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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 19:12:17 +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/t12928724010c95vgbrlvoxb54.htm/, Retrieved Fri, 03 May 2024 18:55:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113077, Retrieved Fri, 03 May 2024 18:55:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127

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 21:02:07] [21eff0c210342db4afbdafe426a7c254]
- RMPD            [Variance Reduction Matrix] [] [2010-12-20 19:12:17] [13a73be5002723d89d3723d5fe97baf8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18.6
19.1
18.8
18.2
18
19
20.7
21.2
20.7
19.6
18.6
18.7
23.8
24.9
24.8
23.8
22.3
21.7
20.7
19.7
18.4
17.4
17
18
23.8
25.5
25.6
23.7
22
21.3
20.7
20.4
20.3
20.4
19.8
19.5
23.1
23.5
23.5
22.9
21.9
21.5
20.5
20.2
19.4
19.2
18.8
18.8
22.6
23.3
23
21.4
19.9
18.8
18.6
18.4
18.6
19.9
19.2
18.4
21.1
20.5
19.1
18.1
17
17.1
17.4
16.8
15.3
14.3
13.4
15.3
22.1
23.7
22.2
19.5
16.6
17.3
19.8
21.2
21.5
20.6
19.1
19.6
23.4
24.3
24.1
22.7
22.5
23.8
25
25.2
24.1
22.3
20.5
20.5
24.9
25.5
24.8
22.5

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113077&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113077&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113077&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)7.17815757575758Range12.2Trim Var.4.85933707865169
V(Y[t],d=1,D=0)2.87077922077922Range9.7Trim Var.1.26298328108673
V(Y[t],d=2,D=0)3.66Range10.2Trim Var.1.87320271682341
V(Y[t],d=3,D=0)7.786389604811Range14Trim Var.3.34010943912449
V(Y[t],d=0,D=1)7.67235109717868Range12.3Trim Var.4.95072927072927
V(Y[t],d=1,D=1)1.53145148356055Range7.1Trim Var.0.797604237867396
V(Y[t],d=2,D=1)1.14310396716826Range5.2Trim Var.0.653670175438597
V(Y[t],d=3,D=1)1.63952380952381Range7.40000000000001Trim Var.0.799468715290636
V(Y[t],d=0,D=2)15.8995701754386Range18.2Trim Var.9.24548168249661
V(Y[t],d=1,D=2)4.96671351351351Range12.3Trim Var.3.04526006331976
V(Y[t],d=2,D=2)3.69746019992595Range8.79999999999999Trim Var.2.30559440559441
V(Y[t],d=3,D=2)4.93469178082193Range13.2Trim Var.2.43191346153847

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 7.17815757575758 & Range & 12.2 & Trim Var. & 4.85933707865169 \tabularnewline
V(Y[t],d=1,D=0) & 2.87077922077922 & Range & 9.7 & Trim Var. & 1.26298328108673 \tabularnewline
V(Y[t],d=2,D=0) & 3.66 & Range & 10.2 & Trim Var. & 1.87320271682341 \tabularnewline
V(Y[t],d=3,D=0) & 7.786389604811 & Range & 14 & Trim Var. & 3.34010943912449 \tabularnewline
V(Y[t],d=0,D=1) & 7.67235109717868 & Range & 12.3 & Trim Var. & 4.95072927072927 \tabularnewline
V(Y[t],d=1,D=1) & 1.53145148356055 & Range & 7.1 & Trim Var. & 0.797604237867396 \tabularnewline
V(Y[t],d=2,D=1) & 1.14310396716826 & Range & 5.2 & Trim Var. & 0.653670175438597 \tabularnewline
V(Y[t],d=3,D=1) & 1.63952380952381 & Range & 7.40000000000001 & Trim Var. & 0.799468715290636 \tabularnewline
V(Y[t],d=0,D=2) & 15.8995701754386 & Range & 18.2 & Trim Var. & 9.24548168249661 \tabularnewline
V(Y[t],d=1,D=2) & 4.96671351351351 & Range & 12.3 & Trim Var. & 3.04526006331976 \tabularnewline
V(Y[t],d=2,D=2) & 3.69746019992595 & Range & 8.79999999999999 & Trim Var. & 2.30559440559441 \tabularnewline
V(Y[t],d=3,D=2) & 4.93469178082193 & Range & 13.2 & Trim Var. & 2.43191346153847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113077&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]7.17815757575758[/C][C]Range[/C][C]12.2[/C][C]Trim Var.[/C][C]4.85933707865169[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]2.87077922077922[/C][C]Range[/C][C]9.7[/C][C]Trim Var.[/C][C]1.26298328108673[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]3.66[/C][C]Range[/C][C]10.2[/C][C]Trim Var.[/C][C]1.87320271682341[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]7.786389604811[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]3.34010943912449[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]7.67235109717868[/C][C]Range[/C][C]12.3[/C][C]Trim Var.[/C][C]4.95072927072927[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.53145148356055[/C][C]Range[/C][C]7.1[/C][C]Trim Var.[/C][C]0.797604237867396[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.14310396716826[/C][C]Range[/C][C]5.2[/C][C]Trim Var.[/C][C]0.653670175438597[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.63952380952381[/C][C]Range[/C][C]7.40000000000001[/C][C]Trim Var.[/C][C]0.799468715290636[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]15.8995701754386[/C][C]Range[/C][C]18.2[/C][C]Trim Var.[/C][C]9.24548168249661[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4.96671351351351[/C][C]Range[/C][C]12.3[/C][C]Trim Var.[/C][C]3.04526006331976[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3.69746019992595[/C][C]Range[/C][C]8.79999999999999[/C][C]Trim Var.[/C][C]2.30559440559441[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4.93469178082193[/C][C]Range[/C][C]13.2[/C][C]Trim Var.[/C][C]2.43191346153847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113077&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113077&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)7.17815757575758Range12.2Trim Var.4.85933707865169
V(Y[t],d=1,D=0)2.87077922077922Range9.7Trim Var.1.26298328108673
V(Y[t],d=2,D=0)3.66Range10.2Trim Var.1.87320271682341
V(Y[t],d=3,D=0)7.786389604811Range14Trim Var.3.34010943912449
V(Y[t],d=0,D=1)7.67235109717868Range12.3Trim Var.4.95072927072927
V(Y[t],d=1,D=1)1.53145148356055Range7.1Trim Var.0.797604237867396
V(Y[t],d=2,D=1)1.14310396716826Range5.2Trim Var.0.653670175438597
V(Y[t],d=3,D=1)1.63952380952381Range7.40000000000001Trim Var.0.799468715290636
V(Y[t],d=0,D=2)15.8995701754386Range18.2Trim Var.9.24548168249661
V(Y[t],d=1,D=2)4.96671351351351Range12.3Trim Var.3.04526006331976
V(Y[t],d=2,D=2)3.69746019992595Range8.79999999999999Trim Var.2.30559440559441
V(Y[t],d=3,D=2)4.93469178082193Range13.2Trim Var.2.43191346153847


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()