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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 computationSat, 17 Dec 2016 12:19:48 +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/17/t1481973622yn0xakmsk5qwxfj.htm/, Retrieved Thu, 02 May 2024 08:55:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300701, Retrieved Thu, 02 May 2024 08:55:01 +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] [] [2016-12-17 11:19:48] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9290
6160
8320
8310
6750
8710
6300
5710
5740
6710
7310
7240
8650
8330
7810
8260
6680
5580
6340
4490
5000
7030
6100
9740
7940
7740
7820
7820
5380
7070
6970
4080
4930
4820
6220
6360
7630
5130
6960
5350
6290
4630
5130
3620
3980
3120
4310
4250
5730
3630
5680

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=300701&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=300701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300701&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)2542980Range6620Trim Var.1730860
V(Y[t],d=1,D=0)2304960Range6770Trim Var.1546290
V(Y[t],d=2,D=0)6786050Range10730Trim Var.4649310
V(Y[t],d=3,D=0)22481700Range18110Trim Var.15896200
V(Y[t],d=0,D=1)1737710Range5880Trim Var.1006240
V(Y[t],d=1,D=1)3885370Range7210Trim Var.2881390
V(Y[t],d=2,D=1)13461900Range13490Trim Var.9673730
V(Y[t],d=3,D=1)48659300Range24560Trim Var.36914700
V(Y[t],d=0,D=2)4342270Range10500Trim Var.1759550
V(Y[t],d=1,D=2)11863200Range13490Trim Var.6343120
V(Y[t],d=2,D=2)42441400Range24560Trim Var.27425400
V(Y[t],d=3,D=2)156930000Range46750Trim Var.97813400

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2542980 & Range & 6620 & Trim Var. & 1730860 \tabularnewline
V(Y[t],d=1,D=0) & 2304960 & Range & 6770 & Trim Var. & 1546290 \tabularnewline
V(Y[t],d=2,D=0) & 6786050 & Range & 10730 & Trim Var. & 4649310 \tabularnewline
V(Y[t],d=3,D=0) & 22481700 & Range & 18110 & Trim Var. & 15896200 \tabularnewline
V(Y[t],d=0,D=1) & 1737710 & Range & 5880 & Trim Var. & 1006240 \tabularnewline
V(Y[t],d=1,D=1) & 3885370 & Range & 7210 & Trim Var. & 2881390 \tabularnewline
V(Y[t],d=2,D=1) & 13461900 & Range & 13490 & Trim Var. & 9673730 \tabularnewline
V(Y[t],d=3,D=1) & 48659300 & Range & 24560 & Trim Var. & 36914700 \tabularnewline
V(Y[t],d=0,D=2) & 4342270 & Range & 10500 & Trim Var. & 1759550 \tabularnewline
V(Y[t],d=1,D=2) & 11863200 & Range & 13490 & Trim Var. & 6343120 \tabularnewline
V(Y[t],d=2,D=2) & 42441400 & Range & 24560 & Trim Var. & 27425400 \tabularnewline
V(Y[t],d=3,D=2) & 156930000 & Range & 46750 & Trim Var. & 97813400 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300701&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2542980[/C][C]Range[/C][C]6620[/C][C]Trim Var.[/C][C]1730860[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2304960[/C][C]Range[/C][C]6770[/C][C]Trim Var.[/C][C]1546290[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]6786050[/C][C]Range[/C][C]10730[/C][C]Trim Var.[/C][C]4649310[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]22481700[/C][C]Range[/C][C]18110[/C][C]Trim Var.[/C][C]15896200[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1737710[/C][C]Range[/C][C]5880[/C][C]Trim Var.[/C][C]1006240[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3885370[/C][C]Range[/C][C]7210[/C][C]Trim Var.[/C][C]2881390[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]13461900[/C][C]Range[/C][C]13490[/C][C]Trim Var.[/C][C]9673730[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]48659300[/C][C]Range[/C][C]24560[/C][C]Trim Var.[/C][C]36914700[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]4342270[/C][C]Range[/C][C]10500[/C][C]Trim Var.[/C][C]1759550[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]11863200[/C][C]Range[/C][C]13490[/C][C]Trim Var.[/C][C]6343120[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]42441400[/C][C]Range[/C][C]24560[/C][C]Trim Var.[/C][C]27425400[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]156930000[/C][C]Range[/C][C]46750[/C][C]Trim Var.[/C][C]97813400[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300701&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)2542980Range6620Trim Var.1730860
V(Y[t],d=1,D=0)2304960Range6770Trim Var.1546290
V(Y[t],d=2,D=0)6786050Range10730Trim Var.4649310
V(Y[t],d=3,D=0)22481700Range18110Trim Var.15896200
V(Y[t],d=0,D=1)1737710Range5880Trim Var.1006240
V(Y[t],d=1,D=1)3885370Range7210Trim Var.2881390
V(Y[t],d=2,D=1)13461900Range13490Trim Var.9673730
V(Y[t],d=3,D=1)48659300Range24560Trim Var.36914700
V(Y[t],d=0,D=2)4342270Range10500Trim Var.1759550
V(Y[t],d=1,D=2)11863200Range13490Trim Var.6343120
V(Y[t],d=2,D=2)42441400Range24560Trim Var.27425400
V(Y[t],d=3,D=2)156930000Range46750Trim Var.97813400


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 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()