FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationSat, 17 Dec 2016 13:48:05 +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/2016/Dec/17/t1481979382znbs6fi7a4x6c8j.htm/, Retrieved Thu, 02 May 2024 09:19:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300764, Retrieved Thu, 02 May 2024 09:19:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [N2568] [2016-12-17 12:48:05] [563c2945bc7c763925d38f2fb19cdb55] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5750.5
3881.6
4350.4
6623.4
3375.5
6651.7
4394.8
4968.3
6355.6
4515.7
4620
5804.4
6254.4
4788.6
4446.4
8018
3745.9
6928.2
5201.7
5520.9
6801.9
5225.1
5149.4
6240.4
7045.4
5402.1
4960.6
9459.3
3979.4
7215.1
5797
5577.6
7380.8
5788.6
5116.3
6819.3
7671
5337
4955.7
9143.8
4624.6
7702.4
6297.4
5652.3
7801.3
5901.2
5296.7
7803.5
8177.1
5546.3
5651.5
12289.7
4769.1
8294.5
6422.3
6021.3
9241
6229.5
5691.5
8546.9
8174
6027.9
6566.4
10926.6
5963.5
9914
6063.1
6939
9774.2
6358.2
6432
9365.5
8930.6
6189.7
6820.5
12889.2
7102.5
10824.9
6619.1
7613.6
9923.3
6842.6
7121.3
8913
9952.4
6514.1
6480.5
13960.4
6918.6
11060.1
7232.9
7846.2
10293.9
7698.6
7050.7
10190
10071.3
6765.7
6480.5
14038
6356
10338.9
7859.3
7642.6
10935
7806.5
7309.5
10363.6
10403.1
6274.7
7212.7
13835.1
6218.4
12087.8
7905
7810.1

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=300764&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=300764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300764&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)5065990Range10662.5Trim Var.2915000
V(Y[t],d=1,D=0)10127100Range15239.5Trim Var.5838120
V(Y[t],d=2,D=0)33386500Range28725.6Trim Var.19280600
V(Y[t],d=3,D=0)114724000Range51263.5Trim Var.64879600
V(Y[t],d=0,D=1)339074Range4509Trim Var.134854
V(Y[t],d=1,D=1)775093Range5558.9Trim Var.353602
V(Y[t],d=2,D=1)2425250Range10287Trim Var.1267960
V(Y[t],d=3,D=1)8035240Range16315.6Trim Var.4190520
V(Y[t],d=0,D=2)879065Range7970.4Trim Var.228432
V(Y[t],d=1,D=2)2014240Range10287Trim Var.627945
V(Y[t],d=2,D=2)6258520Range17654.6Trim Var.2523970
V(Y[t],d=3,D=2)20689800Range30830.3Trim Var.7982010

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 5065990 & Range & 10662.5 & Trim Var. & 2915000 \tabularnewline
V(Y[t],d=1,D=0) & 10127100 & Range & 15239.5 & Trim Var. & 5838120 \tabularnewline
V(Y[t],d=2,D=0) & 33386500 & Range & 28725.6 & Trim Var. & 19280600 \tabularnewline
V(Y[t],d=3,D=0) & 114724000 & Range & 51263.5 & Trim Var. & 64879600 \tabularnewline
V(Y[t],d=0,D=1) & 339074 & Range & 4509 & Trim Var. & 134854 \tabularnewline
V(Y[t],d=1,D=1) & 775093 & Range & 5558.9 & Trim Var. & 353602 \tabularnewline
V(Y[t],d=2,D=1) & 2425250 & Range & 10287 & Trim Var. & 1267960 \tabularnewline
V(Y[t],d=3,D=1) & 8035240 & Range & 16315.6 & Trim Var. & 4190520 \tabularnewline
V(Y[t],d=0,D=2) & 879065 & Range & 7970.4 & Trim Var. & 228432 \tabularnewline
V(Y[t],d=1,D=2) & 2014240 & Range & 10287 & Trim Var. & 627945 \tabularnewline
V(Y[t],d=2,D=2) & 6258520 & Range & 17654.6 & Trim Var. & 2523970 \tabularnewline
V(Y[t],d=3,D=2) & 20689800 & Range & 30830.3 & Trim Var. & 7982010 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300764&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]5065990[/C][C]Range[/C][C]10662.5[/C][C]Trim Var.[/C][C]2915000[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]10127100[/C][C]Range[/C][C]15239.5[/C][C]Trim Var.[/C][C]5838120[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]33386500[/C][C]Range[/C][C]28725.6[/C][C]Trim Var.[/C][C]19280600[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]114724000[/C][C]Range[/C][C]51263.5[/C][C]Trim Var.[/C][C]64879600[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]339074[/C][C]Range[/C][C]4509[/C][C]Trim Var.[/C][C]134854[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]775093[/C][C]Range[/C][C]5558.9[/C][C]Trim Var.[/C][C]353602[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2425250[/C][C]Range[/C][C]10287[/C][C]Trim Var.[/C][C]1267960[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]8035240[/C][C]Range[/C][C]16315.6[/C][C]Trim Var.[/C][C]4190520[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]879065[/C][C]Range[/C][C]7970.4[/C][C]Trim Var.[/C][C]228432[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2014240[/C][C]Range[/C][C]10287[/C][C]Trim Var.[/C][C]627945[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6258520[/C][C]Range[/C][C]17654.6[/C][C]Trim Var.[/C][C]2523970[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]20689800[/C][C]Range[/C][C]30830.3[/C][C]Trim Var.[/C][C]7982010[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300764&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)5065990Range10662.5Trim Var.2915000
V(Y[t],d=1,D=0)10127100Range15239.5Trim Var.5838120
V(Y[t],d=2,D=0)33386500Range28725.6Trim Var.19280600
V(Y[t],d=3,D=0)114724000Range51263.5Trim Var.64879600
V(Y[t],d=0,D=1)339074Range4509Trim Var.134854
V(Y[t],d=1,D=1)775093Range5558.9Trim Var.353602
V(Y[t],d=2,D=1)2425250Range10287Trim Var.1267960
V(Y[t],d=3,D=1)8035240Range16315.6Trim Var.4190520
V(Y[t],d=0,D=2)879065Range7970.4Trim Var.228432
V(Y[t],d=1,D=2)2014240Range10287Trim Var.627945
V(Y[t],d=2,D=2)6258520Range17654.6Trim Var.2523970
V(Y[t],d=3,D=2)20689800Range30830.3Trim Var.7982010


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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()