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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, 23 Dec 2016 08:07:30 +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/23/t1482476867h17xgddj93x977z.htm/, Retrieved Tue, 07 May 2024 11:14:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302741, Retrieved Tue, 07 May 2024 11:14:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

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...] [2016-12-23 07:07:30] [36884fbde1107444791dd71ee0072a5a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8160
6540
6660
8260
6340
6940
6320
8540
8360
8940
8760
8820
8040
8780
7780
6600
6400
7120
6800
8100
9620
9120
7880
7740
7400
7820
6260
5860
5600
5820
6720
6940
7940
7680
8040
8060
6900
5460
6180
5460
5240
5440
5280
7120
6160
7320
7460
5320
6480
5600
6540
4920
5560
6260
5580
6380
6020
6280
6100
5020
5100
5480
5980
5920
5360
4800
4980
5880
5880
7080
7760
4620
5280
5280
5360
4680
5040
5760
6120
5140
5520
5700
4540
4880
5080
5220
4980
5000
4780
5820
5480
4880
5460
5580
5660
5280
5440
4760
4460
5220
4640
4980
4800
5540
5920
5780
6020
5620

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=302741&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=302741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302741&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)1523840Range5160Trim Var.1054200
V(Y[t],d=1,D=0)722031Range5360Trim Var.366731
V(Y[t],d=2,D=0)1840650Range7620Trim Var.982767
V(Y[t],d=3,D=0)5925370Range12960Trim Var.3078100
V(Y[t],d=0,D=1)773388Range5460Trim Var.378794
V(Y[t],d=1,D=1)1196710Range6260Trim Var.681568
V(Y[t],d=2,D=1)3213100Range9260Trim Var.1738760
V(Y[t],d=3,D=1)9945810Range16220Trim Var.5754510
V(Y[t],d=0,D=2)2136560Range9220Trim Var.990477
V(Y[t],d=1,D=2)3469850Range9740Trim Var.2194300
V(Y[t],d=2,D=2)9325930Range15520Trim Var.5494070
V(Y[t],d=3,D=2)29171000Range26720Trim Var.17872900

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1523840 & Range & 5160 & Trim Var. & 1054200 \tabularnewline
V(Y[t],d=1,D=0) & 722031 & Range & 5360 & Trim Var. & 366731 \tabularnewline
V(Y[t],d=2,D=0) & 1840650 & Range & 7620 & Trim Var. & 982767 \tabularnewline
V(Y[t],d=3,D=0) & 5925370 & Range & 12960 & Trim Var. & 3078100 \tabularnewline
V(Y[t],d=0,D=1) & 773388 & Range & 5460 & Trim Var. & 378794 \tabularnewline
V(Y[t],d=1,D=1) & 1196710 & Range & 6260 & Trim Var. & 681568 \tabularnewline
V(Y[t],d=2,D=1) & 3213100 & Range & 9260 & Trim Var. & 1738760 \tabularnewline
V(Y[t],d=3,D=1) & 9945810 & Range & 16220 & Trim Var. & 5754510 \tabularnewline
V(Y[t],d=0,D=2) & 2136560 & Range & 9220 & Trim Var. & 990477 \tabularnewline
V(Y[t],d=1,D=2) & 3469850 & Range & 9740 & Trim Var. & 2194300 \tabularnewline
V(Y[t],d=2,D=2) & 9325930 & Range & 15520 & Trim Var. & 5494070 \tabularnewline
V(Y[t],d=3,D=2) & 29171000 & Range & 26720 & Trim Var. & 17872900 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302741&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1523840[/C][C]Range[/C][C]5160[/C][C]Trim Var.[/C][C]1054200[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]722031[/C][C]Range[/C][C]5360[/C][C]Trim Var.[/C][C]366731[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1840650[/C][C]Range[/C][C]7620[/C][C]Trim Var.[/C][C]982767[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5925370[/C][C]Range[/C][C]12960[/C][C]Trim Var.[/C][C]3078100[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]773388[/C][C]Range[/C][C]5460[/C][C]Trim Var.[/C][C]378794[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1196710[/C][C]Range[/C][C]6260[/C][C]Trim Var.[/C][C]681568[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3213100[/C][C]Range[/C][C]9260[/C][C]Trim Var.[/C][C]1738760[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]9945810[/C][C]Range[/C][C]16220[/C][C]Trim Var.[/C][C]5754510[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2136560[/C][C]Range[/C][C]9220[/C][C]Trim Var.[/C][C]990477[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]3469850[/C][C]Range[/C][C]9740[/C][C]Trim Var.[/C][C]2194300[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]9325930[/C][C]Range[/C][C]15520[/C][C]Trim Var.[/C][C]5494070[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]29171000[/C][C]Range[/C][C]26720[/C][C]Trim Var.[/C][C]17872900[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302741&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)1523840Range5160Trim Var.1054200
V(Y[t],d=1,D=0)722031Range5360Trim Var.366731
V(Y[t],d=2,D=0)1840650Range7620Trim Var.982767
V(Y[t],d=3,D=0)5925370Range12960Trim Var.3078100
V(Y[t],d=0,D=1)773388Range5460Trim Var.378794
V(Y[t],d=1,D=1)1196710Range6260Trim Var.681568
V(Y[t],d=2,D=1)3213100Range9260Trim Var.1738760
V(Y[t],d=3,D=1)9945810Range16220Trim Var.5754510
V(Y[t],d=0,D=2)2136560Range9220Trim Var.990477
V(Y[t],d=1,D=2)3469850Range9740Trim Var.2194300
V(Y[t],d=2,D=2)9325930Range15520Trim Var.5494070
V(Y[t],d=3,D=2)29171000Range26720Trim Var.17872900


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()