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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 computationSat, 17 Dec 2016 16:24:29 +0100
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/Dec/17/t14819882918hvkqcup1ktlhqh.htm/, Retrieved Thu, 02 May 2024 11:36:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300852, Retrieved Thu, 02 May 2024 11:36:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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] [variance reductio...] [2016-12-17 15:24:29] [a7a7548920aea9a2d444ee0f03dc394a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3800
1650
4250
3200
2050
3600
3700
6000
8550
9050
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8550
6700
3850
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4900
6650
10050
8300
7650
5750
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3250
1150
1950
2850
2950
4950
6000
6650
6150
4300
4450
1250
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5050
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5150
6450
3700
3300
2000
2650
900
1350
4550
1850
3650
3250
5950
4050
3250
2200
1050
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2650
650
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2900
6450
3100
6050
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1550
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3850
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4600
3350
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3300

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300852&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300852&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)4183210Range9400Trim Var.2502790
V(Y[t],d=1,D=0)2525120Range6900Trim Var.1578000
V(Y[t],d=2,D=0)6012170Range13200Trim Var.3273930
V(Y[t],d=3,D=0)19184600Range24300Trim Var.10625000
V(Y[t],d=0,D=1)1970950Range7100Trim Var.1052060
V(Y[t],d=1,D=1)3498840Range9550Trim Var.2128210
V(Y[t],d=2,D=1)9795280Range16650Trim Var.5872050
V(Y[t],d=3,D=1)30534900Range30300Trim Var.17907000
V(Y[t],d=0,D=2)5745290Range12800Trim Var.2820610
V(Y[t],d=1,D=2)11010200Range15800Trim Var.6900930
V(Y[t],d=2,D=2)29770100Range25350Trim Var.16659900
V(Y[t],d=3,D=2)89803200Range49600Trim Var.52734300

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 4183210 & Range & 9400 & Trim Var. & 2502790 \tabularnewline
V(Y[t],d=1,D=0) & 2525120 & Range & 6900 & Trim Var. & 1578000 \tabularnewline
V(Y[t],d=2,D=0) & 6012170 & Range & 13200 & Trim Var. & 3273930 \tabularnewline
V(Y[t],d=3,D=0) & 19184600 & Range & 24300 & Trim Var. & 10625000 \tabularnewline
V(Y[t],d=0,D=1) & 1970950 & Range & 7100 & Trim Var. & 1052060 \tabularnewline
V(Y[t],d=1,D=1) & 3498840 & Range & 9550 & Trim Var. & 2128210 \tabularnewline
V(Y[t],d=2,D=1) & 9795280 & Range & 16650 & Trim Var. & 5872050 \tabularnewline
V(Y[t],d=3,D=1) & 30534900 & Range & 30300 & Trim Var. & 17907000 \tabularnewline
V(Y[t],d=0,D=2) & 5745290 & Range & 12800 & Trim Var. & 2820610 \tabularnewline
V(Y[t],d=1,D=2) & 11010200 & Range & 15800 & Trim Var. & 6900930 \tabularnewline
V(Y[t],d=2,D=2) & 29770100 & Range & 25350 & Trim Var. & 16659900 \tabularnewline
V(Y[t],d=3,D=2) & 89803200 & Range & 49600 & Trim Var. & 52734300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300852&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]4183210[/C][C]Range[/C][C]9400[/C][C]Trim Var.[/C][C]2502790[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2525120[/C][C]Range[/C][C]6900[/C][C]Trim Var.[/C][C]1578000[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]6012170[/C][C]Range[/C][C]13200[/C][C]Trim Var.[/C][C]3273930[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]19184600[/C][C]Range[/C][C]24300[/C][C]Trim Var.[/C][C]10625000[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1970950[/C][C]Range[/C][C]7100[/C][C]Trim Var.[/C][C]1052060[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3498840[/C][C]Range[/C][C]9550[/C][C]Trim Var.[/C][C]2128210[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]9795280[/C][C]Range[/C][C]16650[/C][C]Trim Var.[/C][C]5872050[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]30534900[/C][C]Range[/C][C]30300[/C][C]Trim Var.[/C][C]17907000[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]5745290[/C][C]Range[/C][C]12800[/C][C]Trim Var.[/C][C]2820610[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]11010200[/C][C]Range[/C][C]15800[/C][C]Trim Var.[/C][C]6900930[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]29770100[/C][C]Range[/C][C]25350[/C][C]Trim Var.[/C][C]16659900[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]89803200[/C][C]Range[/C][C]49600[/C][C]Trim Var.[/C][C]52734300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300852&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)4183210Range9400Trim Var.2502790
V(Y[t],d=1,D=0)2525120Range6900Trim Var.1578000
V(Y[t],d=2,D=0)6012170Range13200Trim Var.3273930
V(Y[t],d=3,D=0)19184600Range24300Trim Var.10625000
V(Y[t],d=0,D=1)1970950Range7100Trim Var.1052060
V(Y[t],d=1,D=1)3498840Range9550Trim Var.2128210
V(Y[t],d=2,D=1)9795280Range16650Trim Var.5872050
V(Y[t],d=3,D=1)30534900Range30300Trim Var.17907000
V(Y[t],d=0,D=2)5745290Range12800Trim Var.2820610
V(Y[t],d=1,D=2)11010200Range15800Trim Var.6900930
V(Y[t],d=2,D=2)29770100Range25350Trim Var.16659900
V(Y[t],d=3,D=2)89803200Range49600Trim Var.52734300


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()