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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 computationFri, 27 Nov 2009 09:46:34 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/27/t125934043167xr5u5myt0bc82.htm/, Retrieved Sun, 09 Mar 2025 02:43:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60988, Retrieved Sun, 09 Mar 2025 02:43:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Variance Reduction Matrix] [Identifying Integ...] [2009-11-22 12:29:54] [b98453cac15ba1066b407e146608df68]
-    D        [Variance Reduction Matrix] [SHW WS8] [2009-11-24 12:00:42] [253127ae8da904b75450fbd69fe4eb21]
-   PD            [Variance Reduction Matrix] [ws8 model2.1] [2009-11-27 16:46:34] [95523ebdb89b97dbf680ec91e0b4bca2] [Current]
-   PD              [Variance Reduction Matrix] [paper vrm1] [2009-12-13 15:23:40] [95cead3ebb75668735f848316249436a]
-    D                [Variance Reduction Matrix] [deel2 vrm] [2009-12-13 17:15:37] [95cead3ebb75668735f848316249436a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.05
2.11
2.09
2.05
2.08
2.06
2.06
2.08
2.07
2.06
2.07
2.06
2.09
2.07
2.09
2.28
2.33
2.35
2.52
2.63
2.58
2.70
2.81
2.97
3.04
3.28
3.33
3.50
3.56
3.57
3.69
3.82
3.79
3.96
4.06
4.05
4.03
3.94
4.02
3.88
4.02
4.03
4.09
3.99
4.01
4.01
4.19
4.30
4.27
3.82
3.15
2.49
1.81
1.26
1.06
0.84
0.78
0.70
0.36
0.35

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60988&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]0 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=60988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60988&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.20515194915254Range3.95Trim Var.0.91194535290007
V(Y[t],d=1,D=0)0.0421278784336645Range0.92Trim Var.0.0195711901306241
V(Y[t],d=2,D=0)0.0209967634603750Range0.77Trim Var.0.0116544117647059
V(Y[t],d=3,D=0)0.0503848370927317Range0.999999999999998Trim Var.0.0327873725490195
V(Y[t],d=0,D=1)2.30334144503546Range5.21Trim Var.1.52178728222996
V(Y[t],d=1,D=1)0.0561168362627197Range1.08Trim Var.0.0259589102564102
V(Y[t],d=2,D=1)0.0441414492753623Range0.840000000000002Trim Var.0.0276024999999999
V(Y[t],d=3,D=1)0.121524040404040Range1.54Trim Var.0.0711623481781375
V(Y[t],d=0,D=2)2.63180825396825Range5.45Trim Var.2.01605393145161
V(Y[t],d=1,D=2)0.0753541176470588Range1.24Trim Var.0.0386090322580646
V(Y[t],d=2,D=2)0.12120926916221Range1.34000000000000Trim Var.0.0791448275862067
V(Y[t],d=3,D=2)0.375682007575757Range2.58000000000000Trim Var.0.241697536945812

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.20515194915254 & Range & 3.95 & Trim Var. & 0.91194535290007 \tabularnewline
V(Y[t],d=1,D=0) & 0.0421278784336645 & Range & 0.92 & Trim Var. & 0.0195711901306241 \tabularnewline
V(Y[t],d=2,D=0) & 0.0209967634603750 & Range & 0.77 & Trim Var. & 0.0116544117647059 \tabularnewline
V(Y[t],d=3,D=0) & 0.0503848370927317 & Range & 0.999999999999998 & Trim Var. & 0.0327873725490195 \tabularnewline
V(Y[t],d=0,D=1) & 2.30334144503546 & Range & 5.21 & Trim Var. & 1.52178728222996 \tabularnewline
V(Y[t],d=1,D=1) & 0.0561168362627197 & Range & 1.08 & Trim Var. & 0.0259589102564102 \tabularnewline
V(Y[t],d=2,D=1) & 0.0441414492753623 & Range & 0.840000000000002 & Trim Var. & 0.0276024999999999 \tabularnewline
V(Y[t],d=3,D=1) & 0.121524040404040 & Range & 1.54 & Trim Var. & 0.0711623481781375 \tabularnewline
V(Y[t],d=0,D=2) & 2.63180825396825 & Range & 5.45 & Trim Var. & 2.01605393145161 \tabularnewline
V(Y[t],d=1,D=2) & 0.0753541176470588 & Range & 1.24 & Trim Var. & 0.0386090322580646 \tabularnewline
V(Y[t],d=2,D=2) & 0.12120926916221 & Range & 1.34000000000000 & Trim Var. & 0.0791448275862067 \tabularnewline
V(Y[t],d=3,D=2) & 0.375682007575757 & Range & 2.58000000000000 & Trim Var. & 0.241697536945812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60988&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.20515194915254[/C][C]Range[/C][C]3.95[/C][C]Trim Var.[/C][C]0.91194535290007[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0421278784336645[/C][C]Range[/C][C]0.92[/C][C]Trim Var.[/C][C]0.0195711901306241[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0209967634603750[/C][C]Range[/C][C]0.77[/C][C]Trim Var.[/C][C]0.0116544117647059[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0503848370927317[/C][C]Range[/C][C]0.999999999999998[/C][C]Trim Var.[/C][C]0.0327873725490195[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2.30334144503546[/C][C]Range[/C][C]5.21[/C][C]Trim Var.[/C][C]1.52178728222996[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0561168362627197[/C][C]Range[/C][C]1.08[/C][C]Trim Var.[/C][C]0.0259589102564102[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0441414492753623[/C][C]Range[/C][C]0.840000000000002[/C][C]Trim Var.[/C][C]0.0276024999999999[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.121524040404040[/C][C]Range[/C][C]1.54[/C][C]Trim Var.[/C][C]0.0711623481781375[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2.63180825396825[/C][C]Range[/C][C]5.45[/C][C]Trim Var.[/C][C]2.01605393145161[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.0753541176470588[/C][C]Range[/C][C]1.24[/C][C]Trim Var.[/C][C]0.0386090322580646[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.12120926916221[/C][C]Range[/C][C]1.34000000000000[/C][C]Trim Var.[/C][C]0.0791448275862067[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.375682007575757[/C][C]Range[/C][C]2.58000000000000[/C][C]Trim Var.[/C][C]0.241697536945812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60988&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)1.20515194915254Range3.95Trim Var.0.91194535290007
V(Y[t],d=1,D=0)0.0421278784336645Range0.92Trim Var.0.0195711901306241
V(Y[t],d=2,D=0)0.0209967634603750Range0.77Trim Var.0.0116544117647059
V(Y[t],d=3,D=0)0.0503848370927317Range0.999999999999998Trim Var.0.0327873725490195
V(Y[t],d=0,D=1)2.30334144503546Range5.21Trim Var.1.52178728222996
V(Y[t],d=1,D=1)0.0561168362627197Range1.08Trim Var.0.0259589102564102
V(Y[t],d=2,D=1)0.0441414492753623Range0.840000000000002Trim Var.0.0276024999999999
V(Y[t],d=3,D=1)0.121524040404040Range1.54Trim Var.0.0711623481781375
V(Y[t],d=0,D=2)2.63180825396825Range5.45Trim Var.2.01605393145161
V(Y[t],d=1,D=2)0.0753541176470588Range1.24Trim Var.0.0386090322580646
V(Y[t],d=2,D=2)0.12120926916221Range1.34000000000000Trim Var.0.0791448275862067
V(Y[t],d=3,D=2)0.375682007575757Range2.58000000000000Trim Var.0.241697536945812


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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(x,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')