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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 12:30:19 +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/t1481974294x0ajf2xc798b7uu.htm/, Retrieved Thu, 02 May 2024 06:46:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300713, Retrieved Thu, 02 May 2024 06:46:42 +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] [N1730 variance re...] [2016-12-17 11:30:19] [63af9ed1c5670c0e3049894fd77d93e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5610
3530
2370
11610
4630
8760
4130
5400
5630
7050
5620
5510
4240
3620
4220
3480
3400
4830
3060
8030
8480
7270
10030
7810
6470
5150
4580
2640
2180
6250
4310
6160
8560
6250
8940
8040
6290
2630
4760
3820
2350
2420
4780
6120
4290
5540
6120
5110
4800
2670
5120
2370
3280
4090
2250
2520
3670
6440
5490
2000
2130
1210
6770
2380
2380
3760
3860
4590
4580
8030
5880
1770
5440
4090
3360
1240
1890
3390
2980
5030
3720
3530
1620
2290
2050
2070
2760
1500
1850
2760
3360
2120
3970
3760
3630
1850
3160
2700
1080
1150
1230
2180
2310
2940
4370
4750
7810
2880

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=300713&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=300713&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300713&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)4618250Range10530Trim Var.2862470
V(Y[t],d=1,D=0)5075920Range16220Trim Var.2188020
V(Y[t],d=2,D=0)14631400Range27330Trim Var.5932940
V(Y[t],d=3,D=0)48744900Range53950Trim Var.19946500
V(Y[t],d=0,D=1)4062090Range12540Trim Var.2202570
V(Y[t],d=1,D=1)6177360Range16880Trim Var.3205060
V(Y[t],d=2,D=1)17300700Range28620Trim Var.8292140
V(Y[t],d=3,D=1)54647100Range55100Trim Var.24886100
V(Y[t],d=0,D=2)9465090Range13990Trim Var.5888030
V(Y[t],d=1,D=2)14693100Range18180Trim Var.8713820
V(Y[t],d=2,D=2)39760800Range29370Trim Var.23881000
V(Y[t],d=3,D=2)120927000Range56450Trim Var.68554800

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 4618250 & Range & 10530 & Trim Var. & 2862470 \tabularnewline
V(Y[t],d=1,D=0) & 5075920 & Range & 16220 & Trim Var. & 2188020 \tabularnewline
V(Y[t],d=2,D=0) & 14631400 & Range & 27330 & Trim Var. & 5932940 \tabularnewline
V(Y[t],d=3,D=0) & 48744900 & Range & 53950 & Trim Var. & 19946500 \tabularnewline
V(Y[t],d=0,D=1) & 4062090 & Range & 12540 & Trim Var. & 2202570 \tabularnewline
V(Y[t],d=1,D=1) & 6177360 & Range & 16880 & Trim Var. & 3205060 \tabularnewline
V(Y[t],d=2,D=1) & 17300700 & Range & 28620 & Trim Var. & 8292140 \tabularnewline
V(Y[t],d=3,D=1) & 54647100 & Range & 55100 & Trim Var. & 24886100 \tabularnewline
V(Y[t],d=0,D=2) & 9465090 & Range & 13990 & Trim Var. & 5888030 \tabularnewline
V(Y[t],d=1,D=2) & 14693100 & Range & 18180 & Trim Var. & 8713820 \tabularnewline
V(Y[t],d=2,D=2) & 39760800 & Range & 29370 & Trim Var. & 23881000 \tabularnewline
V(Y[t],d=3,D=2) & 120927000 & Range & 56450 & Trim Var. & 68554800 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300713&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]4618250[/C][C]Range[/C][C]10530[/C][C]Trim Var.[/C][C]2862470[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]5075920[/C][C]Range[/C][C]16220[/C][C]Trim Var.[/C][C]2188020[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]14631400[/C][C]Range[/C][C]27330[/C][C]Trim Var.[/C][C]5932940[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]48744900[/C][C]Range[/C][C]53950[/C][C]Trim Var.[/C][C]19946500[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4062090[/C][C]Range[/C][C]12540[/C][C]Trim Var.[/C][C]2202570[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]6177360[/C][C]Range[/C][C]16880[/C][C]Trim Var.[/C][C]3205060[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]17300700[/C][C]Range[/C][C]28620[/C][C]Trim Var.[/C][C]8292140[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]54647100[/C][C]Range[/C][C]55100[/C][C]Trim Var.[/C][C]24886100[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]9465090[/C][C]Range[/C][C]13990[/C][C]Trim Var.[/C][C]5888030[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]14693100[/C][C]Range[/C][C]18180[/C][C]Trim Var.[/C][C]8713820[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]39760800[/C][C]Range[/C][C]29370[/C][C]Trim Var.[/C][C]23881000[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]120927000[/C][C]Range[/C][C]56450[/C][C]Trim Var.[/C][C]68554800[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300713&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300713&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)4618250Range10530Trim Var.2862470
V(Y[t],d=1,D=0)5075920Range16220Trim Var.2188020
V(Y[t],d=2,D=0)14631400Range27330Trim Var.5932940
V(Y[t],d=3,D=0)48744900Range53950Trim Var.19946500
V(Y[t],d=0,D=1)4062090Range12540Trim Var.2202570
V(Y[t],d=1,D=1)6177360Range16880Trim Var.3205060
V(Y[t],d=2,D=1)17300700Range28620Trim Var.8292140
V(Y[t],d=3,D=1)54647100Range55100Trim Var.24886100
V(Y[t],d=0,D=2)9465090Range13990Trim Var.5888030
V(Y[t],d=1,D=2)14693100Range18180Trim Var.8713820
V(Y[t],d=2,D=2)39760800Range29370Trim Var.23881000
V(Y[t],d=3,D=2)120927000Range56450Trim Var.68554800


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()