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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, 02 Dec 2011 12:35:59 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/02/t1322849730dfgtxsxvk7zxkw8.htm/, Retrieved Mon, 29 Apr 2024 01:57:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150330, Retrieved Mon, 29 Apr 2024 01:57:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [ACF van Y(t) (d=0...] [2009-11-26 00:58:58] [9717cb857c153ca3061376906953b329]
- RMPD            [Variance Reduction Matrix] [WS9 VRM] [2011-12-02 17:35:59] [c98b04636162cea751932dfe577607eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150330&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150330&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150330&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)31820139.2596639Range25303Trim Var.19843289.4594595
V(Y[t],d=1,D=0)40470581.1566265Range30831Trim Var.17337182.2608293
V(Y[t],d=2,D=0)109954226.495739Range56102Trim Var.49042777.5658295
V(Y[t],d=3,D=0)363819971.216652Range91616Trim Var.184730393.877152
V(Y[t],d=0,D=1)10052197.3641553Range13003Trim Var.6480796.47211538
V(Y[t],d=1,D=1)8847946.29088419Range14391Trim Var.5651169.03149802
V(Y[t],d=2,D=1)26762141.1983903Range23280Trim Var.16398153.7695853
V(Y[t],d=3,D=1)91246813.8362319Range45511Trim Var.53966681.0407192
V(Y[t],d=0,D=2)33421774.1344262Range23794Trim Var.20804828.8062409
V(Y[t],d=1,D=2)18861203.8372881Range21620Trim Var.11194835.8937806
V(Y[t],d=2,D=2)54939136.0122735Range34184Trim Var.33787669.3236575
V(Y[t],d=3,D=2)187431716.890805Range64342Trim Var.115540013.937783

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 31820139.2596639 & Range & 25303 & Trim Var. & 19843289.4594595 \tabularnewline
V(Y[t],d=1,D=0) & 40470581.1566265 & Range & 30831 & Trim Var. & 17337182.2608293 \tabularnewline
V(Y[t],d=2,D=0) & 109954226.495739 & Range & 56102 & Trim Var. & 49042777.5658295 \tabularnewline
V(Y[t],d=3,D=0) & 363819971.216652 & Range & 91616 & Trim Var. & 184730393.877152 \tabularnewline
V(Y[t],d=0,D=1) & 10052197.3641553 & Range & 13003 & Trim Var. & 6480796.47211538 \tabularnewline
V(Y[t],d=1,D=1) & 8847946.29088419 & Range & 14391 & Trim Var. & 5651169.03149802 \tabularnewline
V(Y[t],d=2,D=1) & 26762141.1983903 & Range & 23280 & Trim Var. & 16398153.7695853 \tabularnewline
V(Y[t],d=3,D=1) & 91246813.8362319 & Range & 45511 & Trim Var. & 53966681.0407192 \tabularnewline
V(Y[t],d=0,D=2) & 33421774.1344262 & Range & 23794 & Trim Var. & 20804828.8062409 \tabularnewline
V(Y[t],d=1,D=2) & 18861203.8372881 & Range & 21620 & Trim Var. & 11194835.8937806 \tabularnewline
V(Y[t],d=2,D=2) & 54939136.0122735 & Range & 34184 & Trim Var. & 33787669.3236575 \tabularnewline
V(Y[t],d=3,D=2) & 187431716.890805 & Range & 64342 & Trim Var. & 115540013.937783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150330&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]31820139.2596639[/C][C]Range[/C][C]25303[/C][C]Trim Var.[/C][C]19843289.4594595[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]40470581.1566265[/C][C]Range[/C][C]30831[/C][C]Trim Var.[/C][C]17337182.2608293[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]109954226.495739[/C][C]Range[/C][C]56102[/C][C]Trim Var.[/C][C]49042777.5658295[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]363819971.216652[/C][C]Range[/C][C]91616[/C][C]Trim Var.[/C][C]184730393.877152[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10052197.3641553[/C][C]Range[/C][C]13003[/C][C]Trim Var.[/C][C]6480796.47211538[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8847946.29088419[/C][C]Range[/C][C]14391[/C][C]Trim Var.[/C][C]5651169.03149802[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]26762141.1983903[/C][C]Range[/C][C]23280[/C][C]Trim Var.[/C][C]16398153.7695853[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]91246813.8362319[/C][C]Range[/C][C]45511[/C][C]Trim Var.[/C][C]53966681.0407192[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]33421774.1344262[/C][C]Range[/C][C]23794[/C][C]Trim Var.[/C][C]20804828.8062409[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]18861203.8372881[/C][C]Range[/C][C]21620[/C][C]Trim Var.[/C][C]11194835.8937806[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]54939136.0122735[/C][C]Range[/C][C]34184[/C][C]Trim Var.[/C][C]33787669.3236575[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]187431716.890805[/C][C]Range[/C][C]64342[/C][C]Trim Var.[/C][C]115540013.937783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150330&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150330&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)31820139.2596639Range25303Trim Var.19843289.4594595
V(Y[t],d=1,D=0)40470581.1566265Range30831Trim Var.17337182.2608293
V(Y[t],d=2,D=0)109954226.495739Range56102Trim Var.49042777.5658295
V(Y[t],d=3,D=0)363819971.216652Range91616Trim Var.184730393.877152
V(Y[t],d=0,D=1)10052197.3641553Range13003Trim Var.6480796.47211538
V(Y[t],d=1,D=1)8847946.29088419Range14391Trim Var.5651169.03149802
V(Y[t],d=2,D=1)26762141.1983903Range23280Trim Var.16398153.7695853
V(Y[t],d=3,D=1)91246813.8362319Range45511Trim Var.53966681.0407192
V(Y[t],d=0,D=2)33421774.1344262Range23794Trim Var.20804828.8062409
V(Y[t],d=1,D=2)18861203.8372881Range21620Trim Var.11194835.8937806
V(Y[t],d=2,D=2)54939136.0122735Range34184Trim Var.33787669.3236575
V(Y[t],d=3,D=2)187431716.890805Range64342Trim Var.115540013.937783


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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)
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,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,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()