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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, 22 Dec 2016 16:37:31 +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/22/t1482421137tm9xz4zreuwrs37.htm/, Retrieved Mon, 29 Apr 2024 00:35:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302547, Retrieved Mon, 29 Apr 2024 00:35:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

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...] [2016-12-22 15:37:31] [55eb8f21ed24cda91766c505eb72bb6f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3949.9
4010.65
4381.8
4238.25
4178.1
4702.25
3944.1
4208.5
4743.45
4948.25
4735.45
4843.15
4757.75
5227.15
5739.65
4981.45
5020.05
5149.15
4513.35
4762.55
4990.45
4963.35
5010
4983.3
4924.7
5175.25
5470.3
4969.4
5020.5
5519.2
4510.75
4934.45
5430.65
5254.7
4897.8
5305.7
5055.7
5409
5683
5125.55
4965.2
5373.3
4556.1
4714.25
5513.85
5258.45
5111.4
5422.25
4753.3
5455.5
5909.15
5524.4
5477.8
5907.75
5072.55
5171
5871.4
5812.45
5692.2
5838.1
5438.2
6041.05
6335.6
5891.8
5909.65
6449.75
5312.25
5828.1
6466.15
6328.35
6131.8
6734.2
6037.25
6412.4
6785.55
6386
6045.25
6597.25
5355.9
5773.35
6539.6
6149.2
6373.45
6504.7
5451.25
6119.9
6954.95
6139.7
6383.25
6643.7
5547.75
5974
6583.6
6571.55
5736.5
6027.2
5302.65
5825.85
5910.6
5733.65
5914.3
6128.25
5680.5
5926.3
6270.5
6263
6064.55
5706.6
5365
5884.2
6504.4
6174.3
6123.65
6698.95
5256.55
5838.2

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=302547&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=302547&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302547&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)475294Range3010.85Trim Var.322443
V(Y[t],d=1,D=0)249991Range2277.45Trim Var.164164
V(Y[t],d=2,D=0)695381Range4041.75Trim Var.442829
V(Y[t],d=3,D=0)2086220Range6727.85Trim Var.1369410
V(Y[t],d=0,D=1)151816Range2402.2Trim Var.81560.4
V(Y[t],d=1,D=1)104465Range1707.5Trim Var.54375.5
V(Y[t],d=2,D=1)298780Range2826.25Trim Var.161077
V(Y[t],d=3,D=1)960807Range4776.3Trim Var.512558
V(Y[t],d=0,D=2)308540Range3265.35Trim Var.163775
V(Y[t],d=1,D=2)303148Range3338.75Trim Var.151461
V(Y[t],d=2,D=2)868900Range4770.2Trim Var.438865
V(Y[t],d=3,D=2)2792630Range8795.45Trim Var.1527270

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 475294 & Range & 3010.85 & Trim Var. & 322443 \tabularnewline
V(Y[t],d=1,D=0) & 249991 & Range & 2277.45 & Trim Var. & 164164 \tabularnewline
V(Y[t],d=2,D=0) & 695381 & Range & 4041.75 & Trim Var. & 442829 \tabularnewline
V(Y[t],d=3,D=0) & 2086220 & Range & 6727.85 & Trim Var. & 1369410 \tabularnewline
V(Y[t],d=0,D=1) & 151816 & Range & 2402.2 & Trim Var. & 81560.4 \tabularnewline
V(Y[t],d=1,D=1) & 104465 & Range & 1707.5 & Trim Var. & 54375.5 \tabularnewline
V(Y[t],d=2,D=1) & 298780 & Range & 2826.25 & Trim Var. & 161077 \tabularnewline
V(Y[t],d=3,D=1) & 960807 & Range & 4776.3 & Trim Var. & 512558 \tabularnewline
V(Y[t],d=0,D=2) & 308540 & Range & 3265.35 & Trim Var. & 163775 \tabularnewline
V(Y[t],d=1,D=2) & 303148 & Range & 3338.75 & Trim Var. & 151461 \tabularnewline
V(Y[t],d=2,D=2) & 868900 & Range & 4770.2 & Trim Var. & 438865 \tabularnewline
V(Y[t],d=3,D=2) & 2792630 & Range & 8795.45 & Trim Var. & 1527270 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302547&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]475294[/C][C]Range[/C][C]3010.85[/C][C]Trim Var.[/C][C]322443[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]249991[/C][C]Range[/C][C]2277.45[/C][C]Trim Var.[/C][C]164164[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]695381[/C][C]Range[/C][C]4041.75[/C][C]Trim Var.[/C][C]442829[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2086220[/C][C]Range[/C][C]6727.85[/C][C]Trim Var.[/C][C]1369410[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]151816[/C][C]Range[/C][C]2402.2[/C][C]Trim Var.[/C][C]81560.4[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]104465[/C][C]Range[/C][C]1707.5[/C][C]Trim Var.[/C][C]54375.5[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]298780[/C][C]Range[/C][C]2826.25[/C][C]Trim Var.[/C][C]161077[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]960807[/C][C]Range[/C][C]4776.3[/C][C]Trim Var.[/C][C]512558[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]308540[/C][C]Range[/C][C]3265.35[/C][C]Trim Var.[/C][C]163775[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]303148[/C][C]Range[/C][C]3338.75[/C][C]Trim Var.[/C][C]151461[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]868900[/C][C]Range[/C][C]4770.2[/C][C]Trim Var.[/C][C]438865[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2792630[/C][C]Range[/C][C]8795.45[/C][C]Trim Var.[/C][C]1527270[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302547&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302547&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)475294Range3010.85Trim Var.322443
V(Y[t],d=1,D=0)249991Range2277.45Trim Var.164164
V(Y[t],d=2,D=0)695381Range4041.75Trim Var.442829
V(Y[t],d=3,D=0)2086220Range6727.85Trim Var.1369410
V(Y[t],d=0,D=1)151816Range2402.2Trim Var.81560.4
V(Y[t],d=1,D=1)104465Range1707.5Trim Var.54375.5
V(Y[t],d=2,D=1)298780Range2826.25Trim Var.161077
V(Y[t],d=3,D=1)960807Range4776.3Trim Var.512558
V(Y[t],d=0,D=2)308540Range3265.35Trim Var.163775
V(Y[t],d=1,D=2)303148Range3338.75Trim Var.151461
V(Y[t],d=2,D=2)868900Range4770.2Trim Var.438865
V(Y[t],d=3,D=2)2792630Range8795.45Trim Var.1527270


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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()