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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, 19 Dec 2017 12:18:05 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/19/t1513682394jimmws1imjoonje.htm/, Retrieved Wed, 15 May 2024 13:51:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310282, Retrieved Wed, 15 May 2024 13:51:46 +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] [] [2017-12-19 11:18:05] [1ea4e9c673228daef4af35aa2d91fd76] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15,4
17,3
19,2
14,5
11,1
7,1
5,1
2,1
1,4
3
9
11,1
15,8
20,2
18,6
14,8
12,8
6,4
6,1
6,1
6,6
9,3
12,4
13,5
16,5
19,3
16,2
16,5
13,6
8,8
4,3
3,5
3,3
6,6
10,3
13,1
16,5
19
19,4
13.5
10.2
10.1
9.6
4.8
4.5
5.3
8.5
14.2
16
18.3
18,1
17.5
9.7
6.1
4.7
1.1
6.1
9.6
8.8
15.5
19.2

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310282&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310282&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)30.3265Range19.1Trim Var.22.1229
V(Y[t],d=1,D=0)11.3702Range14.5Trim Var.7.93452
V(Y[t],d=2,D=0)11.7094Range15.8Trim Var.7.24401
V(Y[t],d=3,D=0)30.1418Range22.3Trim Var.20.588
V(Y[t],d=0,D=1)6.89647Range11.2Trim Var.4.39835
V(Y[t],d=1,D=1)7.29738Range11.5Trim Var.4.59519
V(Y[t],d=2,D=1)16.3842Range15.7Trim Var.9.9373
V(Y[t],d=3,D=1)46.9559Range31.2Trim Var.26.9937
V(Y[t],d=0,D=2)19.4945Range17.3Trim Var.13.2026
V(Y[t],d=1,D=2)20.98Range21.8Trim Var.11.6661
V(Y[t],d=2,D=2)45.6868Range31.2Trim Var.23.7609
V(Y[t],d=3,D=2)132.137Range57.3Trim Var.67.3244

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30.3265 & Range & 19.1 & Trim Var. & 22.1229 \tabularnewline
V(Y[t],d=1,D=0) & 11.3702 & Range & 14.5 & Trim Var. & 7.93452 \tabularnewline
V(Y[t],d=2,D=0) & 11.7094 & Range & 15.8 & Trim Var. & 7.24401 \tabularnewline
V(Y[t],d=3,D=0) & 30.1418 & Range & 22.3 & Trim Var. & 20.588 \tabularnewline
V(Y[t],d=0,D=1) & 6.89647 & Range & 11.2 & Trim Var. & 4.39835 \tabularnewline
V(Y[t],d=1,D=1) & 7.29738 & Range & 11.5 & Trim Var. & 4.59519 \tabularnewline
V(Y[t],d=2,D=1) & 16.3842 & Range & 15.7 & Trim Var. & 9.9373 \tabularnewline
V(Y[t],d=3,D=1) & 46.9559 & Range & 31.2 & Trim Var. & 26.9937 \tabularnewline
V(Y[t],d=0,D=2) & 19.4945 & Range & 17.3 & Trim Var. & 13.2026 \tabularnewline
V(Y[t],d=1,D=2) & 20.98 & Range & 21.8 & Trim Var. & 11.6661 \tabularnewline
V(Y[t],d=2,D=2) & 45.6868 & Range & 31.2 & Trim Var. & 23.7609 \tabularnewline
V(Y[t],d=3,D=2) & 132.137 & Range & 57.3 & Trim Var. & 67.3244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310282&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30.3265[/C][C]Range[/C][C]19.1[/C][C]Trim Var.[/C][C]22.1229[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]11.3702[/C][C]Range[/C][C]14.5[/C][C]Trim Var.[/C][C]7.93452[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]11.7094[/C][C]Range[/C][C]15.8[/C][C]Trim Var.[/C][C]7.24401[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]30.1418[/C][C]Range[/C][C]22.3[/C][C]Trim Var.[/C][C]20.588[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6.89647[/C][C]Range[/C][C]11.2[/C][C]Trim Var.[/C][C]4.39835[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]7.29738[/C][C]Range[/C][C]11.5[/C][C]Trim Var.[/C][C]4.59519[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]16.3842[/C][C]Range[/C][C]15.7[/C][C]Trim Var.[/C][C]9.9373[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]46.9559[/C][C]Range[/C][C]31.2[/C][C]Trim Var.[/C][C]26.9937[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.4945[/C][C]Range[/C][C]17.3[/C][C]Trim Var.[/C][C]13.2026[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]20.98[/C][C]Range[/C][C]21.8[/C][C]Trim Var.[/C][C]11.6661[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]45.6868[/C][C]Range[/C][C]31.2[/C][C]Trim Var.[/C][C]23.7609[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]132.137[/C][C]Range[/C][C]57.3[/C][C]Trim Var.[/C][C]67.3244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310282&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)30.3265Range19.1Trim Var.22.1229
V(Y[t],d=1,D=0)11.3702Range14.5Trim Var.7.93452
V(Y[t],d=2,D=0)11.7094Range15.8Trim Var.7.24401
V(Y[t],d=3,D=0)30.1418Range22.3Trim Var.20.588
V(Y[t],d=0,D=1)6.89647Range11.2Trim Var.4.39835
V(Y[t],d=1,D=1)7.29738Range11.5Trim Var.4.59519
V(Y[t],d=2,D=1)16.3842Range15.7Trim Var.9.9373
V(Y[t],d=3,D=1)46.9559Range31.2Trim Var.26.9937
V(Y[t],d=0,D=2)19.4945Range17.3Trim Var.13.2026
V(Y[t],d=1,D=2)20.98Range21.8Trim Var.11.6661
V(Y[t],d=2,D=2)45.6868Range31.2Trim Var.23.7609
V(Y[t],d=3,D=2)132.137Range57.3Trim Var.67.3244


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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()