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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 computationMon, 05 Dec 2011 16:52:25 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/05/t1323121957pz1hstlpiwoimh0.htm/, Retrieved Wed, 13 May 2026 06:49:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151287, Retrieved Wed, 13 May 2026 06:49:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact339

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] [] [2011-12-05 21:52:25] [fdaf10f0fcbe7b8f79ecbd42ec74e6ad] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27
2513,17
2466,92
2502,66
2539,91
2482,6
2626,15
2656,32
2446,66
2467,38
2462,32
2504,58
2579,39
2649,24
2636,87
2613,94
2634,01
2711,94
2646,43
2717,79
2701,54
2572,98
2488,92
2204,91
2123,99
2149,1

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151287&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151287&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'Gertrude Mary Cox' @ cox.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)781379.884075098Range3026.89Trim Var.627387.150211682
V(Y[t],d=1,D=0)29872.084792998Range998.810000000001Trim Var.14328.3382709678
V(Y[t],d=2,D=0)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=3,D=0)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=0,D=1)29872.084792998Range998.810000000001Trim Var.14328.3382709678
V(Y[t],d=1,D=1)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=2,D=1)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=3,D=1)383655.069076098Range3652.07Trim Var.170065.051352854
V(Y[t],d=0,D=2)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=1,D=2)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=2,D=2)383655.069076098Range3652.07Trim Var.170065.051352854
V(Y[t],d=3,D=2)1278787.51546947Range6174.3Trim Var.629528.028996846

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 781379.884075098 & Range & 3026.89 & Trim Var. & 627387.150211682 \tabularnewline
V(Y[t],d=1,D=0) & 29872.084792998 & Range & 998.810000000001 & Trim Var. & 14328.3382709678 \tabularnewline
V(Y[t],d=2,D=0) & 44357.8470931884 & Range & 1260.98 & Trim Var. & 21005.1067375199 \tabularnewline
V(Y[t],d=3,D=0) & 122374.494109634 & Range & 1886.22 & Trim Var. & 61233.7468443171 \tabularnewline
V(Y[t],d=0,D=1) & 29872.084792998 & Range & 998.810000000001 & Trim Var. & 14328.3382709678 \tabularnewline
V(Y[t],d=1,D=1) & 44357.8470931884 & Range & 1260.98 & Trim Var. & 21005.1067375199 \tabularnewline
V(Y[t],d=2,D=1) & 122374.494109634 & Range & 1886.22 & Trim Var. & 61233.7468443171 \tabularnewline
V(Y[t],d=3,D=1) & 383655.069076098 & Range & 3652.07 & Trim Var. & 170065.051352854 \tabularnewline
V(Y[t],d=0,D=2) & 44357.8470931884 & Range & 1260.98 & Trim Var. & 21005.1067375199 \tabularnewline
V(Y[t],d=1,D=2) & 122374.494109634 & Range & 1886.22 & Trim Var. & 61233.7468443171 \tabularnewline
V(Y[t],d=2,D=2) & 383655.069076098 & Range & 3652.07 & Trim Var. & 170065.051352854 \tabularnewline
V(Y[t],d=3,D=2) & 1278787.51546947 & Range & 6174.3 & Trim Var. & 629528.028996846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151287&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]781379.884075098[/C][C]Range[/C][C]3026.89[/C][C]Trim Var.[/C][C]627387.150211682[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]29872.084792998[/C][C]Range[/C][C]998.810000000001[/C][C]Trim Var.[/C][C]14328.3382709678[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]44357.8470931884[/C][C]Range[/C][C]1260.98[/C][C]Trim Var.[/C][C]21005.1067375199[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]122374.494109634[/C][C]Range[/C][C]1886.22[/C][C]Trim Var.[/C][C]61233.7468443171[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]29872.084792998[/C][C]Range[/C][C]998.810000000001[/C][C]Trim Var.[/C][C]14328.3382709678[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]44357.8470931884[/C][C]Range[/C][C]1260.98[/C][C]Trim Var.[/C][C]21005.1067375199[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]122374.494109634[/C][C]Range[/C][C]1886.22[/C][C]Trim Var.[/C][C]61233.7468443171[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]383655.069076098[/C][C]Range[/C][C]3652.07[/C][C]Trim Var.[/C][C]170065.051352854[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]44357.8470931884[/C][C]Range[/C][C]1260.98[/C][C]Trim Var.[/C][C]21005.1067375199[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]122374.494109634[/C][C]Range[/C][C]1886.22[/C][C]Trim Var.[/C][C]61233.7468443171[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]383655.069076098[/C][C]Range[/C][C]3652.07[/C][C]Trim Var.[/C][C]170065.051352854[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1278787.51546947[/C][C]Range[/C][C]6174.3[/C][C]Trim Var.[/C][C]629528.028996846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151287&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)781379.884075098Range3026.89Trim Var.627387.150211682
V(Y[t],d=1,D=0)29872.084792998Range998.810000000001Trim Var.14328.3382709678
V(Y[t],d=2,D=0)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=3,D=0)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=0,D=1)29872.084792998Range998.810000000001Trim Var.14328.3382709678
V(Y[t],d=1,D=1)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=2,D=1)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=3,D=1)383655.069076098Range3652.07Trim Var.170065.051352854
V(Y[t],d=0,D=2)44357.8470931884Range1260.98Trim Var.21005.1067375199
V(Y[t],d=1,D=2)122374.494109634Range1886.22Trim Var.61233.7468443171
V(Y[t],d=2,D=2)383655.069076098Range3652.07Trim Var.170065.051352854
V(Y[t],d=3,D=2)1278787.51546947Range6174.3Trim Var.629528.028996846


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ;
Parameters (R input):
par1 = 1 ;
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()