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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 16:35:21 +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/t1481902564rh79ezppt31wjpw.htm/, Retrieved Thu, 02 May 2024 14:36:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300371, Retrieved Thu, 02 May 2024 14:36:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

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]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [Variance Reduction Matrix] [] [2016-12-16 15:35:21] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1880
3600
4600
6560
7840
8560
10120
9240
9320
7000
3960
4680
3920
1560
4800
5240
8000
9760
9800
9280
7680
7760
5680
4560
1560
3680
4200
7400
7040
8480
9720
9760
9440
7240
5080
4080
5120
4400
5160
6680
8240
8960
9280
9880
8480
7320
4880
5280
4080
4720
6360
5760
9000
9160
10480
10160
9120
7880
5080
4360
4480
6000
6120
6200
8960
8680
10240
10920
8440
7760
5320
3920
4040
2960
6280
6320
7160
8160

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=300371&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=300371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300371&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)5530010Range9360Trim Var.4038890
V(Y[t],d=1,D=0)2487770Range6360Trim Var.1688030
V(Y[t],d=2,D=0)4062890Range9160Trim Var.2529830
V(Y[t],d=3,D=0)13000200Range15600Trim Var.8635400
V(Y[t],d=0,D=1)1265580Range6600Trim Var.598301
V(Y[t],d=1,D=1)2947820Range8560Trim Var.1649030
V(Y[t],d=2,D=1)8931130Range13920Trim Var.4837240
V(Y[t],d=3,D=1)29632700Range26600Trim Var.16485700
V(Y[t],d=0,D=2)3939520Range10520Trim Var.1808050
V(Y[t],d=1,D=2)9740580Range15880Trim Var.5455130
V(Y[t],d=2,D=2)29133100Range24080Trim Var.16326200
V(Y[t],d=3,D=2)95874400Range42000Trim Var.55061200

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 5530010 & Range & 9360 & Trim Var. & 4038890 \tabularnewline
V(Y[t],d=1,D=0) & 2487770 & Range & 6360 & Trim Var. & 1688030 \tabularnewline
V(Y[t],d=2,D=0) & 4062890 & Range & 9160 & Trim Var. & 2529830 \tabularnewline
V(Y[t],d=3,D=0) & 13000200 & Range & 15600 & Trim Var. & 8635400 \tabularnewline
V(Y[t],d=0,D=1) & 1265580 & Range & 6600 & Trim Var. & 598301 \tabularnewline
V(Y[t],d=1,D=1) & 2947820 & Range & 8560 & Trim Var. & 1649030 \tabularnewline
V(Y[t],d=2,D=1) & 8931130 & Range & 13920 & Trim Var. & 4837240 \tabularnewline
V(Y[t],d=3,D=1) & 29632700 & Range & 26600 & Trim Var. & 16485700 \tabularnewline
V(Y[t],d=0,D=2) & 3939520 & Range & 10520 & Trim Var. & 1808050 \tabularnewline
V(Y[t],d=1,D=2) & 9740580 & Range & 15880 & Trim Var. & 5455130 \tabularnewline
V(Y[t],d=2,D=2) & 29133100 & Range & 24080 & Trim Var. & 16326200 \tabularnewline
V(Y[t],d=3,D=2) & 95874400 & Range & 42000 & Trim Var. & 55061200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300371&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]5530010[/C][C]Range[/C][C]9360[/C][C]Trim Var.[/C][C]4038890[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2487770[/C][C]Range[/C][C]6360[/C][C]Trim Var.[/C][C]1688030[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]4062890[/C][C]Range[/C][C]9160[/C][C]Trim Var.[/C][C]2529830[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]13000200[/C][C]Range[/C][C]15600[/C][C]Trim Var.[/C][C]8635400[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1265580[/C][C]Range[/C][C]6600[/C][C]Trim Var.[/C][C]598301[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2947820[/C][C]Range[/C][C]8560[/C][C]Trim Var.[/C][C]1649030[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]8931130[/C][C]Range[/C][C]13920[/C][C]Trim Var.[/C][C]4837240[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]29632700[/C][C]Range[/C][C]26600[/C][C]Trim Var.[/C][C]16485700[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3939520[/C][C]Range[/C][C]10520[/C][C]Trim Var.[/C][C]1808050[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]9740580[/C][C]Range[/C][C]15880[/C][C]Trim Var.[/C][C]5455130[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]29133100[/C][C]Range[/C][C]24080[/C][C]Trim Var.[/C][C]16326200[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]95874400[/C][C]Range[/C][C]42000[/C][C]Trim Var.[/C][C]55061200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300371&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)5530010Range9360Trim Var.4038890
V(Y[t],d=1,D=0)2487770Range6360Trim Var.1688030
V(Y[t],d=2,D=0)4062890Range9160Trim Var.2529830
V(Y[t],d=3,D=0)13000200Range15600Trim Var.8635400
V(Y[t],d=0,D=1)1265580Range6600Trim Var.598301
V(Y[t],d=1,D=1)2947820Range8560Trim Var.1649030
V(Y[t],d=2,D=1)8931130Range13920Trim Var.4837240
V(Y[t],d=3,D=1)29632700Range26600Trim Var.16485700
V(Y[t],d=0,D=2)3939520Range10520Trim Var.1808050
V(Y[t],d=1,D=2)9740580Range15880Trim Var.5455130
V(Y[t],d=2,D=2)29133100Range24080Trim Var.16326200
V(Y[t],d=3,D=2)95874400Range42000Trim Var.55061200


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()