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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, 12 Dec 2017 14:51:19 +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/12/t15130868170rxnluwq9fx5mwk.htm/, Retrieved Wed, 26 Aug 2026 23:27:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309093, Retrieved Wed, 26 Aug 2026 23:27:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact372

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] [Dataset_3_varianc...] [2017-12-12 13:51:19] [453a4fcb74c301cf89bf197d0ef2c60e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
78
100,1
113,2
93,1
115,4
103,3
45,1
104,7
111,3
111,5
100,9
82,1
85,4
97,7
106,6
92,6
109,2
110
52,5
105,3
102,3
118,5
100
74,4
89,2
91,9
107
103,6
101,8
105,1
55,5
92,1
109,8
112,7
98,5
70,3
84,5
91,1
107,6
102,2
96
107,3
59,9
90,2
116,3
115,6
92
76,5
87,9
95,8
116,9
102,9
95,8
117,3
52,8
100,1
116,3
111,8
98,5
86,2
79,9
92,3
100,5
112,5
101,1
121,5
49,6
104,8
120,4
108,3
105,2
85,7
86,8
95,1
117
100,1
112,3
119,6
51,8
105,5
119,9
115,4
112,8
85,1
96,2
103,6
119,9
103,7
109
119,6
57
109,2
112,6
126
109,7
80,1
105,8
114,1
98,3
125,3
111,6
119,7
65
99
124,5
119
98,8
81,8
90,3
102
119,3
104,3
102,8
118,8
60,9
101
122,6
122,2
95
75,6
83,1
89,8
126,1
108,6
98,9
124,3
56,8
102,7
121,7
118,2
101
69
88,6
109,6
128,2
102
122,7
110,5
54
108,1
125
114,1
112,4
87,3
95,4
96,9
125,8
102
112,5
118,9
62,7
110
114,7
124,4
111,9
77
84,1
96,5
106,8
107,9
107,5
114,3
66,6
97,9
117,8
123,8
103,3
84,2
103,6
103,6
112,2
102,7
100,8
109,4
63,5
92,3
119,2
121,5
97,6
78,3
95,6
97,9
114,4
100,9
94,4
117,2
61
95,8
116,2
118,5
94,3
74,4
94,9
102
102,9
109,5
99,7
118,3
56,2
100,3
116,9
108,7
93,9
85,3
85,3
102,4
121,6
91,4
110,2
112,7
55,7
100,1

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=309093&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=309093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309093&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)328.494Range83.1Trim Var.201.402
V(Y[t],d=1,D=0)668.899Range131.5Trim Var.368.023
V(Y[t],d=2,D=0)1819.28Range220Trim Var.932.128
V(Y[t],d=3,D=0)5683.09Range390.2Trim Var.2940.76
V(Y[t],d=0,D=1)63.8828Range45.4Trim Var.36.0664
V(Y[t],d=1,D=1)155.769Range85.2Trim Var.82.4823
V(Y[t],d=2,D=1)495.768Range150.4Trim Var.255.909
V(Y[t],d=3,D=1)1672.63Range266.8Trim Var.851.125
V(Y[t],d=0,D=2)163.289Range85.2Trim Var.77.3772
V(Y[t],d=1,D=2)401.795Range150.4Trim Var.202.024
V(Y[t],d=2,D=2)1279.92Range266.8Trim Var.654.477
V(Y[t],d=3,D=2)4333.68Range479.9Trim Var.2229.57

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 328.494 & Range & 83.1 & Trim Var. & 201.402 \tabularnewline
V(Y[t],d=1,D=0) & 668.899 & Range & 131.5 & Trim Var. & 368.023 \tabularnewline
V(Y[t],d=2,D=0) & 1819.28 & Range & 220 & Trim Var. & 932.128 \tabularnewline
V(Y[t],d=3,D=0) & 5683.09 & Range & 390.2 & Trim Var. & 2940.76 \tabularnewline
V(Y[t],d=0,D=1) & 63.8828 & Range & 45.4 & Trim Var. & 36.0664 \tabularnewline
V(Y[t],d=1,D=1) & 155.769 & Range & 85.2 & Trim Var. & 82.4823 \tabularnewline
V(Y[t],d=2,D=1) & 495.768 & Range & 150.4 & Trim Var. & 255.909 \tabularnewline
V(Y[t],d=3,D=1) & 1672.63 & Range & 266.8 & Trim Var. & 851.125 \tabularnewline
V(Y[t],d=0,D=2) & 163.289 & Range & 85.2 & Trim Var. & 77.3772 \tabularnewline
V(Y[t],d=1,D=2) & 401.795 & Range & 150.4 & Trim Var. & 202.024 \tabularnewline
V(Y[t],d=2,D=2) & 1279.92 & Range & 266.8 & Trim Var. & 654.477 \tabularnewline
V(Y[t],d=3,D=2) & 4333.68 & Range & 479.9 & Trim Var. & 2229.57 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309093&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]328.494[/C][C]Range[/C][C]83.1[/C][C]Trim Var.[/C][C]201.402[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]668.899[/C][C]Range[/C][C]131.5[/C][C]Trim Var.[/C][C]368.023[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1819.28[/C][C]Range[/C][C]220[/C][C]Trim Var.[/C][C]932.128[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5683.09[/C][C]Range[/C][C]390.2[/C][C]Trim Var.[/C][C]2940.76[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]63.8828[/C][C]Range[/C][C]45.4[/C][C]Trim Var.[/C][C]36.0664[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]155.769[/C][C]Range[/C][C]85.2[/C][C]Trim Var.[/C][C]82.4823[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]495.768[/C][C]Range[/C][C]150.4[/C][C]Trim Var.[/C][C]255.909[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1672.63[/C][C]Range[/C][C]266.8[/C][C]Trim Var.[/C][C]851.125[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]163.289[/C][C]Range[/C][C]85.2[/C][C]Trim Var.[/C][C]77.3772[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]401.795[/C][C]Range[/C][C]150.4[/C][C]Trim Var.[/C][C]202.024[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1279.92[/C][C]Range[/C][C]266.8[/C][C]Trim Var.[/C][C]654.477[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4333.68[/C][C]Range[/C][C]479.9[/C][C]Trim Var.[/C][C]2229.57[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309093&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)328.494Range83.1Trim Var.201.402
V(Y[t],d=1,D=0)668.899Range131.5Trim Var.368.023
V(Y[t],d=2,D=0)1819.28Range220Trim Var.932.128
V(Y[t],d=3,D=0)5683.09Range390.2Trim Var.2940.76
V(Y[t],d=0,D=1)63.8828Range45.4Trim Var.36.0664
V(Y[t],d=1,D=1)155.769Range85.2Trim Var.82.4823
V(Y[t],d=2,D=1)495.768Range150.4Trim Var.255.909
V(Y[t],d=3,D=1)1672.63Range266.8Trim Var.851.125
V(Y[t],d=0,D=2)163.289Range85.2Trim Var.77.3772
V(Y[t],d=1,D=2)401.795Range150.4Trim Var.202.024
V(Y[t],d=2,D=2)1279.92Range266.8Trim Var.654.477
V(Y[t],d=3,D=2)4333.68Range479.9Trim Var.2229.57


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.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()