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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 computationTue, 19 Dec 2017 17:59:34 +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/Dec/19/t1513702799ptmpf9onxvigmgm.htm/, Retrieved Tue, 10 Feb 2026 09:30:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310379, Retrieved Tue, 10 Feb 2026 09:30:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact313

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] [matrix] [2017-12-19 16:59:34] [341fa61cadd50fad972999b365b6b694] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
63,2
68,6
77,7
68,1
75,1
73,3
60,5
65,9
77,7
77,1
77,7
71,3
76
75,3
81,7
72,5
77,4
81,1
65,1
68,7
75,6
79,7
75,3
67,7
73,2
72,2
79,3
77,5
75,6
77,4
69,2
67,1
77,9
82,7
75,7
70,1
76,4
74,3
80,5
78
73,5
78,8
71,2
66,2
82,7
83,8
75
80,4
74,6
77,7
89,8
82,4
77
89,6
75,7
75,1
89,9
88,8
86,5
90
84
82,7
91,7
87,5
82
92,2
73,1
75,6
91,6
87,5
90,1
91,3
87,6
88,4
100,7
85,3
92
96,8
77,9
80,9
95,3
99,3
96,1
92,5
93,7
92,1
103,6
92,5
95,7
103,4
89
89,1
98,7
109,4
101,1
95,4
101,4
102,1
103,6
106
98,4
106,6
95,8
87,2
108,5
107
92
94,9
84,4
85
94
84,5
88,2
92,1
81,1
81,2
96,1
95,3
92,1
91,7
90,3
96,1
108,7
95,9
95,1
109,4
91,2
91,4
107,4
105,6
105,3
103,7
99,5
103,2
123,1
102,2
110
106,2
91,3
99,3
111,8
104,4
102,4
101
100,6
104,5
117,4
97,4
99,5
106,4
95,2
94
104,1
105,8
101,1
93,5
97,9
96,8
108,4
103,5
101,3
107,4
100,7
91,1
105
112,8
105,6
101
101,9
103,5
109,5
105
102,9
108,5
96,9
88,4
112,4
111,3
101,6
101,2
101,8
98,8
114,4
104,5
97,6
109,1
94,5
90,4
111,8
110,5
106,8
101,8
103,7
107,4
117,5
109,6
102,8
115,5
97,8
100,2
112,9
108,7
109
113,9
106,9
109,6
124,5
104,2
110,8
118,7
102,1
105,1

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=310379&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=310379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310379&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)188.402Range64Trim Var.135.322
V(Y[t],d=1,D=0)76.5939Range44.9Trim Var.47.3349
V(Y[t],d=2,D=0)203.62Range73.3Trim Var.134.35
V(Y[t],d=3,D=0)599.695Range127.1Trim Var.371.298
V(Y[t],d=0,D=1)39.7579Range38.8Trim Var.21.3076
V(Y[t],d=1,D=1)34.3726Range33.2Trim Var.20.8014
V(Y[t],d=2,D=1)103.327Range52.5Trim Var.62.25
V(Y[t],d=3,D=1)341.1Range95.9Trim Var.198.443
V(Y[t],d=0,D=2)105.287Range67.9Trim Var.47.3162
V(Y[t],d=1,D=2)85.9985Range57.3Trim Var.49.8651
V(Y[t],d=2,D=2)256.229Range90.4Trim Var.148.881
V(Y[t],d=3,D=2)846.453Range164.8Trim Var.475.079

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 188.402 & Range & 64 & Trim Var. & 135.322 \tabularnewline
V(Y[t],d=1,D=0) & 76.5939 & Range & 44.9 & Trim Var. & 47.3349 \tabularnewline
V(Y[t],d=2,D=0) & 203.62 & Range & 73.3 & Trim Var. & 134.35 \tabularnewline
V(Y[t],d=3,D=0) & 599.695 & Range & 127.1 & Trim Var. & 371.298 \tabularnewline
V(Y[t],d=0,D=1) & 39.7579 & Range & 38.8 & Trim Var. & 21.3076 \tabularnewline
V(Y[t],d=1,D=1) & 34.3726 & Range & 33.2 & Trim Var. & 20.8014 \tabularnewline
V(Y[t],d=2,D=1) & 103.327 & Range & 52.5 & Trim Var. & 62.25 \tabularnewline
V(Y[t],d=3,D=1) & 341.1 & Range & 95.9 & Trim Var. & 198.443 \tabularnewline
V(Y[t],d=0,D=2) & 105.287 & Range & 67.9 & Trim Var. & 47.3162 \tabularnewline
V(Y[t],d=1,D=2) & 85.9985 & Range & 57.3 & Trim Var. & 49.8651 \tabularnewline
V(Y[t],d=2,D=2) & 256.229 & Range & 90.4 & Trim Var. & 148.881 \tabularnewline
V(Y[t],d=3,D=2) & 846.453 & Range & 164.8 & Trim Var. & 475.079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310379&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]188.402[/C][C]Range[/C][C]64[/C][C]Trim Var.[/C][C]135.322[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]76.5939[/C][C]Range[/C][C]44.9[/C][C]Trim Var.[/C][C]47.3349[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]203.62[/C][C]Range[/C][C]73.3[/C][C]Trim Var.[/C][C]134.35[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]599.695[/C][C]Range[/C][C]127.1[/C][C]Trim Var.[/C][C]371.298[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]39.7579[/C][C]Range[/C][C]38.8[/C][C]Trim Var.[/C][C]21.3076[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]34.3726[/C][C]Range[/C][C]33.2[/C][C]Trim Var.[/C][C]20.8014[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]103.327[/C][C]Range[/C][C]52.5[/C][C]Trim Var.[/C][C]62.25[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]341.1[/C][C]Range[/C][C]95.9[/C][C]Trim Var.[/C][C]198.443[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]105.287[/C][C]Range[/C][C]67.9[/C][C]Trim Var.[/C][C]47.3162[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]85.9985[/C][C]Range[/C][C]57.3[/C][C]Trim Var.[/C][C]49.8651[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]256.229[/C][C]Range[/C][C]90.4[/C][C]Trim Var.[/C][C]148.881[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]846.453[/C][C]Range[/C][C]164.8[/C][C]Trim Var.[/C][C]475.079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310379&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)188.402Range64Trim Var.135.322
V(Y[t],d=1,D=0)76.5939Range44.9Trim Var.47.3349
V(Y[t],d=2,D=0)203.62Range73.3Trim Var.134.35
V(Y[t],d=3,D=0)599.695Range127.1Trim Var.371.298
V(Y[t],d=0,D=1)39.7579Range38.8Trim Var.21.3076
V(Y[t],d=1,D=1)34.3726Range33.2Trim Var.20.8014
V(Y[t],d=2,D=1)103.327Range52.5Trim Var.62.25
V(Y[t],d=3,D=1)341.1Range95.9Trim Var.198.443
V(Y[t],d=0,D=2)105.287Range67.9Trim Var.47.3162
V(Y[t],d=1,D=2)85.9985Range57.3Trim Var.49.8651
V(Y[t],d=2,D=2)256.229Range90.4Trim Var.148.881
V(Y[t],d=3,D=2)846.453Range164.8Trim Var.475.079


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = 0 ; par5 = 0 ; par6 = 12 ;
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()