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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 computationThu, 08 Dec 2011 08:47:12 -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/08/t132335205156ljj0x65srnpfb.htm/, Retrieved Fri, 03 May 2024 14:34:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152890, Retrieved Fri, 03 May 2024 14:34:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [] [2010-12-16 20:00:31] [82643889efeee0b265cd2ff213e5137b]
- R  D    [Variance Reduction Matrix] [variantie] [2011-12-08 13:47:12] [c96824ac395d6a5bf5e3e103e13cc1ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.785
4.109
4.026
4.44
3.828
3.953
4.801
4.104
4.57
4.411
4.839
4.736
3.83
4.248
5.657
3.809
4.578
4.3
5.103
4.121
4.205
5.116
4.219
4.736
4.625
4.146
5.299
5.011
4.731
4.619
5.578
5.369
4.904
6.102
5.04
5.731
5.732
4.491
4.755
5.208
4.962
4.163
5.592
5.761
4.929
5.219
4.429
4.143
4.308
3.996
4.634
4.138
3.759
3.922
5.56
4.004
3.937
5.25
3.908
4.814
4.407
3.243
3.74
3.949
3.711
3.796
4.145
3.499
4.164
3.902
3.186
3.353
3.475
3.032
3.341
3.811
3.655
4.058
3.682
3.348
3.848
3.289
3.851
2.766
2.837
2.734
3.764
3.215
3.287
3.507
3.06
3.734
3.849
4.404
3.497
3.389
2.944
3.098
3.48
3.353
3.958
3.504
3.446
3.794
3.676
4.159
3.914
3.595

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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152890&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152890&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' @ yule.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.562321802353756Range3.368Trim Var.0.367698767982456
V(Y[t],d=1,D=0)0.442349768118498Range3.486Trim Var.0.2551208268757
V(Y[t],d=2,D=0)1.32413362524708Range5.874Trim Var.0.79618136993823
V(Y[t],d=3,D=0)4.34611228809524Range10.543Trim Var.2.60046350794764
V(Y[t],d=0,D=1)0.456230638486842Range3.388Trim Var.0.27770739876881
V(Y[t],d=1,D=1)0.606240684658455Range3.822Trim Var.0.390630616806723
V(Y[t],d=2,D=1)1.75262322271791Range7.397Trim Var.1.06225745080321
V(Y[t],d=3,D=1)5.72981185507247Range12.824Trim Var.3.5166257607993
V(Y[t],d=0,D=2)1.11411043717728Range4.842Trim Var.0.676046966493891
V(Y[t],d=1,D=2)1.61118504907435Range6.569Trim Var.0.939913069254186
V(Y[t],d=2,D=2)4.43629545031617Range11.822Trim Var.2.47073764241002
V(Y[t],d=3,D=2)14.0358010993827Range21.073Trim Var.7.23951918712274

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.562321802353756 & Range & 3.368 & Trim Var. & 0.367698767982456 \tabularnewline
V(Y[t],d=1,D=0) & 0.442349768118498 & Range & 3.486 & Trim Var. & 0.2551208268757 \tabularnewline
V(Y[t],d=2,D=0) & 1.32413362524708 & Range & 5.874 & Trim Var. & 0.79618136993823 \tabularnewline
V(Y[t],d=3,D=0) & 4.34611228809524 & Range & 10.543 & Trim Var. & 2.60046350794764 \tabularnewline
V(Y[t],d=0,D=1) & 0.456230638486842 & Range & 3.388 & Trim Var. & 0.27770739876881 \tabularnewline
V(Y[t],d=1,D=1) & 0.606240684658455 & Range & 3.822 & Trim Var. & 0.390630616806723 \tabularnewline
V(Y[t],d=2,D=1) & 1.75262322271791 & Range & 7.397 & Trim Var. & 1.06225745080321 \tabularnewline
V(Y[t],d=3,D=1) & 5.72981185507247 & Range & 12.824 & Trim Var. & 3.5166257607993 \tabularnewline
V(Y[t],d=0,D=2) & 1.11411043717728 & Range & 4.842 & Trim Var. & 0.676046966493891 \tabularnewline
V(Y[t],d=1,D=2) & 1.61118504907435 & Range & 6.569 & Trim Var. & 0.939913069254186 \tabularnewline
V(Y[t],d=2,D=2) & 4.43629545031617 & Range & 11.822 & Trim Var. & 2.47073764241002 \tabularnewline
V(Y[t],d=3,D=2) & 14.0358010993827 & Range & 21.073 & Trim Var. & 7.23951918712274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152890&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.562321802353756[/C][C]Range[/C][C]3.368[/C][C]Trim Var.[/C][C]0.367698767982456[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.442349768118498[/C][C]Range[/C][C]3.486[/C][C]Trim Var.[/C][C]0.2551208268757[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.32413362524708[/C][C]Range[/C][C]5.874[/C][C]Trim Var.[/C][C]0.79618136993823[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4.34611228809524[/C][C]Range[/C][C]10.543[/C][C]Trim Var.[/C][C]2.60046350794764[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.456230638486842[/C][C]Range[/C][C]3.388[/C][C]Trim Var.[/C][C]0.27770739876881[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.606240684658455[/C][C]Range[/C][C]3.822[/C][C]Trim Var.[/C][C]0.390630616806723[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.75262322271791[/C][C]Range[/C][C]7.397[/C][C]Trim Var.[/C][C]1.06225745080321[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]5.72981185507247[/C][C]Range[/C][C]12.824[/C][C]Trim Var.[/C][C]3.5166257607993[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.11411043717728[/C][C]Range[/C][C]4.842[/C][C]Trim Var.[/C][C]0.676046966493891[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1.61118504907435[/C][C]Range[/C][C]6.569[/C][C]Trim Var.[/C][C]0.939913069254186[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4.43629545031617[/C][C]Range[/C][C]11.822[/C][C]Trim Var.[/C][C]2.47073764241002[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]14.0358010993827[/C][C]Range[/C][C]21.073[/C][C]Trim Var.[/C][C]7.23951918712274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152890&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)0.562321802353756Range3.368Trim Var.0.367698767982456
V(Y[t],d=1,D=0)0.442349768118498Range3.486Trim Var.0.2551208268757
V(Y[t],d=2,D=0)1.32413362524708Range5.874Trim Var.0.79618136993823
V(Y[t],d=3,D=0)4.34611228809524Range10.543Trim Var.2.60046350794764
V(Y[t],d=0,D=1)0.456230638486842Range3.388Trim Var.0.27770739876881
V(Y[t],d=1,D=1)0.606240684658455Range3.822Trim Var.0.390630616806723
V(Y[t],d=2,D=1)1.75262322271791Range7.397Trim Var.1.06225745080321
V(Y[t],d=3,D=1)5.72981185507247Range12.824Trim Var.3.5166257607993
V(Y[t],d=0,D=2)1.11411043717728Range4.842Trim Var.0.676046966493891
V(Y[t],d=1,D=2)1.61118504907435Range6.569Trim Var.0.939913069254186
V(Y[t],d=2,D=2)4.43629545031617Range11.822Trim Var.2.47073764241002
V(Y[t],d=3,D=2)14.0358010993827Range21.073Trim Var.7.23951918712274


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()