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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, 21 Nov 2014 16:29:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/21/t1416587557bsi0jm59tn3crh4.htm/, Retrieved Thu, 12 Feb 2026 09:26:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257670, Retrieved Thu, 12 Feb 2026 09:26:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact385

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP     [Variance Reduction Matrix] [] [2014-11-21 16:29:18] [37e054ac358b2aa7c2a1d0b751dfa890] [Current]
- RM        [Variance Reduction Matrix] [] [2014-11-21 16:33:13] [cc401d1001c65f55a3dfc6f2420e9570]
- RMP       [(Partial) Autocorrelation Function] [] [2014-11-21 16:38:49] [cc401d1001c65f55a3dfc6f2420e9570]
- RM          [(Partial) Autocorrelation Function] [] [2014-11-21 16:47:01] [cc401d1001c65f55a3dfc6f2420e9570]
-             [(Partial) Autocorrelation Function] [] [2014-11-21 16:49:55] [cc401d1001c65f55a3dfc6f2420e9570]
- RM          [Spectral Analysis] [] [2014-11-21 16:55:18] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [Variance Reduction Matrix] [] [2014-11-21 17:12:26] [cc401d1001c65f55a3dfc6f2420e9570]
-    D        [(Partial) Autocorrelation Function] [] [2014-11-21 17:14:57] [cc401d1001c65f55a3dfc6f2420e9570]
-    D        [(Partial) Autocorrelation Function] [] [2014-11-21 17:16:42] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [Spectral Analysis] [] [2014-11-21 17:18:15] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [Spectral Analysis] [] [2014-11-21 17:21:42] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [Standard Deviation-Mean Plot] [] [2014-11-21 17:49:01] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [ARIMA Backward Selection] [] [2014-11-21 18:16:23] [cc401d1001c65f55a3dfc6f2420e9570]
- RM D        [ARIMA Forecasting] [] [2014-11-21 18:36:31] [cc401d1001c65f55a3dfc6f2420e9570]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257670&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257670&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)145.731Range52Trim Var.87.8913
V(Y[t],d=1,D=0)271.827Range73Trim Var.176.435
V(Y[t],d=2,D=0)726.85Range111Trim Var.483.099
V(Y[t],d=3,D=0)2183.96Range208Trim Var.1418.16
V(Y[t],d=0,D=1)131.779Range55Trim Var.79.2329
V(Y[t],d=1,D=1)263.925Range64Trim Var.201.459
V(Y[t],d=2,D=1)797.136Range111Trim Var.587.843
V(Y[t],d=3,D=1)2651.61Range209Trim Var.2009.92
V(Y[t],d=0,D=2)391.872Range98Trim Var.211.113
V(Y[t],d=1,D=2)831.144Range100Trim Var.597
V(Y[t],d=2,D=2)2526.44Range197Trim Var.1816.76
V(Y[t],d=3,D=2)8301.16Range332Trim Var.5960.75

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 145.731 & Range & 52 & Trim Var. & 87.8913 \tabularnewline
V(Y[t],d=1,D=0) & 271.827 & Range & 73 & Trim Var. & 176.435 \tabularnewline
V(Y[t],d=2,D=0) & 726.85 & Range & 111 & Trim Var. & 483.099 \tabularnewline
V(Y[t],d=3,D=0) & 2183.96 & Range & 208 & Trim Var. & 1418.16 \tabularnewline
V(Y[t],d=0,D=1) & 131.779 & Range & 55 & Trim Var. & 79.2329 \tabularnewline
V(Y[t],d=1,D=1) & 263.925 & Range & 64 & Trim Var. & 201.459 \tabularnewline
V(Y[t],d=2,D=1) & 797.136 & Range & 111 & Trim Var. & 587.843 \tabularnewline
V(Y[t],d=3,D=1) & 2651.61 & Range & 209 & Trim Var. & 2009.92 \tabularnewline
V(Y[t],d=0,D=2) & 391.872 & Range & 98 & Trim Var. & 211.113 \tabularnewline
V(Y[t],d=1,D=2) & 831.144 & Range & 100 & Trim Var. & 597 \tabularnewline
V(Y[t],d=2,D=2) & 2526.44 & Range & 197 & Trim Var. & 1816.76 \tabularnewline
V(Y[t],d=3,D=2) & 8301.16 & Range & 332 & Trim Var. & 5960.75 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257670&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]145.731[/C][C]Range[/C][C]52[/C][C]Trim Var.[/C][C]87.8913[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]271.827[/C][C]Range[/C][C]73[/C][C]Trim Var.[/C][C]176.435[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]726.85[/C][C]Range[/C][C]111[/C][C]Trim Var.[/C][C]483.099[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2183.96[/C][C]Range[/C][C]208[/C][C]Trim Var.[/C][C]1418.16[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]131.779[/C][C]Range[/C][C]55[/C][C]Trim Var.[/C][C]79.2329[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]263.925[/C][C]Range[/C][C]64[/C][C]Trim Var.[/C][C]201.459[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]797.136[/C][C]Range[/C][C]111[/C][C]Trim Var.[/C][C]587.843[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2651.61[/C][C]Range[/C][C]209[/C][C]Trim Var.[/C][C]2009.92[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]391.872[/C][C]Range[/C][C]98[/C][C]Trim Var.[/C][C]211.113[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]831.144[/C][C]Range[/C][C]100[/C][C]Trim Var.[/C][C]597[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]2526.44[/C][C]Range[/C][C]197[/C][C]Trim Var.[/C][C]1816.76[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]8301.16[/C][C]Range[/C][C]332[/C][C]Trim Var.[/C][C]5960.75[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257670&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)145.731Range52Trim Var.87.8913
V(Y[t],d=1,D=0)271.827Range73Trim Var.176.435
V(Y[t],d=2,D=0)726.85Range111Trim Var.483.099
V(Y[t],d=3,D=0)2183.96Range208Trim Var.1418.16
V(Y[t],d=0,D=1)131.779Range55Trim Var.79.2329
V(Y[t],d=1,D=1)263.925Range64Trim Var.201.459
V(Y[t],d=2,D=1)797.136Range111Trim Var.587.843
V(Y[t],d=3,D=1)2651.61Range209Trim Var.2009.92
V(Y[t],d=0,D=2)391.872Range98Trim Var.211.113
V(Y[t],d=1,D=2)831.144Range100Trim Var.597
V(Y[t],d=2,D=2)2526.44Range197Trim Var.1816.76
V(Y[t],d=3,D=2)8301.16Range332Trim Var.5960.75


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 <- 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)
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()