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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 computationSat, 18 Dec 2010 20:51:03 +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/18/t12927061233dqzucaq9blrnml.htm/, Retrieved Tue, 30 Apr 2024 05:00:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112199, Retrieved Tue, 30 Apr 2024 05:00:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [VRM] [2010-12-18 20:51:03] [c2514e24605d0513c6bae17788e1fef3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5745
4549
5074
3602
2732
2589
2148
2330
2752
3241
4517
6550
6778
6240
5570
3558
3299
2447
2380
2378
2947
3651
4816
6436
7090
4682
4198
3860
3056
2563
2568
2472
2821
4015
4686
5418
5649
4572
4695
3766
2900
2528
2549
2478
2828
4139
5390
5621
5291
5272
4677
3520
2842
2723
2581
2429
2606
3787
4630
5505
5577
4911
4701
3557
2921
2734
2636
2433
2640
3794
4745
5698
5909
5119
5200
3876
3104
2251
2386
2794
2967
3392
4741
5909

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'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112199&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112199&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)1752429.93617326Range4942Trim Var.1304361.71417993
V(Y[t],d=1,D=0)682635.243314722Range4441Trim Var.400584.697488584
V(Y[t],d=2,D=0)693505.353206865Range4986Trim Var.329506.732198748
V(Y[t],d=3,D=0)1712309.55277778Range8704Trim Var.705132.428169014
V(Y[t],d=0,D=1)234002.901212833Range3249Trim Var.66304.7142857143
V(Y[t],d=1,D=1)290116.304627767Range3544Trim Var.127980.903225806
V(Y[t],d=2,D=1)717501.702070393Range4352Trim Var.337347.347435219
V(Y[t],d=3,D=1)2032740.39940324Range8059Trim Var.936786.146448087
V(Y[t],d=0,D=2)615397.531073446Range5118Trim Var.231672.51572327
V(Y[t],d=1,D=2)804698.908825248Range5729Trim Var.292206.375907112
V(Y[t],d=2,D=2)1912228.82183908Range7420Trim Var.847874.378582202
V(Y[t],d=3,D=2)5128201.01879699Range12424Trim Var.2364078.71843137

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1752429.93617326 & Range & 4942 & Trim Var. & 1304361.71417993 \tabularnewline
V(Y[t],d=1,D=0) & 682635.243314722 & Range & 4441 & Trim Var. & 400584.697488584 \tabularnewline
V(Y[t],d=2,D=0) & 693505.353206865 & Range & 4986 & Trim Var. & 329506.732198748 \tabularnewline
V(Y[t],d=3,D=0) & 1712309.55277778 & Range & 8704 & Trim Var. & 705132.428169014 \tabularnewline
V(Y[t],d=0,D=1) & 234002.901212833 & Range & 3249 & Trim Var. & 66304.7142857143 \tabularnewline
V(Y[t],d=1,D=1) & 290116.304627767 & Range & 3544 & Trim Var. & 127980.903225806 \tabularnewline
V(Y[t],d=2,D=1) & 717501.702070393 & Range & 4352 & Trim Var. & 337347.347435219 \tabularnewline
V(Y[t],d=3,D=1) & 2032740.39940324 & Range & 8059 & Trim Var. & 936786.146448087 \tabularnewline
V(Y[t],d=0,D=2) & 615397.531073446 & Range & 5118 & Trim Var. & 231672.51572327 \tabularnewline
V(Y[t],d=1,D=2) & 804698.908825248 & Range & 5729 & Trim Var. & 292206.375907112 \tabularnewline
V(Y[t],d=2,D=2) & 1912228.82183908 & Range & 7420 & Trim Var. & 847874.378582202 \tabularnewline
V(Y[t],d=3,D=2) & 5128201.01879699 & Range & 12424 & Trim Var. & 2364078.71843137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112199&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1752429.93617326[/C][C]Range[/C][C]4942[/C][C]Trim Var.[/C][C]1304361.71417993[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]682635.243314722[/C][C]Range[/C][C]4441[/C][C]Trim Var.[/C][C]400584.697488584[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]693505.353206865[/C][C]Range[/C][C]4986[/C][C]Trim Var.[/C][C]329506.732198748[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1712309.55277778[/C][C]Range[/C][C]8704[/C][C]Trim Var.[/C][C]705132.428169014[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]234002.901212833[/C][C]Range[/C][C]3249[/C][C]Trim Var.[/C][C]66304.7142857143[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]290116.304627767[/C][C]Range[/C][C]3544[/C][C]Trim Var.[/C][C]127980.903225806[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]717501.702070393[/C][C]Range[/C][C]4352[/C][C]Trim Var.[/C][C]337347.347435219[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2032740.39940324[/C][C]Range[/C][C]8059[/C][C]Trim Var.[/C][C]936786.146448087[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]615397.531073446[/C][C]Range[/C][C]5118[/C][C]Trim Var.[/C][C]231672.51572327[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]804698.908825248[/C][C]Range[/C][C]5729[/C][C]Trim Var.[/C][C]292206.375907112[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1912228.82183908[/C][C]Range[/C][C]7420[/C][C]Trim Var.[/C][C]847874.378582202[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]5128201.01879699[/C][C]Range[/C][C]12424[/C][C]Trim Var.[/C][C]2364078.71843137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112199&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)1752429.93617326Range4942Trim Var.1304361.71417993
V(Y[t],d=1,D=0)682635.243314722Range4441Trim Var.400584.697488584
V(Y[t],d=2,D=0)693505.353206865Range4986Trim Var.329506.732198748
V(Y[t],d=3,D=0)1712309.55277778Range8704Trim Var.705132.428169014
V(Y[t],d=0,D=1)234002.901212833Range3249Trim Var.66304.7142857143
V(Y[t],d=1,D=1)290116.304627767Range3544Trim Var.127980.903225806
V(Y[t],d=2,D=1)717501.702070393Range4352Trim Var.337347.347435219
V(Y[t],d=3,D=1)2032740.39940324Range8059Trim Var.936786.146448087
V(Y[t],d=0,D=2)615397.531073446Range5118Trim Var.231672.51572327
V(Y[t],d=1,D=2)804698.908825248Range5729Trim Var.292206.375907112
V(Y[t],d=2,D=2)1912228.82183908Range7420Trim Var.847874.378582202
V(Y[t],d=3,D=2)5128201.01879699Range12424Trim Var.2364078.71843137


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()