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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, 16 Dec 2014 00:01:06 +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/2014/Dec/16/t14186883353hmjxjkvt9ivzrs.htm/, Retrieved Thu, 16 May 2024 06:26:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269110, Retrieved Thu, 16 May 2024 06:26:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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] [] [2014-12-16 00:01:06] [6993448de96b8662e47595bfdf466bf3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.35
12.7
18.1
17.85


17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6

14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1

17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85


18.95
15.6




17.1
16.1









15.4
15.4

13.35
19.1

7.6


19.1













14.75



19.25

13.6

12.75

9.85




15.25
11.9

16.35
12.4

18.15


17.75

12.35
15.6
19.3

17.1

18.4
19.05
18.55
19.1

12.85
9.5
4.5

13.6
11.7

13.35





17.6
14.05
16.1
13.35
11.85
11.95


13.2


7.7

















14.6

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'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269110&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269110&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269110&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'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Variance Reduction Matrix
V(Y[t],d=0,D=0)10.9506Range14.95Trim Var.5.895
V(Y[t],d=1,D=0)17.8801Range23Trim Var.9.33412
V(Y[t],d=2,D=0)53.5542Range40.25Trim Var.29.1786
V(Y[t],d=3,D=0)186.446Range79.1Trim Var.98.4535
V(Y[t],d=0,D=1)19.024Range25.5Trim Var.8.89356
V(Y[t],d=1,D=1)28.9078Range28.8Trim Var.15.0643
V(Y[t],d=2,D=1)87.1816Range52.5Trim Var.52.3257
V(Y[t],d=3,D=1)317.537Range91.6Trim Var.205.007
V(Y[t],d=0,D=2)57.3794Range38.65Trim Var.32.1093
V(Y[t],d=1,D=2)87.7174Range44.95Trim Var.55.6649
V(Y[t],d=2,D=2)273.599Range73.05Trim Var.201.586
V(Y[t],d=3,D=2)1013.25Range130.45Trim Var.764.563

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 10.9506 & Range & 14.95 & Trim Var. & 5.895 \tabularnewline
V(Y[t],d=1,D=0) & 17.8801 & Range & 23 & Trim Var. & 9.33412 \tabularnewline
V(Y[t],d=2,D=0) & 53.5542 & Range & 40.25 & Trim Var. & 29.1786 \tabularnewline
V(Y[t],d=3,D=0) & 186.446 & Range & 79.1 & Trim Var. & 98.4535 \tabularnewline
V(Y[t],d=0,D=1) & 19.024 & Range & 25.5 & Trim Var. & 8.89356 \tabularnewline
V(Y[t],d=1,D=1) & 28.9078 & Range & 28.8 & Trim Var. & 15.0643 \tabularnewline
V(Y[t],d=2,D=1) & 87.1816 & Range & 52.5 & Trim Var. & 52.3257 \tabularnewline
V(Y[t],d=3,D=1) & 317.537 & Range & 91.6 & Trim Var. & 205.007 \tabularnewline
V(Y[t],d=0,D=2) & 57.3794 & Range & 38.65 & Trim Var. & 32.1093 \tabularnewline
V(Y[t],d=1,D=2) & 87.7174 & Range & 44.95 & Trim Var. & 55.6649 \tabularnewline
V(Y[t],d=2,D=2) & 273.599 & Range & 73.05 & Trim Var. & 201.586 \tabularnewline
V(Y[t],d=3,D=2) & 1013.25 & Range & 130.45 & Trim Var. & 764.563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269110&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]10.9506[/C][C]Range[/C][C]14.95[/C][C]Trim Var.[/C][C]5.895[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]17.8801[/C][C]Range[/C][C]23[/C][C]Trim Var.[/C][C]9.33412[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]53.5542[/C][C]Range[/C][C]40.25[/C][C]Trim Var.[/C][C]29.1786[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]186.446[/C][C]Range[/C][C]79.1[/C][C]Trim Var.[/C][C]98.4535[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]19.024[/C][C]Range[/C][C]25.5[/C][C]Trim Var.[/C][C]8.89356[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]28.9078[/C][C]Range[/C][C]28.8[/C][C]Trim Var.[/C][C]15.0643[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]87.1816[/C][C]Range[/C][C]52.5[/C][C]Trim Var.[/C][C]52.3257[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]317.537[/C][C]Range[/C][C]91.6[/C][C]Trim Var.[/C][C]205.007[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]57.3794[/C][C]Range[/C][C]38.65[/C][C]Trim Var.[/C][C]32.1093[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]87.7174[/C][C]Range[/C][C]44.95[/C][C]Trim Var.[/C][C]55.6649[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]273.599[/C][C]Range[/C][C]73.05[/C][C]Trim Var.[/C][C]201.586[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1013.25[/C][C]Range[/C][C]130.45[/C][C]Trim Var.[/C][C]764.563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269110&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269110&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)10.9506Range14.95Trim Var.5.895
V(Y[t],d=1,D=0)17.8801Range23Trim Var.9.33412
V(Y[t],d=2,D=0)53.5542Range40.25Trim Var.29.1786
V(Y[t],d=3,D=0)186.446Range79.1Trim Var.98.4535
V(Y[t],d=0,D=1)19.024Range25.5Trim Var.8.89356
V(Y[t],d=1,D=1)28.9078Range28.8Trim Var.15.0643
V(Y[t],d=2,D=1)87.1816Range52.5Trim Var.52.3257
V(Y[t],d=3,D=1)317.537Range91.6Trim Var.205.007
V(Y[t],d=0,D=2)57.3794Range38.65Trim Var.32.1093
V(Y[t],d=1,D=2)87.7174Range44.95Trim Var.55.6649
V(Y[t],d=2,D=2)273.599Range73.05Trim Var.201.586
V(Y[t],d=3,D=2)1013.25Range130.45Trim Var.764.563


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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()