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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 computationTue, 21 Dec 2010 15:43:53 +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/21/t129294628201jayjwjpyg27ca.htm/, Retrieved Sun, 19 May 2024 02:42:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113686, Retrieved Sun, 19 May 2024 02:42:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [CPI-VRM] [2010-12-21 15:43:53] [4c7d8c32b2e34fcaa7f14928b91d45ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104,8
105,2
105,6
105,8
106,1
106,5
106,71
106,68
107,41
107,15
107,5
107,22
107,11
107,57
107,81
108,75
109,43
109,62
109,54
109,53
109,84
109,67
109,79
109,56
110,22
110,4
110,69
110,72
110,89
110,58
110,94
110,91
111,22
111,09
111
111,06
111,55
112,32
112,64
112,36
112,04
112,37
112,59
112,89
113,22
112,85
113,06
112,99
113,32
113,74
113,91
114,52
114,96
114,91
115,3
115,44
115,52
116,08
115,94
115,56
115,88
116,66
117,41
117,68
117,85
118,21
118,92
119,03
119,17
118,95
118,92
118,9
118,92
119,44
119,40
119,98
120,43
120,41
120,82
120,97
120,63
120,38
120,68
120,84
120,90
121,56
121,57
122,12
121,97
121,96
122,48
122,33
122,44
123,08
124,23
124,58
125,08
125,98
126,90
127,19
128,33
129,04
129,72
128,92
129,13
128,90
128,13
127,85
127,98
128,42
127,68
127,95
127,85
127,61
127,53
127,92
127,59
127,65
127,98
128,19
128,77
129,31
129,80
130,24
130,76
130,75
130,81
130,89
131,30
131,49
131,65

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'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113686&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113686&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)62.5635264826776Range26.85Trim Var.50.7873209696434
V(Y[t],d=1,D=0)0.130018157423972Range1.95000000000002Trim Var.0.0757474362818589
V(Y[t],d=2,D=0)0.215271511627908Range2.49000000000004Trim Var.0.134873381462507
V(Y[t],d=3,D=0)0.640714117864176Range4.23999999999999Trim Var.0.407364384412362
V(Y[t],d=0,D=1)2.45492456914969Range9.43Trim Var.0.911161153235761
V(Y[t],d=1,D=1)0.291360046356658Range3.21000000000004Trim Var.0.153270619946092
V(Y[t],d=2,D=1)0.462053860890071Range3.68000000000004Trim Var.0.289693186813188
V(Y[t],d=3,D=1)1.38155952023989Range6.51999999999998Trim Var.0.82106683159074
V(Y[t],d=0,D=2)8.18374976194674Range15.01Trim Var.3.29301652855543
V(Y[t],d=1,D=2)0.989031985624442Range5.79000000000003Trim Var.0.48176917181423
V(Y[t],d=2,D=2)1.5674986813187Range5.58000000000008Trim Var.0.967718793828896
V(Y[t],d=3,D=2)4.71894858103067Range10.7600000000002Trim Var.2.66435341614907

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 62.5635264826776 & Range & 26.85 & Trim Var. & 50.7873209696434 \tabularnewline
V(Y[t],d=1,D=0) & 0.130018157423972 & Range & 1.95000000000002 & Trim Var. & 0.0757474362818589 \tabularnewline
V(Y[t],d=2,D=0) & 0.215271511627908 & Range & 2.49000000000004 & Trim Var. & 0.134873381462507 \tabularnewline
V(Y[t],d=3,D=0) & 0.640714117864176 & Range & 4.23999999999999 & Trim Var. & 0.407364384412362 \tabularnewline
V(Y[t],d=0,D=1) & 2.45492456914969 & Range & 9.43 & Trim Var. & 0.911161153235761 \tabularnewline
V(Y[t],d=1,D=1) & 0.291360046356658 & Range & 3.21000000000004 & Trim Var. & 0.153270619946092 \tabularnewline
V(Y[t],d=2,D=1) & 0.462053860890071 & Range & 3.68000000000004 & Trim Var. & 0.289693186813188 \tabularnewline
V(Y[t],d=3,D=1) & 1.38155952023989 & Range & 6.51999999999998 & Trim Var. & 0.82106683159074 \tabularnewline
V(Y[t],d=0,D=2) & 8.18374976194674 & Range & 15.01 & Trim Var. & 3.29301652855543 \tabularnewline
V(Y[t],d=1,D=2) & 0.989031985624442 & Range & 5.79000000000003 & Trim Var. & 0.48176917181423 \tabularnewline
V(Y[t],d=2,D=2) & 1.5674986813187 & Range & 5.58000000000008 & Trim Var. & 0.967718793828896 \tabularnewline
V(Y[t],d=3,D=2) & 4.71894858103067 & Range & 10.7600000000002 & Trim Var. & 2.66435341614907 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113686&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]62.5635264826776[/C][C]Range[/C][C]26.85[/C][C]Trim Var.[/C][C]50.7873209696434[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.130018157423972[/C][C]Range[/C][C]1.95000000000002[/C][C]Trim Var.[/C][C]0.0757474362818589[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.215271511627908[/C][C]Range[/C][C]2.49000000000004[/C][C]Trim Var.[/C][C]0.134873381462507[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.640714117864176[/C][C]Range[/C][C]4.23999999999999[/C][C]Trim Var.[/C][C]0.407364384412362[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2.45492456914969[/C][C]Range[/C][C]9.43[/C][C]Trim Var.[/C][C]0.911161153235761[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.291360046356658[/C][C]Range[/C][C]3.21000000000004[/C][C]Trim Var.[/C][C]0.153270619946092[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.462053860890071[/C][C]Range[/C][C]3.68000000000004[/C][C]Trim Var.[/C][C]0.289693186813188[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1.38155952023989[/C][C]Range[/C][C]6.51999999999998[/C][C]Trim Var.[/C][C]0.82106683159074[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]8.18374976194674[/C][C]Range[/C][C]15.01[/C][C]Trim Var.[/C][C]3.29301652855543[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.989031985624442[/C][C]Range[/C][C]5.79000000000003[/C][C]Trim Var.[/C][C]0.48176917181423[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1.5674986813187[/C][C]Range[/C][C]5.58000000000008[/C][C]Trim Var.[/C][C]0.967718793828896[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4.71894858103067[/C][C]Range[/C][C]10.7600000000002[/C][C]Trim Var.[/C][C]2.66435341614907[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113686&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)62.5635264826776Range26.85Trim Var.50.7873209696434
V(Y[t],d=1,D=0)0.130018157423972Range1.95000000000002Trim Var.0.0757474362818589
V(Y[t],d=2,D=0)0.215271511627908Range2.49000000000004Trim Var.0.134873381462507
V(Y[t],d=3,D=0)0.640714117864176Range4.23999999999999Trim Var.0.407364384412362
V(Y[t],d=0,D=1)2.45492456914969Range9.43Trim Var.0.911161153235761
V(Y[t],d=1,D=1)0.291360046356658Range3.21000000000004Trim Var.0.153270619946092
V(Y[t],d=2,D=1)0.462053860890071Range3.68000000000004Trim Var.0.289693186813188
V(Y[t],d=3,D=1)1.38155952023989Range6.51999999999998Trim Var.0.82106683159074
V(Y[t],d=0,D=2)8.18374976194674Range15.01Trim Var.3.29301652855543
V(Y[t],d=1,D=2)0.989031985624442Range5.79000000000003Trim Var.0.48176917181423
V(Y[t],d=2,D=2)1.5674986813187Range5.58000000000008Trim Var.0.967718793828896
V(Y[t],d=3,D=2)4.71894858103067Range10.7600000000002Trim Var.2.66435341614907


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()