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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, 20 Dec 2010 12:08:58 +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/20/t1292846845bw8xklbusnwu8fc.htm/, Retrieved Fri, 03 May 2024 20:30:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112863, Retrieved Fri, 03 May 2024 20:30:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- RMPD      [Variance Reduction Matrix] [Eonia-VRM] [2010-12-20 12:08:58] [4c7d8c32b2e34fcaa7f14928b91d45ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.04
3.28
3.51
3.69
3.92
4.29
4.31
4.42
4.59
4.76
4.83
4.83
4.76
4.99
4.78
5.06
4.65
4.54
4.51
4.49
3.99
3.97
3.51
3.34
3.29
3.28
3.26
3.32
3.31
3.35
3.30
3.29
3.32
3.30
3.30
3.09
2.79
2.76
2.75
2.56
2.56
2.21
2.08
2.10
2.02
2.01
1.97
2.06
2.02
2.03
2.01
2.08
2.02
2.03
2.07
2.04
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
0.36
0.36
0.36
0.35
0.34
0.34
0.35
0.35
0.34
0.35
0.48
0.43
0.45
0.70
0.59

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=112863&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=112863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112863&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)1.74375695830887Range4.72Trim Var.1.29714416791604
V(Y[t],d=1,D=0)0.0322056350626118Range1.05Trim Var.0.0116918382913806
V(Y[t],d=2,D=0)0.0310105499031008Range1.18000000000000Trim Var.0.0129944622425629
V(Y[t],d=3,D=0)0.0945696296751968Range2.17000000000000Trim Var.0.0343235600062102
V(Y[t],d=0,D=1)1.55070465745620Range5.67Trim Var.0.933552530417916
V(Y[t],d=1,D=1)0.0712810734463277Range1.49Trim Var.0.0336723809523809
V(Y[t],d=2,D=1)0.070780297671677Range1.36000000000000Trim Var.0.0449283047050037
V(Y[t],d=3,D=1)0.210330937031484Range2.31000000000000Trim Var.0.12361821321882
V(Y[t],d=0,D=2)3.13694478927879Range8.23Trim Var.1.77129099664054
V(Y[t],d=1,D=2)0.193997026055705Range2.39Trim Var.0.0874154312514299
V(Y[t],d=2,D=2)0.207544413919414Range2.37000000000000Trim Var.0.122624193548387
V(Y[t],d=3,D=2)0.605550112023898Range4.3800Trim Var.0.311537840420449

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.74375695830887 & Range & 4.72 & Trim Var. & 1.29714416791604 \tabularnewline
V(Y[t],d=1,D=0) & 0.0322056350626118 & Range & 1.05 & Trim Var. & 0.0116918382913806 \tabularnewline
V(Y[t],d=2,D=0) & 0.0310105499031008 & Range & 1.18000000000000 & Trim Var. & 0.0129944622425629 \tabularnewline
V(Y[t],d=3,D=0) & 0.0945696296751968 & Range & 2.17000000000000 & Trim Var. & 0.0343235600062102 \tabularnewline
V(Y[t],d=0,D=1) & 1.55070465745620 & Range & 5.67 & Trim Var. & 0.933552530417916 \tabularnewline
V(Y[t],d=1,D=1) & 0.0712810734463277 & Range & 1.49 & Trim Var. & 0.0336723809523809 \tabularnewline
V(Y[t],d=2,D=1) & 0.070780297671677 & Range & 1.36000000000000 & Trim Var. & 0.0449283047050037 \tabularnewline
V(Y[t],d=3,D=1) & 0.210330937031484 & Range & 2.31000000000000 & Trim Var. & 0.12361821321882 \tabularnewline
V(Y[t],d=0,D=2) & 3.13694478927879 & Range & 8.23 & Trim Var. & 1.77129099664054 \tabularnewline
V(Y[t],d=1,D=2) & 0.193997026055705 & Range & 2.39 & Trim Var. & 0.0874154312514299 \tabularnewline
V(Y[t],d=2,D=2) & 0.207544413919414 & Range & 2.37000000000000 & Trim Var. & 0.122624193548387 \tabularnewline
V(Y[t],d=3,D=2) & 0.605550112023898 & Range & 4.3800 & Trim Var. & 0.311537840420449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112863&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.74375695830887[/C][C]Range[/C][C]4.72[/C][C]Trim Var.[/C][C]1.29714416791604[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0322056350626118[/C][C]Range[/C][C]1.05[/C][C]Trim Var.[/C][C]0.0116918382913806[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0310105499031008[/C][C]Range[/C][C]1.18000000000000[/C][C]Trim Var.[/C][C]0.0129944622425629[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0945696296751968[/C][C]Range[/C][C]2.17000000000000[/C][C]Trim Var.[/C][C]0.0343235600062102[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.55070465745620[/C][C]Range[/C][C]5.67[/C][C]Trim Var.[/C][C]0.933552530417916[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0712810734463277[/C][C]Range[/C][C]1.49[/C][C]Trim Var.[/C][C]0.0336723809523809[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.070780297671677[/C][C]Range[/C][C]1.36000000000000[/C][C]Trim Var.[/C][C]0.0449283047050037[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.210330937031484[/C][C]Range[/C][C]2.31000000000000[/C][C]Trim Var.[/C][C]0.12361821321882[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3.13694478927879[/C][C]Range[/C][C]8.23[/C][C]Trim Var.[/C][C]1.77129099664054[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.193997026055705[/C][C]Range[/C][C]2.39[/C][C]Trim Var.[/C][C]0.0874154312514299[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.207544413919414[/C][C]Range[/C][C]2.37000000000000[/C][C]Trim Var.[/C][C]0.122624193548387[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.605550112023898[/C][C]Range[/C][C]4.3800[/C][C]Trim Var.[/C][C]0.311537840420449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112863&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)1.74375695830887Range4.72Trim Var.1.29714416791604
V(Y[t],d=1,D=0)0.0322056350626118Range1.05Trim Var.0.0116918382913806
V(Y[t],d=2,D=0)0.0310105499031008Range1.18000000000000Trim Var.0.0129944622425629
V(Y[t],d=3,D=0)0.0945696296751968Range2.17000000000000Trim Var.0.0343235600062102
V(Y[t],d=0,D=1)1.55070465745620Range5.67Trim Var.0.933552530417916
V(Y[t],d=1,D=1)0.0712810734463277Range1.49Trim Var.0.0336723809523809
V(Y[t],d=2,D=1)0.070780297671677Range1.36000000000000Trim Var.0.0449283047050037
V(Y[t],d=3,D=1)0.210330937031484Range2.31000000000000Trim Var.0.12361821321882
V(Y[t],d=0,D=2)3.13694478927879Range8.23Trim Var.1.77129099664054
V(Y[t],d=1,D=2)0.193997026055705Range2.39Trim Var.0.0874154312514299
V(Y[t],d=2,D=2)0.207544413919414Range2.37000000000000Trim Var.0.122624193548387
V(Y[t],d=3,D=2)0.605550112023898Range4.3800Trim Var.0.311537840420449


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()