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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 computationFri, 16 Dec 2016 15:27:44 +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/16/t14818984895250agayy8tu9tr.htm/, Retrieved Thu, 03 Apr 2025 05:47:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300308, Retrieved Thu, 03 Apr 2025 05:47:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- RM D      [Variance Reduction Matrix] [] [2016-12-16 14:27:44] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5495
5365
5315
5335
5330
5365
5435
5535
5585
5615
5610
5585
5820
5645
5650
5725
5825
5870
5860
5835
5840
5805
5770
5680
5675
5690
5610
5610
5630
5615
5585
5555
5585
5530
5425
5630
5560
5435
5320
5150
5125
5025
5020
4935
4880
4870
4920
4935
5000
4955
4970
4990
4920
4930
4955
5000
5025
5075
5075
5105
5050
5055
5095
5025
5050
5035
4985
5005
4910
4910
4870
4850
4810
4810
4730
4850
4895
4845
4805
4825
4830
4720
4785
4705
4840
4820
4795
4810
4840
4810
4835
4860
4845
4935
4870
4830
4895
4920
4925
4860
4820
4790
4775
4735
4755
4745
4705
4665
4650
4590
4625
4685
4665
4675
4690
4600

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=300308&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=300308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300308&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)139059Range1280Trim Var.110717
V(Y[t],d=1,D=0)4088.68Range410Trim Var.1929.25
V(Y[t],d=2,D=0)8653.42Range720Trim Var.3256.01
V(Y[t],d=3,D=0)27035Range1260Trim Var.10061.9
V(Y[t],d=0,D=1)63379.6Range1210Trim Var.34701
V(Y[t],d=1,D=1)8351.92Range535Trim Var.4531.26
V(Y[t],d=2,D=1)18992.8Range790Trim Var.8563.17
V(Y[t],d=3,D=1)62079.8Range1395Trim Var.30252.8
V(Y[t],d=0,D=2)137578Range1625Trim Var.86056.1
V(Y[t],d=1,D=2)25212.5Range845Trim Var.14730.7
V(Y[t],d=2,D=2)59411.4Range1395Trim Var.32674.5
V(Y[t],d=3,D=2)194626Range2370Trim Var.113836

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 139059 & Range & 1280 & Trim Var. & 110717 \tabularnewline
V(Y[t],d=1,D=0) & 4088.68 & Range & 410 & Trim Var. & 1929.25 \tabularnewline
V(Y[t],d=2,D=0) & 8653.42 & Range & 720 & Trim Var. & 3256.01 \tabularnewline
V(Y[t],d=3,D=0) & 27035 & Range & 1260 & Trim Var. & 10061.9 \tabularnewline
V(Y[t],d=0,D=1) & 63379.6 & Range & 1210 & Trim Var. & 34701 \tabularnewline
V(Y[t],d=1,D=1) & 8351.92 & Range & 535 & Trim Var. & 4531.26 \tabularnewline
V(Y[t],d=2,D=1) & 18992.8 & Range & 790 & Trim Var. & 8563.17 \tabularnewline
V(Y[t],d=3,D=1) & 62079.8 & Range & 1395 & Trim Var. & 30252.8 \tabularnewline
V(Y[t],d=0,D=2) & 137578 & Range & 1625 & Trim Var. & 86056.1 \tabularnewline
V(Y[t],d=1,D=2) & 25212.5 & Range & 845 & Trim Var. & 14730.7 \tabularnewline
V(Y[t],d=2,D=2) & 59411.4 & Range & 1395 & Trim Var. & 32674.5 \tabularnewline
V(Y[t],d=3,D=2) & 194626 & Range & 2370 & Trim Var. & 113836 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300308&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]139059[/C][C]Range[/C][C]1280[/C][C]Trim Var.[/C][C]110717[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]4088.68[/C][C]Range[/C][C]410[/C][C]Trim Var.[/C][C]1929.25[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]8653.42[/C][C]Range[/C][C]720[/C][C]Trim Var.[/C][C]3256.01[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]27035[/C][C]Range[/C][C]1260[/C][C]Trim Var.[/C][C]10061.9[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]63379.6[/C][C]Range[/C][C]1210[/C][C]Trim Var.[/C][C]34701[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8351.92[/C][C]Range[/C][C]535[/C][C]Trim Var.[/C][C]4531.26[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]18992.8[/C][C]Range[/C][C]790[/C][C]Trim Var.[/C][C]8563.17[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]62079.8[/C][C]Range[/C][C]1395[/C][C]Trim Var.[/C][C]30252.8[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]137578[/C][C]Range[/C][C]1625[/C][C]Trim Var.[/C][C]86056.1[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]25212.5[/C][C]Range[/C][C]845[/C][C]Trim Var.[/C][C]14730.7[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]59411.4[/C][C]Range[/C][C]1395[/C][C]Trim Var.[/C][C]32674.5[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]194626[/C][C]Range[/C][C]2370[/C][C]Trim Var.[/C][C]113836[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300308&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)139059Range1280Trim Var.110717
V(Y[t],d=1,D=0)4088.68Range410Trim Var.1929.25
V(Y[t],d=2,D=0)8653.42Range720Trim Var.3256.01
V(Y[t],d=3,D=0)27035Range1260Trim Var.10061.9
V(Y[t],d=0,D=1)63379.6Range1210Trim Var.34701
V(Y[t],d=1,D=1)8351.92Range535Trim Var.4531.26
V(Y[t],d=2,D=1)18992.8Range790Trim Var.8563.17
V(Y[t],d=3,D=1)62079.8Range1395Trim Var.30252.8
V(Y[t],d=0,D=2)137578Range1625Trim Var.86056.1
V(Y[t],d=1,D=2)25212.5Range845Trim Var.14730.7
V(Y[t],d=2,D=2)59411.4Range1395Trim Var.32674.5
V(Y[t],d=3,D=2)194626Range2370Trim Var.113836


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
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()