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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, 24 Dec 2010 13:59:08 +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/24/t1293199008ew5bumza3usabnw.htm/, Retrieved Tue, 30 Apr 2024 06:22:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114972, Retrieved Tue, 30 Apr 2024 06:22:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [ARIMA Forecasting] [] [2010-12-14 14:23:29] [abe7df3fc544bbb0ed435b4e9982bc91]
- RMPD      [Variance Reduction Matrix] [] [2010-12-24 13:59:08] [29eeba0e6ce2cd83aa315a4a7ff8c4aa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.4
7.7
9.2
8.6
7.4
8.6
6.2
6
6.6
5.1
4.7
5
3.6
1.9
-0.1
-5.7
-5.6
-6.4
-7.7
-8
-11.9
-15.4
-15.5
-13.4
-10.9
-10.8
-7.3
-6.5
-5.1
-5.3
-6.8
-8.4
-8.4
-9.7
-8.8
-9.6
-11.5
-11
-14.9
-16.2
-14.4
-17.3
-15.7
-12.6
-9.4
-8.1
-5.4
-4.6
-4.9
-4
-3.1
-1.3
0
-0.4
3
0.4
1.2
0.6
-1.3
-3.2
-1.8
-3.6
-4.2
-6.9
-8
-7.5
-8.2
-7.6
-3.7
-1.7
-0.7
0.2
0.6
2.2
3.3
5.3
5.5
6.3
7.7
6.5
5.5
6.9
5.7
6.9
6.1
4.8
3.7
5.8
6.8
8.5
7.2
5
4.7
2.3
2.4
0.1
1.9
1.7
2
-1.9
0.5
-1.3
-3.3
-2.8
-8
-13.9
-21.9
-28.8
-27.6
-31.4
-31.8
-29.4
-27.6
-23.6
-22.8
-18.2
-17.8
-14.2
-8.8
-7.9
-7
-7
-3.6
-2.4
-4.9
-7.7
-6.5
-5.1
-3.4
-2.8
0.8

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114972&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114972&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)86.6040035231944Range41Trim Var.51.1525596816976
V(Y[t],d=1,D=0)5.11068813357185Range13.4Trim Var.2.64649475262369
V(Y[t],d=2,D=0)6.58897650193798Range14.1Trim Var.4.08165980167811
V(Y[t],d=3,D=0)19.7196751968504Range23.6Trim Var.11.8927868343425
V(Y[t],d=0,D=1)168.719480131035Range62Trim Var.103.667801093282
V(Y[t],d=1,D=1)12.5767260611328Range21.5Trim Var.7.31137466307278
V(Y[t],d=2,D=1)13.8385145888594Range15.5Trim Var.9.35270512820513
V(Y[t],d=3,D=1)40.3210877061469Range28.7Trim Var.27.2948917102315
V(Y[t],d=0,D=2)413.045531652266Range94.1Trim Var.238.503668533035
V(Y[t],d=1,D=2)40.5360539083558Range36.7Trim Var.22.933470601693
V(Y[t],d=2,D=2)41.6520238095238Range29.1Trim Var.27.7134665731650
V(Y[t],d=3,D=2)121.320312733383Range54.3Trim Var.83.4209746774964

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 86.6040035231944 & Range & 41 & Trim Var. & 51.1525596816976 \tabularnewline
V(Y[t],d=1,D=0) & 5.11068813357185 & Range & 13.4 & Trim Var. & 2.64649475262369 \tabularnewline
V(Y[t],d=2,D=0) & 6.58897650193798 & Range & 14.1 & Trim Var. & 4.08165980167811 \tabularnewline
V(Y[t],d=3,D=0) & 19.7196751968504 & Range & 23.6 & Trim Var. & 11.8927868343425 \tabularnewline
V(Y[t],d=0,D=1) & 168.719480131035 & Range & 62 & Trim Var. & 103.667801093282 \tabularnewline
V(Y[t],d=1,D=1) & 12.5767260611328 & Range & 21.5 & Trim Var. & 7.31137466307278 \tabularnewline
V(Y[t],d=2,D=1) & 13.8385145888594 & Range & 15.5 & Trim Var. & 9.35270512820513 \tabularnewline
V(Y[t],d=3,D=1) & 40.3210877061469 & Range & 28.7 & Trim Var. & 27.2948917102315 \tabularnewline
V(Y[t],d=0,D=2) & 413.045531652266 & Range & 94.1 & Trim Var. & 238.503668533035 \tabularnewline
V(Y[t],d=1,D=2) & 40.5360539083558 & Range & 36.7 & Trim Var. & 22.933470601693 \tabularnewline
V(Y[t],d=2,D=2) & 41.6520238095238 & Range & 29.1 & Trim Var. & 27.7134665731650 \tabularnewline
V(Y[t],d=3,D=2) & 121.320312733383 & Range & 54.3 & Trim Var. & 83.4209746774964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114972&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]86.6040035231944[/C][C]Range[/C][C]41[/C][C]Trim Var.[/C][C]51.1525596816976[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]5.11068813357185[/C][C]Range[/C][C]13.4[/C][C]Trim Var.[/C][C]2.64649475262369[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]6.58897650193798[/C][C]Range[/C][C]14.1[/C][C]Trim Var.[/C][C]4.08165980167811[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]19.7196751968504[/C][C]Range[/C][C]23.6[/C][C]Trim Var.[/C][C]11.8927868343425[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]168.719480131035[/C][C]Range[/C][C]62[/C][C]Trim Var.[/C][C]103.667801093282[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]12.5767260611328[/C][C]Range[/C][C]21.5[/C][C]Trim Var.[/C][C]7.31137466307278[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]13.8385145888594[/C][C]Range[/C][C]15.5[/C][C]Trim Var.[/C][C]9.35270512820513[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]40.3210877061469[/C][C]Range[/C][C]28.7[/C][C]Trim Var.[/C][C]27.2948917102315[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]413.045531652266[/C][C]Range[/C][C]94.1[/C][C]Trim Var.[/C][C]238.503668533035[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]40.5360539083558[/C][C]Range[/C][C]36.7[/C][C]Trim Var.[/C][C]22.933470601693[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]41.6520238095238[/C][C]Range[/C][C]29.1[/C][C]Trim Var.[/C][C]27.7134665731650[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]121.320312733383[/C][C]Range[/C][C]54.3[/C][C]Trim Var.[/C][C]83.4209746774964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114972&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)86.6040035231944Range41Trim Var.51.1525596816976
V(Y[t],d=1,D=0)5.11068813357185Range13.4Trim Var.2.64649475262369
V(Y[t],d=2,D=0)6.58897650193798Range14.1Trim Var.4.08165980167811
V(Y[t],d=3,D=0)19.7196751968504Range23.6Trim Var.11.8927868343425
V(Y[t],d=0,D=1)168.719480131035Range62Trim Var.103.667801093282
V(Y[t],d=1,D=1)12.5767260611328Range21.5Trim Var.7.31137466307278
V(Y[t],d=2,D=1)13.8385145888594Range15.5Trim Var.9.35270512820513
V(Y[t],d=3,D=1)40.3210877061469Range28.7Trim Var.27.2948917102315
V(Y[t],d=0,D=2)413.045531652266Range94.1Trim Var.238.503668533035
V(Y[t],d=1,D=2)40.5360539083558Range36.7Trim Var.22.933470601693
V(Y[t],d=2,D=2)41.6520238095238Range29.1Trim Var.27.7134665731650
V(Y[t],d=3,D=2)121.320312733383Range54.3Trim Var.83.4209746774964


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()