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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 computationFri, 02 Dec 2011 06:22:20 -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/02/t1322825180ovec1e9laqdcmn9.htm/, Retrieved Mon, 29 Apr 2024 02:56:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150117, Retrieved Mon, 29 Apr 2024 02:56:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

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] [] [2011-12-02 11:22:20] [13d85cac30d4a10947636c080219d4f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150117&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150117&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150117&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'Herman Ole Andreas Wold' @ wold.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.269121854237288Range2.377Trim Var.0.176922530048917
V(Y[t],d=1,D=0)0.368091219754529Range2.325Trim Var.0.283277996371553
V(Y[t],d=2,D=0)1.15754943012704Range4.148Trim Var.0.876590875942684
V(Y[t],d=3,D=0)3.92149561152882Range7.564Trim Var.2.90271555843137
V(Y[t],d=0,D=1)0.101623487588652Range1.663Trim Var.0.0559610220673635
V(Y[t],d=1,D=1)0.243425456059204Range2.449Trim Var.0.118212509756097
V(Y[t],d=2,D=1)0.77436743816425Range4.561Trim Var.0.375940342948718
V(Y[t],d=3,D=1)2.66938857272727Range8.37099999999999Trim Var.1.29309381511471
V(Y[t],d=0,D=2)0.212024535714286Range2.262Trim Var.0.115890673387097
V(Y[t],d=1,D=2)0.467201828571428Range3.105Trim Var.0.254033359139785
V(Y[t],d=2,D=2)1.45179121568627Range5.752Trim Var.0.730688050574714
V(Y[t],d=3,D=2)5.03593886363636Range10.21Trim Var.2.80265323399015

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.269121854237288 & Range & 2.377 & Trim Var. & 0.176922530048917 \tabularnewline
V(Y[t],d=1,D=0) & 0.368091219754529 & Range & 2.325 & Trim Var. & 0.283277996371553 \tabularnewline
V(Y[t],d=2,D=0) & 1.15754943012704 & Range & 4.148 & Trim Var. & 0.876590875942684 \tabularnewline
V(Y[t],d=3,D=0) & 3.92149561152882 & Range & 7.564 & Trim Var. & 2.90271555843137 \tabularnewline
V(Y[t],d=0,D=1) & 0.101623487588652 & Range & 1.663 & Trim Var. & 0.0559610220673635 \tabularnewline
V(Y[t],d=1,D=1) & 0.243425456059204 & Range & 2.449 & Trim Var. & 0.118212509756097 \tabularnewline
V(Y[t],d=2,D=1) & 0.77436743816425 & Range & 4.561 & Trim Var. & 0.375940342948718 \tabularnewline
V(Y[t],d=3,D=1) & 2.66938857272727 & Range & 8.37099999999999 & Trim Var. & 1.29309381511471 \tabularnewline
V(Y[t],d=0,D=2) & 0.212024535714286 & Range & 2.262 & Trim Var. & 0.115890673387097 \tabularnewline
V(Y[t],d=1,D=2) & 0.467201828571428 & Range & 3.105 & Trim Var. & 0.254033359139785 \tabularnewline
V(Y[t],d=2,D=2) & 1.45179121568627 & Range & 5.752 & Trim Var. & 0.730688050574714 \tabularnewline
V(Y[t],d=3,D=2) & 5.03593886363636 & Range & 10.21 & Trim Var. & 2.80265323399015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150117&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.269121854237288[/C][C]Range[/C][C]2.377[/C][C]Trim Var.[/C][C]0.176922530048917[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.368091219754529[/C][C]Range[/C][C]2.325[/C][C]Trim Var.[/C][C]0.283277996371553[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.15754943012704[/C][C]Range[/C][C]4.148[/C][C]Trim Var.[/C][C]0.876590875942684[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3.92149561152882[/C][C]Range[/C][C]7.564[/C][C]Trim Var.[/C][C]2.90271555843137[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.101623487588652[/C][C]Range[/C][C]1.663[/C][C]Trim Var.[/C][C]0.0559610220673635[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.243425456059204[/C][C]Range[/C][C]2.449[/C][C]Trim Var.[/C][C]0.118212509756097[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.77436743816425[/C][C]Range[/C][C]4.561[/C][C]Trim Var.[/C][C]0.375940342948718[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2.66938857272727[/C][C]Range[/C][C]8.37099999999999[/C][C]Trim Var.[/C][C]1.29309381511471[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.212024535714286[/C][C]Range[/C][C]2.262[/C][C]Trim Var.[/C][C]0.115890673387097[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.467201828571428[/C][C]Range[/C][C]3.105[/C][C]Trim Var.[/C][C]0.254033359139785[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1.45179121568627[/C][C]Range[/C][C]5.752[/C][C]Trim Var.[/C][C]0.730688050574714[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]5.03593886363636[/C][C]Range[/C][C]10.21[/C][C]Trim Var.[/C][C]2.80265323399015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150117&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150117&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)0.269121854237288Range2.377Trim Var.0.176922530048917
V(Y[t],d=1,D=0)0.368091219754529Range2.325Trim Var.0.283277996371553
V(Y[t],d=2,D=0)1.15754943012704Range4.148Trim Var.0.876590875942684
V(Y[t],d=3,D=0)3.92149561152882Range7.564Trim Var.2.90271555843137
V(Y[t],d=0,D=1)0.101623487588652Range1.663Trim Var.0.0559610220673635
V(Y[t],d=1,D=1)0.243425456059204Range2.449Trim Var.0.118212509756097
V(Y[t],d=2,D=1)0.77436743816425Range4.561Trim Var.0.375940342948718
V(Y[t],d=3,D=1)2.66938857272727Range8.37099999999999Trim Var.1.29309381511471
V(Y[t],d=0,D=2)0.212024535714286Range2.262Trim Var.0.115890673387097
V(Y[t],d=1,D=2)0.467201828571428Range3.105Trim Var.0.254033359139785
V(Y[t],d=2,D=2)1.45179121568627Range5.752Trim Var.0.730688050574714
V(Y[t],d=3,D=2)5.03593886363636Range10.21Trim Var.2.80265323399015


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 2 ; par4 = 1 ;
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()