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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 computationFri, 16 Dec 2016 15:05:33 +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/16/t1481897157w5n8tgq3goscygo.htm/, Retrieved Thu, 20 Feb 2025 19:09:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300282, Retrieved Thu, 20 Feb 2025 19:09:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-16 14:05:33] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4838
5531
5367.5
5013.5
5959.5
6334
5919
6248.5
5701
6530.5
7145.5
6819
7037
7809
6300
7143.5
7234.5
6567.5
6090
5654
6608
7566
6352.5
8592
6631.5
6852
7538
8407
7541
9904.5
9371
8091.5
8303.5
8617.5
10453.5
9990.5
8337
8336.5
10345.5
11060.5
9384.5
8357
8366
8404.5
8068
6518.5
9355
7298.5
8012
7189
6992
10277
7146.5
7102
7257
7088.5
9070.5
9606.5
6280
6248
6311.5
6434
7096.5
6601.5
5905
7006.5
6113.5
6911.5
6450.5
6504
7710
7045
6302.5
6810
7567
7051
7820
8514
8180
8140
8349.5
8474
7880
8130.5
8020.5
8232.5
8457
7468.5
6763
7877.5
7438
7131
7270
7203.5
7010
6564.5
6734.5
7571.5
6491
6489.5
6883.5
6958.5
5731.5
7157.5
6336
6862.5
7175.5
7408.5
7052
6685.5
7098.5
7048
7017
7099
7310
7868

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300282&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300282&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)1346650Range6222.5Trim Var.734267
V(Y[t],d=1,D=0)1021780Range6611.5Trim Var.437592
V(Y[t],d=2,D=0)2812270Range10801.5Trim Var.1304950
V(Y[t],d=3,D=0)8934490Range19399Trim Var.3740080
V(Y[t],d=0,D=1)2447870Range7776.5Trim Var.1439450
V(Y[t],d=1,D=1)2311340Range10695.5Trim Var.1063540
V(Y[t],d=2,D=1)6501380Range16436Trim Var.3143590
V(Y[t],d=3,D=1)20605500Range27298Trim Var.10598100
V(Y[t],d=0,D=2)6811810Range11377.5Trim Var.4412190
V(Y[t],d=1,D=2)7332510Range17859Trim Var.3365460
V(Y[t],d=2,D=2)20611800Range26616.5Trim Var.9803190
V(Y[t],d=3,D=2)65079600Range48510.5Trim Var.31605800

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1346650 & Range & 6222.5 & Trim Var. & 734267 \tabularnewline
V(Y[t],d=1,D=0) & 1021780 & Range & 6611.5 & Trim Var. & 437592 \tabularnewline
V(Y[t],d=2,D=0) & 2812270 & Range & 10801.5 & Trim Var. & 1304950 \tabularnewline
V(Y[t],d=3,D=0) & 8934490 & Range & 19399 & Trim Var. & 3740080 \tabularnewline
V(Y[t],d=0,D=1) & 2447870 & Range & 7776.5 & Trim Var. & 1439450 \tabularnewline
V(Y[t],d=1,D=1) & 2311340 & Range & 10695.5 & Trim Var. & 1063540 \tabularnewline
V(Y[t],d=2,D=1) & 6501380 & Range & 16436 & Trim Var. & 3143590 \tabularnewline
V(Y[t],d=3,D=1) & 20605500 & Range & 27298 & Trim Var. & 10598100 \tabularnewline
V(Y[t],d=0,D=2) & 6811810 & Range & 11377.5 & Trim Var. & 4412190 \tabularnewline
V(Y[t],d=1,D=2) & 7332510 & Range & 17859 & Trim Var. & 3365460 \tabularnewline
V(Y[t],d=2,D=2) & 20611800 & Range & 26616.5 & Trim Var. & 9803190 \tabularnewline
V(Y[t],d=3,D=2) & 65079600 & Range & 48510.5 & Trim Var. & 31605800 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300282&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1346650[/C][C]Range[/C][C]6222.5[/C][C]Trim Var.[/C][C]734267[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1021780[/C][C]Range[/C][C]6611.5[/C][C]Trim Var.[/C][C]437592[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2812270[/C][C]Range[/C][C]10801.5[/C][C]Trim Var.[/C][C]1304950[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]8934490[/C][C]Range[/C][C]19399[/C][C]Trim Var.[/C][C]3740080[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2447870[/C][C]Range[/C][C]7776.5[/C][C]Trim Var.[/C][C]1439450[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2311340[/C][C]Range[/C][C]10695.5[/C][C]Trim Var.[/C][C]1063540[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]6501380[/C][C]Range[/C][C]16436[/C][C]Trim Var.[/C][C]3143590[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]20605500[/C][C]Range[/C][C]27298[/C][C]Trim Var.[/C][C]10598100[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6811810[/C][C]Range[/C][C]11377.5[/C][C]Trim Var.[/C][C]4412190[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]7332510[/C][C]Range[/C][C]17859[/C][C]Trim Var.[/C][C]3365460[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]20611800[/C][C]Range[/C][C]26616.5[/C][C]Trim Var.[/C][C]9803190[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]65079600[/C][C]Range[/C][C]48510.5[/C][C]Trim Var.[/C][C]31605800[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300282&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)1346650Range6222.5Trim Var.734267
V(Y[t],d=1,D=0)1021780Range6611.5Trim Var.437592
V(Y[t],d=2,D=0)2812270Range10801.5Trim Var.1304950
V(Y[t],d=3,D=0)8934490Range19399Trim Var.3740080
V(Y[t],d=0,D=1)2447870Range7776.5Trim Var.1439450
V(Y[t],d=1,D=1)2311340Range10695.5Trim Var.1063540
V(Y[t],d=2,D=1)6501380Range16436Trim Var.3143590
V(Y[t],d=3,D=1)20605500Range27298Trim Var.10598100
V(Y[t],d=0,D=2)6811810Range11377.5Trim Var.4412190
V(Y[t],d=1,D=2)7332510Range17859Trim Var.3365460
V(Y[t],d=2,D=2)20611800Range26616.5Trim Var.9803190
V(Y[t],d=3,D=2)65079600Range48510.5Trim Var.31605800


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
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()