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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, 21 Dec 2010 17:09:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292951419onp9rwljgjsmhy2.htm/, Retrieved Sat, 11 May 2024 22:47:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113763, Retrieved Sat, 11 May 2024 22:47:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Goudprijs-ACF] [2010-12-20 12:17:14] [d672a41e0af7ff107c03f1d65e47fd32]
- RMPD        [Variance Reduction Matrix] [Variance Reductio...] [2010-12-21 17:09:21] [c6b3e187a4a1689d42fffda4bc860ab5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.026
9.787
9.536
9.490
9.736
9.694
9.647
9.753
10.070
10.137
9.984
9.732
9.103
9.155
9.308
9.394
9.948
10.177
10.002
9.728
10.002
10.063
10.018
9.960
10.236
10.893
10.756
10.940
10.997
10.827
10.166
10.186
10.457
10.368
10.244
10.511
10.812
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113763&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113763&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 time7 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)37.1948307552554Range23.41Trim Var.23.3855849068671
V(Y[t],d=1,D=0)0.472210824090638Range5.446Trim Var.0.161002542953523
V(Y[t],d=2,D=0)0.829992757751938Range6.795Trim Var.0.283496209305873
V(Y[t],d=3,D=0)2.19874637296998Range11.377Trim Var.0.734803978031361
V(Y[t],d=0,D=1)5.94683274562028Range11.878Trim Var.3.1563241904426
V(Y[t],d=1,D=1)0.733732245762712Range5.603Trim Var.0.340466180862533
V(Y[t],d=2,D=1)1.42269373975833Range7.357Trim Var.0.606596444139193
V(Y[t],d=3,D=1)4.08814435382309Range12.624Trim Var.1.91337679126213
V(Y[t],d=0,D=2)6.57370913807089Range14.762Trim Var.3.46238002082867
V(Y[t],d=1,D=2)1.82875223872417Range8.46Trim Var.0.968959033745137
V(Y[t],d=2,D=2)3.89441334835165Range12.624Trim Var.1.71079984595605
V(Y[t],d=3,D=2)11.9733697086445Range22.593Trim Var.5.31359641376014

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 37.1948307552554 & Range & 23.41 & Trim Var. & 23.3855849068671 \tabularnewline
V(Y[t],d=1,D=0) & 0.472210824090638 & Range & 5.446 & Trim Var. & 0.161002542953523 \tabularnewline
V(Y[t],d=2,D=0) & 0.829992757751938 & Range & 6.795 & Trim Var. & 0.283496209305873 \tabularnewline
V(Y[t],d=3,D=0) & 2.19874637296998 & Range & 11.377 & Trim Var. & 0.734803978031361 \tabularnewline
V(Y[t],d=0,D=1) & 5.94683274562028 & Range & 11.878 & Trim Var. & 3.1563241904426 \tabularnewline
V(Y[t],d=1,D=1) & 0.733732245762712 & Range & 5.603 & Trim Var. & 0.340466180862533 \tabularnewline
V(Y[t],d=2,D=1) & 1.42269373975833 & Range & 7.357 & Trim Var. & 0.606596444139193 \tabularnewline
V(Y[t],d=3,D=1) & 4.08814435382309 & Range & 12.624 & Trim Var. & 1.91337679126213 \tabularnewline
V(Y[t],d=0,D=2) & 6.57370913807089 & Range & 14.762 & Trim Var. & 3.46238002082867 \tabularnewline
V(Y[t],d=1,D=2) & 1.82875223872417 & Range & 8.46 & Trim Var. & 0.968959033745137 \tabularnewline
V(Y[t],d=2,D=2) & 3.89441334835165 & Range & 12.624 & Trim Var. & 1.71079984595605 \tabularnewline
V(Y[t],d=3,D=2) & 11.9733697086445 & Range & 22.593 & Trim Var. & 5.31359641376014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113763&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]37.1948307552554[/C][C]Range[/C][C]23.41[/C][C]Trim Var.[/C][C]23.3855849068671[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.472210824090638[/C][C]Range[/C][C]5.446[/C][C]Trim Var.[/C][C]0.161002542953523[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.829992757751938[/C][C]Range[/C][C]6.795[/C][C]Trim Var.[/C][C]0.283496209305873[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2.19874637296998[/C][C]Range[/C][C]11.377[/C][C]Trim Var.[/C][C]0.734803978031361[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5.94683274562028[/C][C]Range[/C][C]11.878[/C][C]Trim Var.[/C][C]3.1563241904426[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.733732245762712[/C][C]Range[/C][C]5.603[/C][C]Trim Var.[/C][C]0.340466180862533[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.42269373975833[/C][C]Range[/C][C]7.357[/C][C]Trim Var.[/C][C]0.606596444139193[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4.08814435382309[/C][C]Range[/C][C]12.624[/C][C]Trim Var.[/C][C]1.91337679126213[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6.57370913807089[/C][C]Range[/C][C]14.762[/C][C]Trim Var.[/C][C]3.46238002082867[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.82875223872417[/C][C]Range[/C][C]8.46[/C][C]Trim Var.[/C][C]0.968959033745137[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3.89441334835165[/C][C]Range[/C][C]12.624[/C][C]Trim Var.[/C][C]1.71079984595605[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]11.9733697086445[/C][C]Range[/C][C]22.593[/C][C]Trim Var.[/C][C]5.31359641376014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113763&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)37.1948307552554Range23.41Trim Var.23.3855849068671
V(Y[t],d=1,D=0)0.472210824090638Range5.446Trim Var.0.161002542953523
V(Y[t],d=2,D=0)0.829992757751938Range6.795Trim Var.0.283496209305873
V(Y[t],d=3,D=0)2.19874637296998Range11.377Trim Var.0.734803978031361
V(Y[t],d=0,D=1)5.94683274562028Range11.878Trim Var.3.1563241904426
V(Y[t],d=1,D=1)0.733732245762712Range5.603Trim Var.0.340466180862533
V(Y[t],d=2,D=1)1.42269373975833Range7.357Trim Var.0.606596444139193
V(Y[t],d=3,D=1)4.08814435382309Range12.624Trim Var.1.91337679126213
V(Y[t],d=0,D=2)6.57370913807089Range14.762Trim Var.3.46238002082867
V(Y[t],d=1,D=2)1.82875223872417Range8.46Trim Var.0.968959033745137
V(Y[t],d=2,D=2)3.89441334835165Range12.624Trim Var.1.71079984595605
V(Y[t],d=3,D=2)11.9733697086445Range22.593Trim Var.5.31359641376014


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()