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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 computationWed, 21 Dec 2016 14:51:13 +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/21/t14823288526ytbrgn3m3lg7ba.htm/, Retrieved Mon, 06 May 2024 12:07:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302303, Retrieved Mon, 06 May 2024 12:07:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75

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] [N1791] [2016-12-21 13:51:13] [0fbc99f8be9cad246c7cf6558103ab95] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3370
2740
2920
2730
2920
4260
3210
6280
6930
4190
4740
4800
3850
2970
3450
2150
1900
2910
2200
3570
5120
4980
3990
3350
3850
3520
1790
1660
1540
2210
2060
2580
4590
4120
4700
3470
2850
1950
3190
2130
1350
1510
1470
3210
2150
3210
2540
2330
3230
1810
2060
1360
990
2310
1020
1350
2570
3170
2170
1370
1330
770
2160
1520
1070
810
1030
2640
2060
4180
2160
1500
1930
2300
1680
1070
700
1390
1250
1120
2170
1510
1630
960
1700
1390
880
860
800
1410
1200
1240
1920
1440
1940
1380
1660
1450
820
1020
820
1320
780
1340
1630
2210
2010
2100

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=302303&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=302303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302303&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)1574760Range6230Trim Var.927745
V(Y[t],d=1,D=0)812083Range5810Trim Var.426343
V(Y[t],d=2,D=0)2059920Range8260Trim Var.1209350
V(Y[t],d=3,D=0)6576780Range13520Trim Var.3652990
V(Y[t],d=0,D=1)725068Range4240Trim Var.414886
V(Y[t],d=1,D=1)1222510Range6040Trim Var.685482
V(Y[t],d=2,D=1)3494560Range9330Trim Var.1956290
V(Y[t],d=3,D=1)11277800Range17110Trim Var.6166230
V(Y[t],d=0,D=2)2066090Range6830Trim Var.1208100
V(Y[t],d=1,D=2)4092460Range9650Trim Var.2437610
V(Y[t],d=2,D=2)11932800Range15710Trim Var.6836460
V(Y[t],d=3,D=2)38785400Range30510Trim Var.22244400

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1574760 & Range & 6230 & Trim Var. & 927745 \tabularnewline
V(Y[t],d=1,D=0) & 812083 & Range & 5810 & Trim Var. & 426343 \tabularnewline
V(Y[t],d=2,D=0) & 2059920 & Range & 8260 & Trim Var. & 1209350 \tabularnewline
V(Y[t],d=3,D=0) & 6576780 & Range & 13520 & Trim Var. & 3652990 \tabularnewline
V(Y[t],d=0,D=1) & 725068 & Range & 4240 & Trim Var. & 414886 \tabularnewline
V(Y[t],d=1,D=1) & 1222510 & Range & 6040 & Trim Var. & 685482 \tabularnewline
V(Y[t],d=2,D=1) & 3494560 & Range & 9330 & Trim Var. & 1956290 \tabularnewline
V(Y[t],d=3,D=1) & 11277800 & Range & 17110 & Trim Var. & 6166230 \tabularnewline
V(Y[t],d=0,D=2) & 2066090 & Range & 6830 & Trim Var. & 1208100 \tabularnewline
V(Y[t],d=1,D=2) & 4092460 & Range & 9650 & Trim Var. & 2437610 \tabularnewline
V(Y[t],d=2,D=2) & 11932800 & Range & 15710 & Trim Var. & 6836460 \tabularnewline
V(Y[t],d=3,D=2) & 38785400 & Range & 30510 & Trim Var. & 22244400 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302303&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1574760[/C][C]Range[/C][C]6230[/C][C]Trim Var.[/C][C]927745[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]812083[/C][C]Range[/C][C]5810[/C][C]Trim Var.[/C][C]426343[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2059920[/C][C]Range[/C][C]8260[/C][C]Trim Var.[/C][C]1209350[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6576780[/C][C]Range[/C][C]13520[/C][C]Trim Var.[/C][C]3652990[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]725068[/C][C]Range[/C][C]4240[/C][C]Trim Var.[/C][C]414886[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1222510[/C][C]Range[/C][C]6040[/C][C]Trim Var.[/C][C]685482[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3494560[/C][C]Range[/C][C]9330[/C][C]Trim Var.[/C][C]1956290[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11277800[/C][C]Range[/C][C]17110[/C][C]Trim Var.[/C][C]6166230[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2066090[/C][C]Range[/C][C]6830[/C][C]Trim Var.[/C][C]1208100[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4092460[/C][C]Range[/C][C]9650[/C][C]Trim Var.[/C][C]2437610[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11932800[/C][C]Range[/C][C]15710[/C][C]Trim Var.[/C][C]6836460[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38785400[/C][C]Range[/C][C]30510[/C][C]Trim Var.[/C][C]22244400[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302303&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)1574760Range6230Trim Var.927745
V(Y[t],d=1,D=0)812083Range5810Trim Var.426343
V(Y[t],d=2,D=0)2059920Range8260Trim Var.1209350
V(Y[t],d=3,D=0)6576780Range13520Trim Var.3652990
V(Y[t],d=0,D=1)725068Range4240Trim Var.414886
V(Y[t],d=1,D=1)1222510Range6040Trim Var.685482
V(Y[t],d=2,D=1)3494560Range9330Trim Var.1956290
V(Y[t],d=3,D=1)11277800Range17110Trim Var.6166230
V(Y[t],d=0,D=2)2066090Range6830Trim Var.1208100
V(Y[t],d=1,D=2)4092460Range9650Trim Var.2437610
V(Y[t],d=2,D=2)11932800Range15710Trim Var.6836460
V(Y[t],d=3,D=2)38785400Range30510Trim Var.22244400


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()