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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, 19 Dec 2017 19:53:12 +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/2017/Dec/19/t1513709777zwshznm4dg636fc.htm/, Retrieved Thu, 16 May 2024 00:35:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310396, Retrieved Thu, 16 May 2024 00:35:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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...] [2017-12-19 18:53:12] [814e681488f8450cd741da3dc59dcc6f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8
8
3
5
7
3
5
7
2
2
9
1
4
2
8
5
1
1
4
8
8
9
1
7
9
6
2
9
9
5
7
4
8
5
6
5
2
7
6
1
8
2
2
1
3
5
9
6
7
6
5
7
8
1
8
7
2
1
8
2
8
4
7
5
4
2
9
5
5
7
9
5
2
7
1
6
2
9
5
1
3
1
5
2
4
5
4
8
4
6
9
3
8
8
8
5
5
8
2
7
7
5
8
1
4
1
5
7
3
6
6
9
4
9
9
8
9
5
9
2
1
3
7
6
8
3
3
7
7
1
7
7
5
4
5
2
7
8
6
7
6
9
2
1
8
5
3
2
4
9
8
6
7
3
9
1
4
1
7
6
2
7
8
8
2
4
2
4
2
3
3
5
5
9
3
2
2
5
9
6
6
8
8
9
2
7
1
8
9
6
6
8

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310396&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310396&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)6.86377Range8Trim Var.4.38896
V(Y[t],d=1,D=0)13.9263Range15Trim Var.7.76435
V(Y[t],d=2,D=0)42.5819Range29Trim Var.26.0863
V(Y[t],d=3,D=0)143.961Range51Trim Var.97.2885
V(Y[t],d=0,D=1)14.9173Range16Trim Var.9.80369
V(Y[t],d=1,D=1)26.9202Range29Trim Var.16.3459
V(Y[t],d=2,D=1)78.0832Range51Trim Var.44.5086
V(Y[t],d=3,D=1)254.897Range89Trim Var.150.55
V(Y[t],d=0,D=2)45.9639Range28Trim Var.32.1615
V(Y[t],d=1,D=2)80.4248Range48Trim Var.42.3677
V(Y[t],d=2,D=2)233.579Range87Trim Var.136.208
V(Y[t],d=3,D=2)764.63Range146Trim Var.433.286

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 6.86377 & Range & 8 & Trim Var. & 4.38896 \tabularnewline
V(Y[t],d=1,D=0) & 13.9263 & Range & 15 & Trim Var. & 7.76435 \tabularnewline
V(Y[t],d=2,D=0) & 42.5819 & Range & 29 & Trim Var. & 26.0863 \tabularnewline
V(Y[t],d=3,D=0) & 143.961 & Range & 51 & Trim Var. & 97.2885 \tabularnewline
V(Y[t],d=0,D=1) & 14.9173 & Range & 16 & Trim Var. & 9.80369 \tabularnewline
V(Y[t],d=1,D=1) & 26.9202 & Range & 29 & Trim Var. & 16.3459 \tabularnewline
V(Y[t],d=2,D=1) & 78.0832 & Range & 51 & Trim Var. & 44.5086 \tabularnewline
V(Y[t],d=3,D=1) & 254.897 & Range & 89 & Trim Var. & 150.55 \tabularnewline
V(Y[t],d=0,D=2) & 45.9639 & Range & 28 & Trim Var. & 32.1615 \tabularnewline
V(Y[t],d=1,D=2) & 80.4248 & Range & 48 & Trim Var. & 42.3677 \tabularnewline
V(Y[t],d=2,D=2) & 233.579 & Range & 87 & Trim Var. & 136.208 \tabularnewline
V(Y[t],d=3,D=2) & 764.63 & Range & 146 & Trim Var. & 433.286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310396&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]6.86377[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]4.38896[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]13.9263[/C][C]Range[/C][C]15[/C][C]Trim Var.[/C][C]7.76435[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]42.5819[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]26.0863[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]143.961[/C][C]Range[/C][C]51[/C][C]Trim Var.[/C][C]97.2885[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.9173[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]9.80369[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]26.9202[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]16.3459[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]78.0832[/C][C]Range[/C][C]51[/C][C]Trim Var.[/C][C]44.5086[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]254.897[/C][C]Range[/C][C]89[/C][C]Trim Var.[/C][C]150.55[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]45.9639[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]32.1615[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]80.4248[/C][C]Range[/C][C]48[/C][C]Trim Var.[/C][C]42.3677[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]233.579[/C][C]Range[/C][C]87[/C][C]Trim Var.[/C][C]136.208[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]764.63[/C][C]Range[/C][C]146[/C][C]Trim Var.[/C][C]433.286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310396&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)6.86377Range8Trim Var.4.38896
V(Y[t],d=1,D=0)13.9263Range15Trim Var.7.76435
V(Y[t],d=2,D=0)42.5819Range29Trim Var.26.0863
V(Y[t],d=3,D=0)143.961Range51Trim Var.97.2885
V(Y[t],d=0,D=1)14.9173Range16Trim Var.9.80369
V(Y[t],d=1,D=1)26.9202Range29Trim Var.16.3459
V(Y[t],d=2,D=1)78.0832Range51Trim Var.44.5086
V(Y[t],d=3,D=1)254.897Range89Trim Var.150.55
V(Y[t],d=0,D=2)45.9639Range28Trim Var.32.1615
V(Y[t],d=1,D=2)80.4248Range48Trim Var.42.3677
V(Y[t],d=2,D=2)233.579Range87Trim Var.136.208
V(Y[t],d=3,D=2)764.63Range146Trim Var.433.286


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()