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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 computationWed, 07 Dec 2016 19:14:48 +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/07/t1481134525b10hg2h2upvfz54.htm/, Retrieved Tue, 07 May 2024 20:20:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298275, Retrieved Tue, 07 May 2024 20:20:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [N1316] [2016-12-07 18:14:48] [85f5800284aab30c091766186b093bb4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4440
4835
4055
3645
3425
3350
3670
5130
5930
6185
6240
5790
5475
5561.65
8031.65
8961.65
8045
7588.35
8200
7290
6661.65
6385
6268.35
6248.35
6165
6196.65
6050
5705
5530
5311.65
5145
4855
4556.65
4356.65
3823.35
3570
3735
4191.65
3990
3705
4065
3766.65
3666.65
3681.65
3931.65
4268.35
4291.65
4530
5053.35
4996.65
4913.35
4935
4848.35
4788.35
4771.65
4643.35
4778
4983.35
4953.35
5581.65
5185
5746.65
4240
4095

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=298275&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=298275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298275&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)1630150Range5611.65Trim Var.916909
V(Y[t],d=1,D=0)308164Range3976.65Trim Var.88127.3
V(Y[t],d=2,D=0)506013Range4451.65Trim Var.160696
V(Y[t],d=3,D=0)1293010Range7353.3Trim Var.344443
V(Y[t],d=0,D=1)4228190Range8573.3Trim Var.2626430
V(Y[t],d=1,D=1)755087Range5866.65Trim Var.236302
V(Y[t],d=2,D=1)1226650Range6220Trim Var.539394
V(Y[t],d=3,D=1)2957550Range9371.65Trim Var.1169470
V(Y[t],d=0,D=2)10909600Range12321.6Trim Var.7834640
V(Y[t],d=1,D=2)2053750Range8856.65Trim Var.627040
V(Y[t],d=2,D=2)3310240Range10179.9Trim Var.1362990
V(Y[t],d=3,D=2)7586260Range14663.2Trim Var.3112190

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1630150 & Range & 5611.65 & Trim Var. & 916909 \tabularnewline
V(Y[t],d=1,D=0) & 308164 & Range & 3976.65 & Trim Var. & 88127.3 \tabularnewline
V(Y[t],d=2,D=0) & 506013 & Range & 4451.65 & Trim Var. & 160696 \tabularnewline
V(Y[t],d=3,D=0) & 1293010 & Range & 7353.3 & Trim Var. & 344443 \tabularnewline
V(Y[t],d=0,D=1) & 4228190 & Range & 8573.3 & Trim Var. & 2626430 \tabularnewline
V(Y[t],d=1,D=1) & 755087 & Range & 5866.65 & Trim Var. & 236302 \tabularnewline
V(Y[t],d=2,D=1) & 1226650 & Range & 6220 & Trim Var. & 539394 \tabularnewline
V(Y[t],d=3,D=1) & 2957550 & Range & 9371.65 & Trim Var. & 1169470 \tabularnewline
V(Y[t],d=0,D=2) & 10909600 & Range & 12321.6 & Trim Var. & 7834640 \tabularnewline
V(Y[t],d=1,D=2) & 2053750 & Range & 8856.65 & Trim Var. & 627040 \tabularnewline
V(Y[t],d=2,D=2) & 3310240 & Range & 10179.9 & Trim Var. & 1362990 \tabularnewline
V(Y[t],d=3,D=2) & 7586260 & Range & 14663.2 & Trim Var. & 3112190 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298275&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1630150[/C][C]Range[/C][C]5611.65[/C][C]Trim Var.[/C][C]916909[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]308164[/C][C]Range[/C][C]3976.65[/C][C]Trim Var.[/C][C]88127.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]506013[/C][C]Range[/C][C]4451.65[/C][C]Trim Var.[/C][C]160696[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1293010[/C][C]Range[/C][C]7353.3[/C][C]Trim Var.[/C][C]344443[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4228190[/C][C]Range[/C][C]8573.3[/C][C]Trim Var.[/C][C]2626430[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]755087[/C][C]Range[/C][C]5866.65[/C][C]Trim Var.[/C][C]236302[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1226650[/C][C]Range[/C][C]6220[/C][C]Trim Var.[/C][C]539394[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2957550[/C][C]Range[/C][C]9371.65[/C][C]Trim Var.[/C][C]1169470[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]10909600[/C][C]Range[/C][C]12321.6[/C][C]Trim Var.[/C][C]7834640[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2053750[/C][C]Range[/C][C]8856.65[/C][C]Trim Var.[/C][C]627040[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3310240[/C][C]Range[/C][C]10179.9[/C][C]Trim Var.[/C][C]1362990[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]7586260[/C][C]Range[/C][C]14663.2[/C][C]Trim Var.[/C][C]3112190[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298275&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)1630150Range5611.65Trim Var.916909
V(Y[t],d=1,D=0)308164Range3976.65Trim Var.88127.3
V(Y[t],d=2,D=0)506013Range4451.65Trim Var.160696
V(Y[t],d=3,D=0)1293010Range7353.3Trim Var.344443
V(Y[t],d=0,D=1)4228190Range8573.3Trim Var.2626430
V(Y[t],d=1,D=1)755087Range5866.65Trim Var.236302
V(Y[t],d=2,D=1)1226650Range6220Trim Var.539394
V(Y[t],d=3,D=1)2957550Range9371.65Trim Var.1169470
V(Y[t],d=0,D=2)10909600Range12321.6Trim Var.7834640
V(Y[t],d=1,D=2)2053750Range8856.65Trim Var.627040
V(Y[t],d=2,D=2)3310240Range10179.9Trim Var.1362990
V(Y[t],d=3,D=2)7586260Range14663.2Trim Var.3112190


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;
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()