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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, 20 Dec 2010 20:00:09 +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/20/t129287534590sfar7hs29dgrm.htm/, Retrieved Fri, 03 May 2024 21:51:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113104, Retrieved Fri, 03 May 2024 21:51:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-12-13 08:35:23] [21eff0c210342db4afbdafe426a7c254]
-   PD  [(Partial) Autocorrelation Function] [] [2010-12-13 09:29:04] [21eff0c210342db4afbdafe426a7c254]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-13 10:05:17] [21eff0c210342db4afbdafe426a7c254]
- RM D      [ARIMA Forecasting] [] [2010-12-13 10:48:48] [21eff0c210342db4afbdafe426a7c254]
- RMPD        [Univariate Data Series] [] [2010-12-13 20:53:52] [21eff0c210342db4afbdafe426a7c254]
- RMPD          [Histogram] [] [2010-12-14 14:33:39] [21eff0c210342db4afbdafe426a7c254]
- RMPD            [Univariate Explorative Data Analysis] [] [2010-12-16 14:27:05] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Variance Reduction Matrix] [] [2010-12-20 20:00:09] [13a73be5002723d89d3723d5fe97baf8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21.3
21.1
20.6
20.5
20.5
20.8
21.1
21.3
21.3
21.1
20.9
19.9
19.8
19.5
19.6
19.6
19.7
20.2
19.7
19.3
18.9
18.4
18
17.8
17.8
17.7
17.5
17.4
17.1
17.1
17.2
17.8
18.6
18.9
18.9
18.7
18.6
19.1
20.3
21.1
21.6
21.5
21.5
21.7
21.9
22.2
22.6
22.5
23.2
23.6
23.8
23.9
23.8
23.5
23.3
23.2
23.5
23.5
23.5
23.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 9 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113104&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113104&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 time9 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)4.23833615819209Range6.8Trim Var.3.44704402515723
V(Y[t],d=1,D=0)0.140210403272940Range2.2Trim Var.0.0720475113122172
V(Y[t],d=2,D=0)0.125964912280702Range1.90000000000000Trim Var.0.063529411764706
V(Y[t],d=3,D=0)0.305175438596492Range3.1Trim Var.0.116330612244898
V(Y[t],d=0,D=1)6.18542109929078Range7.7Trim Var.5.06290360046458
V(Y[t],d=1,D=1)0.300814061054579Range2.4Trim Var.0.184621951219512
V(Y[t],d=2,D=1)0.252888888888889Range2.10000000000000Trim Var.0.151532051282052
V(Y[t],d=3,D=1)0.543555555555555Range2.9Trim Var.0.327651821862348
V(Y[t],d=0,D=2)10.2277142857143Range10.5Trim Var.8.07479838709677
V(Y[t],d=1,D=2)1.04974789915966Range4.1Trim Var.0.711247311827956
V(Y[t],d=2,D=2)0.803716577540106Range3.8Trim Var.0.470197044334976
V(Y[t],d=3,D=2)1.48880681818181Range4.89999999999998Trim Var.0.941871921182265

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 4.23833615819209 & Range & 6.8 & Trim Var. & 3.44704402515723 \tabularnewline
V(Y[t],d=1,D=0) & 0.140210403272940 & Range & 2.2 & Trim Var. & 0.0720475113122172 \tabularnewline
V(Y[t],d=2,D=0) & 0.125964912280702 & Range & 1.90000000000000 & Trim Var. & 0.063529411764706 \tabularnewline
V(Y[t],d=3,D=0) & 0.305175438596492 & Range & 3.1 & Trim Var. & 0.116330612244898 \tabularnewline
V(Y[t],d=0,D=1) & 6.18542109929078 & Range & 7.7 & Trim Var. & 5.06290360046458 \tabularnewline
V(Y[t],d=1,D=1) & 0.300814061054579 & Range & 2.4 & Trim Var. & 0.184621951219512 \tabularnewline
V(Y[t],d=2,D=1) & 0.252888888888889 & Range & 2.10000000000000 & Trim Var. & 0.151532051282052 \tabularnewline
V(Y[t],d=3,D=1) & 0.543555555555555 & Range & 2.9 & Trim Var. & 0.327651821862348 \tabularnewline
V(Y[t],d=0,D=2) & 10.2277142857143 & Range & 10.5 & Trim Var. & 8.07479838709677 \tabularnewline
V(Y[t],d=1,D=2) & 1.04974789915966 & Range & 4.1 & Trim Var. & 0.711247311827956 \tabularnewline
V(Y[t],d=2,D=2) & 0.803716577540106 & Range & 3.8 & Trim Var. & 0.470197044334976 \tabularnewline
V(Y[t],d=3,D=2) & 1.48880681818181 & Range & 4.89999999999998 & Trim Var. & 0.941871921182265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113104&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]4.23833615819209[/C][C]Range[/C][C]6.8[/C][C]Trim Var.[/C][C]3.44704402515723[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.140210403272940[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.0720475113122172[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.125964912280702[/C][C]Range[/C][C]1.90000000000000[/C][C]Trim Var.[/C][C]0.063529411764706[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.305175438596492[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.116330612244898[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6.18542109929078[/C][C]Range[/C][C]7.7[/C][C]Trim Var.[/C][C]5.06290360046458[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.300814061054579[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.184621951219512[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.252888888888889[/C][C]Range[/C][C]2.10000000000000[/C][C]Trim Var.[/C][C]0.151532051282052[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.543555555555555[/C][C]Range[/C][C]2.9[/C][C]Trim Var.[/C][C]0.327651821862348[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]10.2277142857143[/C][C]Range[/C][C]10.5[/C][C]Trim Var.[/C][C]8.07479838709677[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.04974789915966[/C][C]Range[/C][C]4.1[/C][C]Trim Var.[/C][C]0.711247311827956[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.803716577540106[/C][C]Range[/C][C]3.8[/C][C]Trim Var.[/C][C]0.470197044334976[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.48880681818181[/C][C]Range[/C][C]4.89999999999998[/C][C]Trim Var.[/C][C]0.941871921182265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113104&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)4.23833615819209Range6.8Trim Var.3.44704402515723
V(Y[t],d=1,D=0)0.140210403272940Range2.2Trim Var.0.0720475113122172
V(Y[t],d=2,D=0)0.125964912280702Range1.90000000000000Trim Var.0.063529411764706
V(Y[t],d=3,D=0)0.305175438596492Range3.1Trim Var.0.116330612244898
V(Y[t],d=0,D=1)6.18542109929078Range7.7Trim Var.5.06290360046458
V(Y[t],d=1,D=1)0.300814061054579Range2.4Trim Var.0.184621951219512
V(Y[t],d=2,D=1)0.252888888888889Range2.10000000000000Trim Var.0.151532051282052
V(Y[t],d=3,D=1)0.543555555555555Range2.9Trim Var.0.327651821862348
V(Y[t],d=0,D=2)10.2277142857143Range10.5Trim Var.8.07479838709677
V(Y[t],d=1,D=2)1.04974789915966Range4.1Trim Var.0.711247311827956
V(Y[t],d=2,D=2)0.803716577540106Range3.8Trim Var.0.470197044334976
V(Y[t],d=3,D=2)1.48880681818181Range4.89999999999998Trim Var.0.941871921182265


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()