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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 19:17:02 +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/t1482344256a396z6z2c2o53vi.htm/, Retrieved Mon, 06 May 2024 11:01:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302458, Retrieved Mon, 06 May 2024 11:01:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49

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...] [2016-12-21 18:17:02] [94c1b173d9287822f5e2740a4a602bdd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13430
13020
11710
9265
7280
5040
3860
6160
13610
15455
14530
13815
12860
11500
10660
9340
8050
6540
5060
6350
14130
16380
16160
15850
15930
15320
13420
12255
8785
6380
4760
5730
10810
12845
12865
13515
13880
12960
12090
9510
8130
6625
4920
4650
10085
13960
14495
14340
13875
13135
13415
9280
7075
5660
4270
5085
11945
14335
14105
13755
12920
11650
10720
8600
7795
6550
4800
5900
14095
15170
14875
15230
13685
12780
11510
9915
8740
7870
6650
5285
13195
13390
13490
13445
13070
12480
11550
10725
9130
7885
6415
5540
9350
12645
11985
10055
10295
10280
9420
9575
8090
5855
4445
3555
12870
14750
13615
13705
13940
11900
9000
7340
6425
5535
4050
3485
8090
11380
11355
10530
9285

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=302458&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=302458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302458&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)12559500Range12895Trim Var.9634830
V(Y[t],d=1,D=0)5992970Range13450Trim Var.2497430
V(Y[t],d=2,D=0)7634060Range17920Trim Var.2840300
V(Y[t],d=3,D=0)17899000Range27325Trim Var.5461820
V(Y[t],d=0,D=1)3283800Range8600Trim Var.1970980
V(Y[t],d=1,D=1)1715840Range10215Trim Var.701078
V(Y[t],d=2,D=1)3825100Range14120Trim Var.1383660
V(Y[t],d=3,D=1)11435900Range24230Trim Var.4125160
V(Y[t],d=0,D=2)9704920Range15665Trim Var.5591070
V(Y[t],d=1,D=2)5036830Range19820Trim Var.1933640
V(Y[t],d=2,D=2)11902300Range27160Trim Var.3725120
V(Y[t],d=3,D=2)36381700Range47825Trim Var.10326300

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 12559500 & Range & 12895 & Trim Var. & 9634830 \tabularnewline
V(Y[t],d=1,D=0) & 5992970 & Range & 13450 & Trim Var. & 2497430 \tabularnewline
V(Y[t],d=2,D=0) & 7634060 & Range & 17920 & Trim Var. & 2840300 \tabularnewline
V(Y[t],d=3,D=0) & 17899000 & Range & 27325 & Trim Var. & 5461820 \tabularnewline
V(Y[t],d=0,D=1) & 3283800 & Range & 8600 & Trim Var. & 1970980 \tabularnewline
V(Y[t],d=1,D=1) & 1715840 & Range & 10215 & Trim Var. & 701078 \tabularnewline
V(Y[t],d=2,D=1) & 3825100 & Range & 14120 & Trim Var. & 1383660 \tabularnewline
V(Y[t],d=3,D=1) & 11435900 & Range & 24230 & Trim Var. & 4125160 \tabularnewline
V(Y[t],d=0,D=2) & 9704920 & Range & 15665 & Trim Var. & 5591070 \tabularnewline
V(Y[t],d=1,D=2) & 5036830 & Range & 19820 & Trim Var. & 1933640 \tabularnewline
V(Y[t],d=2,D=2) & 11902300 & Range & 27160 & Trim Var. & 3725120 \tabularnewline
V(Y[t],d=3,D=2) & 36381700 & Range & 47825 & Trim Var. & 10326300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302458&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]12559500[/C][C]Range[/C][C]12895[/C][C]Trim Var.[/C][C]9634830[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]5992970[/C][C]Range[/C][C]13450[/C][C]Trim Var.[/C][C]2497430[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]7634060[/C][C]Range[/C][C]17920[/C][C]Trim Var.[/C][C]2840300[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]17899000[/C][C]Range[/C][C]27325[/C][C]Trim Var.[/C][C]5461820[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3283800[/C][C]Range[/C][C]8600[/C][C]Trim Var.[/C][C]1970980[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1715840[/C][C]Range[/C][C]10215[/C][C]Trim Var.[/C][C]701078[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3825100[/C][C]Range[/C][C]14120[/C][C]Trim Var.[/C][C]1383660[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11435900[/C][C]Range[/C][C]24230[/C][C]Trim Var.[/C][C]4125160[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]9704920[/C][C]Range[/C][C]15665[/C][C]Trim Var.[/C][C]5591070[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5036830[/C][C]Range[/C][C]19820[/C][C]Trim Var.[/C][C]1933640[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11902300[/C][C]Range[/C][C]27160[/C][C]Trim Var.[/C][C]3725120[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36381700[/C][C]Range[/C][C]47825[/C][C]Trim Var.[/C][C]10326300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302458&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)12559500Range12895Trim Var.9634830
V(Y[t],d=1,D=0)5992970Range13450Trim Var.2497430
V(Y[t],d=2,D=0)7634060Range17920Trim Var.2840300
V(Y[t],d=3,D=0)17899000Range27325Trim Var.5461820
V(Y[t],d=0,D=1)3283800Range8600Trim Var.1970980
V(Y[t],d=1,D=1)1715840Range10215Trim Var.701078
V(Y[t],d=2,D=1)3825100Range14120Trim Var.1383660
V(Y[t],d=3,D=1)11435900Range24230Trim Var.4125160
V(Y[t],d=0,D=2)9704920Range15665Trim Var.5591070
V(Y[t],d=1,D=2)5036830Range19820Trim Var.1933640
V(Y[t],d=2,D=2)11902300Range27160Trim Var.3725120
V(Y[t],d=3,D=2)36381700Range47825Trim Var.10326300


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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()