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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 computationTue, 06 Dec 2011 03:04:41 -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/06/t1323158910x0xlwvifcku3lzb.htm/, Retrieved Sun, 28 Apr 2024 22:20:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151370, Retrieved Sun, 28 Apr 2024 22:20:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

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] [] [2011-12-06 08:04:41] [204816f6f70a8d342ddc2b9d4f4a80d3] [Current]
- RMP     [(Partial) Autocorrelation Function] [] [2011-12-06 08:29:14] [80bca13c5f9401fbb753952fd2952f4a]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-06 08:31:19] [80bca13c5f9401fbb753952fd2952f4a]
- RMP         [Variance Reduction Matrix] [] [2011-12-06 08:45:18] [80bca13c5f9401fbb753952fd2952f4a]
- RM            [ARIMA Backward Selection] [] [2011-12-06 09:03:08] [80bca13c5f9401fbb753952fd2952f4a]
- RM              [ARIMA Forecasting] [] [2011-12-06 09:14:29] [80bca13c5f9401fbb753952fd2952f4a]
-   PD              [ARIMA Forecasting] [Paper arima forec...] [2011-12-23 12:03:11] [805a2cd4f7b6665cd8870eed4006f53c]
- R  D    [Variance Reduction Matrix] [Paper VRM] [2011-12-23 10:59:49] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [Spectral Analysis] [Paper CP] [2011-12-23 11:12:08] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [(Partial) Autocorrelation Function] [Paper autocorr] [2011-12-23 11:17:12] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [Spectral Analysis] [Paper CP2] [2011-12-23 11:23:33] [805a2cd4f7b6665cd8870eed4006f53c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.008
9.169
8.788
8.417
8.247
8.197
8.236
8.253
7.733
8.366
8.626
8.863
10.102
8.463
9.114
8.563
8.872
8.301
8.301
8.278
7.736
7.973
8.268
9.476
11.100
8.962
9.173
8.738
8.459
8.078
8.411
8.291
7.810
8.616
8.312
9.692
9.911
8.915
9.452
9.112
8.472
8.230
8.384
8.625
8.221
8.649
8.625
10.443
10.357
8.586
8.892
8.329
8.101
7.922
8.120
7.838
7.735
8.406
8.209
9.451
10.041
9.411
10.405
8.467
8.464
8.102
7.627
7.513
7.510
8.291
8.064
9.383
9.706
8.579
9.474
8.318
8.213
8.059
9.111
7.708
7.680
8.014
8.007
8.718
9.486
9.113
9.025
8.476
7.952
7.759
7.835
7.600
7.651
8.319
8.812
8.630

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'AstonUniversity' @ aston.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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151370&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151370&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 time1 seconds
R Server'AstonUniversity' @ aston.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.64181355614035Range4.498Trim Var.0.330694134062928
V(Y[t],d=1,D=0)0.596455398208287Range4.657Trim Var.0.271974875910364
V(Y[t],d=2,D=0)1.36962365968886Range6.22Trim Var.0.730277140992542
V(Y[t],d=3,D=0)4.35326380388032Range10.667Trim Var.2.43482439494564
V(Y[t],d=0,D=1)0.296934709552496Range3.419Trim Var.0.128022742687893
V(Y[t],d=1,D=1)0.340116527181898Range2.932Trim Var.0.176447629756469
V(Y[t],d=2,D=1)0.798458227792833Range5.363Trim Var.0.382336491197183
V(Y[t],d=3,D=1)2.4862142845679Range8.259Trim Var.1.14088678792756
V(Y[t],d=0,D=2)0.907238812010954Range5.664Trim Var.0.375806412698413
V(Y[t],d=1,D=2)0.963270548490945Range4.96Trim Var.0.518012128008192
V(Y[t],d=2,D=2)2.13236566956522Range8.617Trim Var.1.04845612189318
V(Y[t],d=3,D=2)6.45127542966752Range14.529Trim Var.3.19420762185792

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.64181355614035 & Range & 4.498 & Trim Var. & 0.330694134062928 \tabularnewline
V(Y[t],d=1,D=0) & 0.596455398208287 & Range & 4.657 & Trim Var. & 0.271974875910364 \tabularnewline
V(Y[t],d=2,D=0) & 1.36962365968886 & Range & 6.22 & Trim Var. & 0.730277140992542 \tabularnewline
V(Y[t],d=3,D=0) & 4.35326380388032 & Range & 10.667 & Trim Var. & 2.43482439494564 \tabularnewline
V(Y[t],d=0,D=1) & 0.296934709552496 & Range & 3.419 & Trim Var. & 0.128022742687893 \tabularnewline
V(Y[t],d=1,D=1) & 0.340116527181898 & Range & 2.932 & Trim Var. & 0.176447629756469 \tabularnewline
V(Y[t],d=2,D=1) & 0.798458227792833 & Range & 5.363 & Trim Var. & 0.382336491197183 \tabularnewline
V(Y[t],d=3,D=1) & 2.4862142845679 & Range & 8.259 & Trim Var. & 1.14088678792756 \tabularnewline
V(Y[t],d=0,D=2) & 0.907238812010954 & Range & 5.664 & Trim Var. & 0.375806412698413 \tabularnewline
V(Y[t],d=1,D=2) & 0.963270548490945 & Range & 4.96 & Trim Var. & 0.518012128008192 \tabularnewline
V(Y[t],d=2,D=2) & 2.13236566956522 & Range & 8.617 & Trim Var. & 1.04845612189318 \tabularnewline
V(Y[t],d=3,D=2) & 6.45127542966752 & Range & 14.529 & Trim Var. & 3.19420762185792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151370&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.64181355614035[/C][C]Range[/C][C]4.498[/C][C]Trim Var.[/C][C]0.330694134062928[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.596455398208287[/C][C]Range[/C][C]4.657[/C][C]Trim Var.[/C][C]0.271974875910364[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.36962365968886[/C][C]Range[/C][C]6.22[/C][C]Trim Var.[/C][C]0.730277140992542[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4.35326380388032[/C][C]Range[/C][C]10.667[/C][C]Trim Var.[/C][C]2.43482439494564[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.296934709552496[/C][C]Range[/C][C]3.419[/C][C]Trim Var.[/C][C]0.128022742687893[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.340116527181898[/C][C]Range[/C][C]2.932[/C][C]Trim Var.[/C][C]0.176447629756469[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.798458227792833[/C][C]Range[/C][C]5.363[/C][C]Trim Var.[/C][C]0.382336491197183[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2.4862142845679[/C][C]Range[/C][C]8.259[/C][C]Trim Var.[/C][C]1.14088678792756[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.907238812010954[/C][C]Range[/C][C]5.664[/C][C]Trim Var.[/C][C]0.375806412698413[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.963270548490945[/C][C]Range[/C][C]4.96[/C][C]Trim Var.[/C][C]0.518012128008192[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2.13236566956522[/C][C]Range[/C][C]8.617[/C][C]Trim Var.[/C][C]1.04845612189318[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]6.45127542966752[/C][C]Range[/C][C]14.529[/C][C]Trim Var.[/C][C]3.19420762185792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151370&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)0.64181355614035Range4.498Trim Var.0.330694134062928
V(Y[t],d=1,D=0)0.596455398208287Range4.657Trim Var.0.271974875910364
V(Y[t],d=2,D=0)1.36962365968886Range6.22Trim Var.0.730277140992542
V(Y[t],d=3,D=0)4.35326380388032Range10.667Trim Var.2.43482439494564
V(Y[t],d=0,D=1)0.296934709552496Range3.419Trim Var.0.128022742687893
V(Y[t],d=1,D=1)0.340116527181898Range2.932Trim Var.0.176447629756469
V(Y[t],d=2,D=1)0.798458227792833Range5.363Trim Var.0.382336491197183
V(Y[t],d=3,D=1)2.4862142845679Range8.259Trim Var.1.14088678792756
V(Y[t],d=0,D=2)0.907238812010954Range5.664Trim Var.0.375806412698413
V(Y[t],d=1,D=2)0.963270548490945Range4.96Trim Var.0.518012128008192
V(Y[t],d=2,D=2)2.13236566956522Range8.617Trim Var.1.04845612189318
V(Y[t],d=3,D=2)6.45127542966752Range14.529Trim Var.3.19420762185792


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 <- 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()