238914
05,487288
05,759462
05,993215
07,474726
07,348907
07,303379
07,119314
06,993780
06,958153
07,595706
08,088153
07,555753
07,315433
07,893427
08,858794
08,839367
08,014733
07,873465
08,930377
10,500550
12,611440
11,417870
11,872490
11,060820
12,043310
09,776299
09,557194
09,202590
10,224020
09,350807
08,300913
08,365779
08,133595
07,660470
08,074839
07,848597
07,998220
07,396895
07,900419
08,100500
07,899453
07,599783
08,100929
09,002175
10,298900
10,101520
10,699150
09,698140
09,800951
10,900470
10,697850
09,297252
10,397440
10,900720
12,901270
13,099060
11,698280
11,099870
11,301570
10,702110
10,099310
09,591119

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=116793&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=116793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116793&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)2.66641782699171Range7.611772Trim Var.1.61736409088787
V(Y[t],d=1,D=0)0.669084933880776Range4.377901Trim Var.0.364781385851227
V(Y[t],d=2,D=0)1.36386482972239Range6.191189Trim Var.0.705141922348545
V(Y[t],d=3,D=0)4.16242474901661Range11.356146Trim Var.2.04809437693972
V(Y[t],d=0,D=1)5.67709902619859Range10.199493Trim Var.3.93482136458724
V(Y[t],d=1,D=1)1.54070491332192Range5.120182Trim Var.1.05683006002187
V(Y[t],d=2,D=1)2.80427728306164Range8.321622Trim Var.1.64318751727232
V(Y[t],d=3,D=1)8.07247143728395Range14.021459Trim Var.5.06758417015892
V(Y[t],d=0,D=2)19.1787875405627Range17.207733Trim Var.13.2363630096754
V(Y[t],d=1,D=2)4.81766065561454Range9.000282Trim Var.3.10252632258273
V(Y[t],d=2,D=2)8.15949480066866Range14.923135Trim Var.4.18811892742196
V(Y[t],d=3,D=2)22.8830625513947Range23.078091Trim Var.12.5063070869714

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2.66641782699171 & Range & 7.611772 & Trim Var. & 1.61736409088787 \tabularnewline
V(Y[t],d=1,D=0) & 0.669084933880776 & Range & 4.377901 & Trim Var. & 0.364781385851227 \tabularnewline
V(Y[t],d=2,D=0) & 1.36386482972239 & Range & 6.191189 & Trim Var. & 0.705141922348545 \tabularnewline
V(Y[t],d=3,D=0) & 4.16242474901661 & Range & 11.356146 & Trim Var. & 2.04809437693972 \tabularnewline
V(Y[t],d=0,D=1) & 5.67709902619859 & Range & 10.199493 & Trim Var. & 3.93482136458724 \tabularnewline
V(Y[t],d=1,D=1) & 1.54070491332192 & Range & 5.120182 & Trim Var. & 1.05683006002187 \tabularnewline
V(Y[t],d=2,D=1) & 2.80427728306164 & Range & 8.321622 & Trim Var. & 1.64318751727232 \tabularnewline
V(Y[t],d=3,D=1) & 8.07247143728395 & Range & 14.021459 & Trim Var. & 5.06758417015892 \tabularnewline
V(Y[t],d=0,D=2) & 19.1787875405627 & Range & 17.207733 & Trim Var. & 13.2363630096754 \tabularnewline
V(Y[t],d=1,D=2) & 4.81766065561454 & Range & 9.000282 & Trim Var. & 3.10252632258273 \tabularnewline
V(Y[t],d=2,D=2) & 8.15949480066866 & Range & 14.923135 & Trim Var. & 4.18811892742196 \tabularnewline
V(Y[t],d=3,D=2) & 22.8830625513947 & Range & 23.078091 & Trim Var. & 12.5063070869714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116793&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2.66641782699171[/C][C]Range[/C][C]7.611772[/C][C]Trim Var.[/C][C]1.61736409088787[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.669084933880776[/C][C]Range[/C][C]4.377901[/C][C]Trim Var.[/C][C]0.364781385851227[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.36386482972239[/C][C]Range[/C][C]6.191189[/C][C]Trim Var.[/C][C]0.705141922348545[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4.16242474901661[/C][C]Range[/C][C]11.356146[/C][C]Trim Var.[/C][C]2.04809437693972[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5.67709902619859[/C][C]Range[/C][C]10.199493[/C][C]Trim Var.[/C][C]3.93482136458724[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.54070491332192[/C][C]Range[/C][C]5.120182[/C][C]Trim Var.[/C][C]1.05683006002187[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2.80427728306164[/C][C]Range[/C][C]8.321622[/C][C]Trim Var.[/C][C]1.64318751727232[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]8.07247143728395[/C][C]Range[/C][C]14.021459[/C][C]Trim Var.[/C][C]5.06758417015892[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.1787875405627[/C][C]Range[/C][C]17.207733[/C][C]Trim Var.[/C][C]13.2363630096754[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4.81766065561454[/C][C]Range[/C][C]9.000282[/C][C]Trim Var.[/C][C]3.10252632258273[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]8.15949480066866[/C][C]Range[/C][C]14.923135[/C][C]Trim Var.[/C][C]4.18811892742196[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]22.8830625513947[/C][C]Range[/C][C]23.078091[/C][C]Trim Var.[/C][C]12.5063070869714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116793&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)2.66641782699171Range7.611772Trim Var.1.61736409088787
V(Y[t],d=1,D=0)0.669084933880776Range4.377901Trim Var.0.364781385851227
V(Y[t],d=2,D=0)1.36386482972239Range6.191189Trim Var.0.705141922348545
V(Y[t],d=3,D=0)4.16242474901661Range11.356146Trim Var.2.04809437693972
V(Y[t],d=0,D=1)5.67709902619859Range10.199493Trim Var.3.93482136458724
V(Y[t],d=1,D=1)1.54070491332192Range5.120182Trim Var.1.05683006002187
V(Y[t],d=2,D=1)2.80427728306164Range8.321622Trim Var.1.64318751727232
V(Y[t],d=3,D=1)8.07247143728395Range14.021459Trim Var.5.06758417015892
V(Y[t],d=0,D=2)19.1787875405627Range17.207733Trim Var.13.2363630096754
V(Y[t],d=1,D=2)4.81766065561454Range9.000282Trim Var.3.10252632258273
V(Y[t],d=2,D=2)8.15949480066866Range14.923135Trim Var.4.18811892742196
V(Y[t],d=3,D=2)22.8830625513947Range23.078091Trim Var.12.5063070869714


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()