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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 computationMon, 27 Dec 2010 09:53:20 +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/27/t1293443546oatzl3wcf2c76ph.htm/, Retrieved Mon, 06 May 2024 23:54:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115870, Retrieved Mon, 06 May 2024 23:54:30 +0000
QR Codes:

Original text written by user:Prijsverandering in Nederland
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact240

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D        [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [299afd6311e4c20059ea2f05c8dd029d]
-    D          [Standard Deviation-Mean Plot] [Totale Uitvoer - SMP] [2008-12-17 15:57:12] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD            [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-24 14:15:31] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Variance Reduction Matrix] [Variance Reductio...] [2010-12-27 09:53:20] [fba9c6aa004af59d8497d682e70ddad5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13.7
13.7
13.7
1.3
1.3
1.3
-7.4
-7.4
-7.4
-12.9
-12.9
-12.9
-9.6
-9.6
-9.6
-11.1
-11.1
-11.1
-8.3
-8.3
-8.3
-2.7
-2.7
-2.7
5.1
5.1
5.1
4.6
4.6
4.6
5.6
5.6
5.6
5.1
5.1
5.1
0.8
0.8
0.8
6
6
6
9.3
9.3
9.3
8.7
8.7
8.7
11
11
11
8.5
8.5
8.5
4.4
4.4
4.4
2.5
2.5
2.5
0.3
0.3
0.3
-3
-3
-3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115870&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115870&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115870&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)54.7917692307692Range26.6Trim Var.32.8879245283019
V(Y[t],d=1,D=0)7.41499038461538Range20.2Trim Var.1.04507792207792
V(Y[t],d=2,D=0)15.2015873015873Range24.8Trim Var.5.71636363636364
V(Y[t],d=3,D=0)46.3403225806452Range40.4Trim Var.20.0394141414141
V(Y[t],d=0,D=1)112.058270440252Range39Trim Var.75.131130319149
V(Y[t],d=1,D=1)15.3410159651669Range23.6Trim Var.3.58666049953747
V(Y[t],d=2,D=1)31.3866666666667Range24.2Trim Var.17.7106666666667
V(Y[t],d=3,D=1)96.0432Range47.2Trim Var.51.3570909090909
V(Y[t],d=0,D=2)304.13043554007Range58.9Trim Var.191.232
V(Y[t],d=1,D=2)41.2712195121951Range35.9Trim Var.14.5495294117647
V(Y[t],d=2,D=2)88.0410256410256Range37.4Trim Var.61.2154285714286
V(Y[t],d=3,D=2)271.073684210526Range71.8Trim Var.182.552762923351

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 54.7917692307692 & Range & 26.6 & Trim Var. & 32.8879245283019 \tabularnewline
V(Y[t],d=1,D=0) & 7.41499038461538 & Range & 20.2 & Trim Var. & 1.04507792207792 \tabularnewline
V(Y[t],d=2,D=0) & 15.2015873015873 & Range & 24.8 & Trim Var. & 5.71636363636364 \tabularnewline
V(Y[t],d=3,D=0) & 46.3403225806452 & Range & 40.4 & Trim Var. & 20.0394141414141 \tabularnewline
V(Y[t],d=0,D=1) & 112.058270440252 & Range & 39 & Trim Var. & 75.131130319149 \tabularnewline
V(Y[t],d=1,D=1) & 15.3410159651669 & Range & 23.6 & Trim Var. & 3.58666049953747 \tabularnewline
V(Y[t],d=2,D=1) & 31.3866666666667 & Range & 24.2 & Trim Var. & 17.7106666666667 \tabularnewline
V(Y[t],d=3,D=1) & 96.0432 & Range & 47.2 & Trim Var. & 51.3570909090909 \tabularnewline
V(Y[t],d=0,D=2) & 304.13043554007 & Range & 58.9 & Trim Var. & 191.232 \tabularnewline
V(Y[t],d=1,D=2) & 41.2712195121951 & Range & 35.9 & Trim Var. & 14.5495294117647 \tabularnewline
V(Y[t],d=2,D=2) & 88.0410256410256 & Range & 37.4 & Trim Var. & 61.2154285714286 \tabularnewline
V(Y[t],d=3,D=2) & 271.073684210526 & Range & 71.8 & Trim Var. & 182.552762923351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115870&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]54.7917692307692[/C][C]Range[/C][C]26.6[/C][C]Trim Var.[/C][C]32.8879245283019[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]7.41499038461538[/C][C]Range[/C][C]20.2[/C][C]Trim Var.[/C][C]1.04507792207792[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]15.2015873015873[/C][C]Range[/C][C]24.8[/C][C]Trim Var.[/C][C]5.71636363636364[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]46.3403225806452[/C][C]Range[/C][C]40.4[/C][C]Trim Var.[/C][C]20.0394141414141[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]112.058270440252[/C][C]Range[/C][C]39[/C][C]Trim Var.[/C][C]75.131130319149[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]15.3410159651669[/C][C]Range[/C][C]23.6[/C][C]Trim Var.[/C][C]3.58666049953747[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]31.3866666666667[/C][C]Range[/C][C]24.2[/C][C]Trim Var.[/C][C]17.7106666666667[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]96.0432[/C][C]Range[/C][C]47.2[/C][C]Trim Var.[/C][C]51.3570909090909[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]304.13043554007[/C][C]Range[/C][C]58.9[/C][C]Trim Var.[/C][C]191.232[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]41.2712195121951[/C][C]Range[/C][C]35.9[/C][C]Trim Var.[/C][C]14.5495294117647[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]88.0410256410256[/C][C]Range[/C][C]37.4[/C][C]Trim Var.[/C][C]61.2154285714286[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]271.073684210526[/C][C]Range[/C][C]71.8[/C][C]Trim Var.[/C][C]182.552762923351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115870&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115870&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)54.7917692307692Range26.6Trim Var.32.8879245283019
V(Y[t],d=1,D=0)7.41499038461538Range20.2Trim Var.1.04507792207792
V(Y[t],d=2,D=0)15.2015873015873Range24.8Trim Var.5.71636363636364
V(Y[t],d=3,D=0)46.3403225806452Range40.4Trim Var.20.0394141414141
V(Y[t],d=0,D=1)112.058270440252Range39Trim Var.75.131130319149
V(Y[t],d=1,D=1)15.3410159651669Range23.6Trim Var.3.58666049953747
V(Y[t],d=2,D=1)31.3866666666667Range24.2Trim Var.17.7106666666667
V(Y[t],d=3,D=1)96.0432Range47.2Trim Var.51.3570909090909
V(Y[t],d=0,D=2)304.13043554007Range58.9Trim Var.191.232
V(Y[t],d=1,D=2)41.2712195121951Range35.9Trim Var.14.5495294117647
V(Y[t],d=2,D=2)88.0410256410256Range37.4Trim Var.61.2154285714286
V(Y[t],d=3,D=2)271.073684210526Range71.8Trim Var.182.552762923351


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()