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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 computationSat, 21 Jan 2017 18:41:50 +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/Jan/21/t1485020558dvg2ew5p8jlvksm.htm/, Retrieved Tue, 14 May 2024 23:05:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=303286, Retrieved Tue, 14 May 2024 23:05:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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] [] [2017-01-21 17:41:50] [673dd365cbcfe0c4e35658a2fe545652] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4678.2
3300.8
3823
4085.4
3742.4
4505
4259.4
4236
4529.8
4982
5151
5077.6
4944.2
4986
5949.8
4649.4
4564.4
4634
4993.6
4686.2
4511
4554.6
5447.2
5150.8
5184
4671
4640.6
4773
5019.8
5627.4
5273
5626.4
5574.4
5414.4
4517.8
5889.6
6024.4
5354.6
5883.6
5233.4
5268.2
4790.6
5607
4922.6
5610.8
5442.8
5517
5902.6
5576.8
5675
6109.6
5839.6
6175.8
5784.6
6059.6
5424.6
5184.2
5742.6
5835.8
6002.6
6490.2
6231.4
6016.6
6399.2
5666.8
6612.6
6290.4
6496.6
6271
6948.8
6216.4
8094.8
7462.2
6713.6
7390
7272.6
6258
6377.2
6981
6569
6289
6208
7210
7919.6
5471.8
6113.4
7464.2
6250.2
6601.8
6489.2
6545.6
6559.4
6385.8
7090.4
5306.6
6509
6020.2
5984.8
5505.8
5347.2
5656.2
5571.8
7332.8
6561.4
5677
6298.6
6511.4
5587.4
5867.6
5857.6
6315
6585
6151.2
6216.6
5517.2
5689

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=303286&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=303286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303286&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)789012Range4794Trim Var.470250
V(Y[t],d=1,D=0)431436Range4326.2Trim Var.207033
V(Y[t],d=2,D=0)1226880Range6246.8Trim Var.599822
V(Y[t],d=3,D=0)3913220Range11368.6Trim Var.2132200
V(Y[t],d=0,D=1)664979Range4117.2Trim Var.358192
V(Y[t],d=1,D=1)925288Range4782.4Trim Var.519474
V(Y[t],d=2,D=1)2594990Range7580.4Trim Var.1582630
V(Y[t],d=3,D=1)8203230Range13221Trim Var.5310380
V(Y[t],d=0,D=2)1764570Range6544.2Trim Var.1048510
V(Y[t],d=1,D=2)2855610Range9302.6Trim Var.1695710
V(Y[t],d=2,D=2)7952050Range13583.4Trim Var.4765400
V(Y[t],d=3,D=2)24948700Range25299Trim Var.16740400

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 789012 & Range & 4794 & Trim Var. & 470250 \tabularnewline
V(Y[t],d=1,D=0) & 431436 & Range & 4326.2 & Trim Var. & 207033 \tabularnewline
V(Y[t],d=2,D=0) & 1226880 & Range & 6246.8 & Trim Var. & 599822 \tabularnewline
V(Y[t],d=3,D=0) & 3913220 & Range & 11368.6 & Trim Var. & 2132200 \tabularnewline
V(Y[t],d=0,D=1) & 664979 & Range & 4117.2 & Trim Var. & 358192 \tabularnewline
V(Y[t],d=1,D=1) & 925288 & Range & 4782.4 & Trim Var. & 519474 \tabularnewline
V(Y[t],d=2,D=1) & 2594990 & Range & 7580.4 & Trim Var. & 1582630 \tabularnewline
V(Y[t],d=3,D=1) & 8203230 & Range & 13221 & Trim Var. & 5310380 \tabularnewline
V(Y[t],d=0,D=2) & 1764570 & Range & 6544.2 & Trim Var. & 1048510 \tabularnewline
V(Y[t],d=1,D=2) & 2855610 & Range & 9302.6 & Trim Var. & 1695710 \tabularnewline
V(Y[t],d=2,D=2) & 7952050 & Range & 13583.4 & Trim Var. & 4765400 \tabularnewline
V(Y[t],d=3,D=2) & 24948700 & Range & 25299 & Trim Var. & 16740400 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=303286&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]789012[/C][C]Range[/C][C]4794[/C][C]Trim Var.[/C][C]470250[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]431436[/C][C]Range[/C][C]4326.2[/C][C]Trim Var.[/C][C]207033[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1226880[/C][C]Range[/C][C]6246.8[/C][C]Trim Var.[/C][C]599822[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3913220[/C][C]Range[/C][C]11368.6[/C][C]Trim Var.[/C][C]2132200[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]664979[/C][C]Range[/C][C]4117.2[/C][C]Trim Var.[/C][C]358192[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]925288[/C][C]Range[/C][C]4782.4[/C][C]Trim Var.[/C][C]519474[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2594990[/C][C]Range[/C][C]7580.4[/C][C]Trim Var.[/C][C]1582630[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]8203230[/C][C]Range[/C][C]13221[/C][C]Trim Var.[/C][C]5310380[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1764570[/C][C]Range[/C][C]6544.2[/C][C]Trim Var.[/C][C]1048510[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2855610[/C][C]Range[/C][C]9302.6[/C][C]Trim Var.[/C][C]1695710[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]7952050[/C][C]Range[/C][C]13583.4[/C][C]Trim Var.[/C][C]4765400[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]24948700[/C][C]Range[/C][C]25299[/C][C]Trim Var.[/C][C]16740400[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=303286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=303286&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)789012Range4794Trim Var.470250
V(Y[t],d=1,D=0)431436Range4326.2Trim Var.207033
V(Y[t],d=2,D=0)1226880Range6246.8Trim Var.599822
V(Y[t],d=3,D=0)3913220Range11368.6Trim Var.2132200
V(Y[t],d=0,D=1)664979Range4117.2Trim Var.358192
V(Y[t],d=1,D=1)925288Range4782.4Trim Var.519474
V(Y[t],d=2,D=1)2594990Range7580.4Trim Var.1582630
V(Y[t],d=3,D=1)8203230Range13221Trim Var.5310380
V(Y[t],d=0,D=2)1764570Range6544.2Trim Var.1048510
V(Y[t],d=1,D=2)2855610Range9302.6Trim Var.1695710
V(Y[t],d=2,D=2)7952050Range13583.4Trim Var.4765400
V(Y[t],d=3,D=2)24948700Range25299Trim Var.16740400


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()