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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 computationThu, 21 Jan 2016 19:08:26 +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/2016/Jan/21/t145340332907rvhwo2w23thbh.htm/, Retrieved Mon, 29 Apr 2024 03:04:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289953, Retrieved Mon, 29 Apr 2024 03:04:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMPD      [Variance Reduction Matrix] [] [2016-01-21 19:08:26] [b4db83eca3959643135a70d21d8ecc04] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289953&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289953&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.500757Range3Trim Var.0.27874
V(Y[t],d=1,D=0)0.0766941Range2Trim Var.0.0269405
V(Y[t],d=2,D=0)0.121357Range2.3Trim Var.0.0425039
V(Y[t],d=3,D=0)0.338873Range4.2Trim Var.0.122571
V(Y[t],d=0,D=1)1.14281Range5.1Trim Var.0.596657
V(Y[t],d=1,D=1)0.23192Range3.8Trim Var.0.0689401
V(Y[t],d=2,D=1)0.362609Range4.2Trim Var.0.108683
V(Y[t],d=3,D=1)1.02833Range7.4Trim Var.0.310366
V(Y[t],d=0,D=2)3.53999Range9.4Trim Var.1.70858
V(Y[t],d=1,D=2)0.805915Range6.4Trim Var.0.209557
V(Y[t],d=2,D=2)1.31053Range7.4Trim Var.0.457632
V(Y[t],d=3,D=2)3.78087Range12.9Trim Var.1.2169

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.500757 & Range & 3 & Trim Var. & 0.27874 \tabularnewline
V(Y[t],d=1,D=0) & 0.0766941 & Range & 2 & Trim Var. & 0.0269405 \tabularnewline
V(Y[t],d=2,D=0) & 0.121357 & Range & 2.3 & Trim Var. & 0.0425039 \tabularnewline
V(Y[t],d=3,D=0) & 0.338873 & Range & 4.2 & Trim Var. & 0.122571 \tabularnewline
V(Y[t],d=0,D=1) & 1.14281 & Range & 5.1 & Trim Var. & 0.596657 \tabularnewline
V(Y[t],d=1,D=1) & 0.23192 & Range & 3.8 & Trim Var. & 0.0689401 \tabularnewline
V(Y[t],d=2,D=1) & 0.362609 & Range & 4.2 & Trim Var. & 0.108683 \tabularnewline
V(Y[t],d=3,D=1) & 1.02833 & Range & 7.4 & Trim Var. & 0.310366 \tabularnewline
V(Y[t],d=0,D=2) & 3.53999 & Range & 9.4 & Trim Var. & 1.70858 \tabularnewline
V(Y[t],d=1,D=2) & 0.805915 & Range & 6.4 & Trim Var. & 0.209557 \tabularnewline
V(Y[t],d=2,D=2) & 1.31053 & Range & 7.4 & Trim Var. & 0.457632 \tabularnewline
V(Y[t],d=3,D=2) & 3.78087 & Range & 12.9 & Trim Var. & 1.2169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289953&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.500757[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.27874[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0766941[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]0.0269405[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.121357[/C][C]Range[/C][C]2.3[/C][C]Trim Var.[/C][C]0.0425039[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.338873[/C][C]Range[/C][C]4.2[/C][C]Trim Var.[/C][C]0.122571[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.14281[/C][C]Range[/C][C]5.1[/C][C]Trim Var.[/C][C]0.596657[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.23192[/C][C]Range[/C][C]3.8[/C][C]Trim Var.[/C][C]0.0689401[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.362609[/C][C]Range[/C][C]4.2[/C][C]Trim Var.[/C][C]0.108683[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.02833[/C][C]Range[/C][C]7.4[/C][C]Trim Var.[/C][C]0.310366[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3.53999[/C][C]Range[/C][C]9.4[/C][C]Trim Var.[/C][C]1.70858[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.805915[/C][C]Range[/C][C]6.4[/C][C]Trim Var.[/C][C]0.209557[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1.31053[/C][C]Range[/C][C]7.4[/C][C]Trim Var.[/C][C]0.457632[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]3.78087[/C][C]Range[/C][C]12.9[/C][C]Trim Var.[/C][C]1.2169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289953&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)0.500757Range3Trim Var.0.27874
V(Y[t],d=1,D=0)0.0766941Range2Trim Var.0.0269405
V(Y[t],d=2,D=0)0.121357Range2.3Trim Var.0.0425039
V(Y[t],d=3,D=0)0.338873Range4.2Trim Var.0.122571
V(Y[t],d=0,D=1)1.14281Range5.1Trim Var.0.596657
V(Y[t],d=1,D=1)0.23192Range3.8Trim Var.0.0689401
V(Y[t],d=2,D=1)0.362609Range4.2Trim Var.0.108683
V(Y[t],d=3,D=1)1.02833Range7.4Trim Var.0.310366
V(Y[t],d=0,D=2)3.53999Range9.4Trim Var.1.70858
V(Y[t],d=1,D=2)0.805915Range6.4Trim Var.0.209557
V(Y[t],d=2,D=2)1.31053Range7.4Trim Var.0.457632
V(Y[t],d=3,D=2)3.78087Range12.9Trim Var.1.2169


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()