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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 computationTue, 21 Dec 2010 19:19:39 +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/21/t1292959087fqujn3oudkjjcc6.htm/, Retrieved Sun, 19 May 2024 18:07:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113859, Retrieved Sun, 19 May 2024 18:07:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

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] [paper variance re...] [2010-12-21 19:19:39] [06510e00f8d0c95cc2ff019b83c7c2eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2350,44
2440,25
2408,64
2472,81
2407,6
2454,62
2448,05
2497,84
2645,64
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
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

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=113859&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=113859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113859&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)711512.786427664Range3026.89Trim Var.552089.385765625
V(Y[t],d=1,D=0)28300.7126243936Range998.81Trim Var.12081.5205846974
V(Y[t],d=2,D=0)40340.2333656338Range1260.98Trim Var.16850.7621967742
V(Y[t],d=3,D=0)111097.147221139Range1886.22Trim Var.49520.6308543893
V(Y[t],d=0,D=1)1050488.02194240Range3305.13Trim Var.798187.570113788
V(Y[t],d=1,D=1)62898.7704773729Range1737.68Trim Var.25334.8535720825
V(Y[t],d=2,D=1)98343.8637545295Range1774.54Trim Var.44212.0326483309
V(Y[t],d=3,D=1)287266.954505868Range3134.28Trim Var.122197.686044155
V(Y[t],d=0,D=2)1552929.19779388Range5427.8Trim Var.824152.26831052
V(Y[t],d=1,D=2)192899.082726551Range2611.26Trim Var.78817.763397503
V(Y[t],d=2,D=2)352328.249794357Range3158.78000000000Trim Var.145926.532176951
V(Y[t],d=3,D=2)1022277.87222053Range5192.03Trim Var.408876.217113847

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 711512.786427664 & Range & 3026.89 & Trim Var. & 552089.385765625 \tabularnewline
V(Y[t],d=1,D=0) & 28300.7126243936 & Range & 998.81 & Trim Var. & 12081.5205846974 \tabularnewline
V(Y[t],d=2,D=0) & 40340.2333656338 & Range & 1260.98 & Trim Var. & 16850.7621967742 \tabularnewline
V(Y[t],d=3,D=0) & 111097.147221139 & Range & 1886.22 & Trim Var. & 49520.6308543893 \tabularnewline
V(Y[t],d=0,D=1) & 1050488.02194240 & Range & 3305.13 & Trim Var. & 798187.570113788 \tabularnewline
V(Y[t],d=1,D=1) & 62898.7704773729 & Range & 1737.68 & Trim Var. & 25334.8535720825 \tabularnewline
V(Y[t],d=2,D=1) & 98343.8637545295 & Range & 1774.54 & Trim Var. & 44212.0326483309 \tabularnewline
V(Y[t],d=3,D=1) & 287266.954505868 & Range & 3134.28 & Trim Var. & 122197.686044155 \tabularnewline
V(Y[t],d=0,D=2) & 1552929.19779388 & Range & 5427.8 & Trim Var. & 824152.26831052 \tabularnewline
V(Y[t],d=1,D=2) & 192899.082726551 & Range & 2611.26 & Trim Var. & 78817.763397503 \tabularnewline
V(Y[t],d=2,D=2) & 352328.249794357 & Range & 3158.78000000000 & Trim Var. & 145926.532176951 \tabularnewline
V(Y[t],d=3,D=2) & 1022277.87222053 & Range & 5192.03 & Trim Var. & 408876.217113847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113859&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]711512.786427664[/C][C]Range[/C][C]3026.89[/C][C]Trim Var.[/C][C]552089.385765625[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]28300.7126243936[/C][C]Range[/C][C]998.81[/C][C]Trim Var.[/C][C]12081.5205846974[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]40340.2333656338[/C][C]Range[/C][C]1260.98[/C][C]Trim Var.[/C][C]16850.7621967742[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]111097.147221139[/C][C]Range[/C][C]1886.22[/C][C]Trim Var.[/C][C]49520.6308543893[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1050488.02194240[/C][C]Range[/C][C]3305.13[/C][C]Trim Var.[/C][C]798187.570113788[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]62898.7704773729[/C][C]Range[/C][C]1737.68[/C][C]Trim Var.[/C][C]25334.8535720825[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]98343.8637545295[/C][C]Range[/C][C]1774.54[/C][C]Trim Var.[/C][C]44212.0326483309[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]287266.954505868[/C][C]Range[/C][C]3134.28[/C][C]Trim Var.[/C][C]122197.686044155[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1552929.19779388[/C][C]Range[/C][C]5427.8[/C][C]Trim Var.[/C][C]824152.26831052[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]192899.082726551[/C][C]Range[/C][C]2611.26[/C][C]Trim Var.[/C][C]78817.763397503[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]352328.249794357[/C][C]Range[/C][C]3158.78000000000[/C][C]Trim Var.[/C][C]145926.532176951[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1022277.87222053[/C][C]Range[/C][C]5192.03[/C][C]Trim Var.[/C][C]408876.217113847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113859&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)711512.786427664Range3026.89Trim Var.552089.385765625
V(Y[t],d=1,D=0)28300.7126243936Range998.81Trim Var.12081.5205846974
V(Y[t],d=2,D=0)40340.2333656338Range1260.98Trim Var.16850.7621967742
V(Y[t],d=3,D=0)111097.147221139Range1886.22Trim Var.49520.6308543893
V(Y[t],d=0,D=1)1050488.02194240Range3305.13Trim Var.798187.570113788
V(Y[t],d=1,D=1)62898.7704773729Range1737.68Trim Var.25334.8535720825
V(Y[t],d=2,D=1)98343.8637545295Range1774.54Trim Var.44212.0326483309
V(Y[t],d=3,D=1)287266.954505868Range3134.28Trim Var.122197.686044155
V(Y[t],d=0,D=2)1552929.19779388Range5427.8Trim Var.824152.26831052
V(Y[t],d=1,D=2)192899.082726551Range2611.26Trim Var.78817.763397503
V(Y[t],d=2,D=2)352328.249794357Range3158.78000000000Trim Var.145926.532176951
V(Y[t],d=3,D=2)1022277.87222053Range5192.03Trim Var.408876.217113847


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()