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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 computationWed, 20 Dec 2017 16:03:17 +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/20/t15137824109nihngjowqcws7n.htm/, Retrieved Tue, 14 May 2024 00:22:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310518, Retrieved Tue, 14 May 2024 00:22:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [variance reduction] [2017-12-20 15:03:17] [84592a6ba07caf36916a6fee2e3505cc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67
61
113
61
43
105
63
64
69
60
59
71
66
65
76
64
41
106
52
62
49
106
75
54
63
48
64
65
69
31
51
52
78
72
80
53
69
61
52
82
100
73
71
62
80
85
65
59
78
92
89
82
83
79
80
50
40
58
56
52
55
59
45
77
48
46
41
35
47
47
26
39
33
40
43
41
24
41
25
22
36
24
27
36
27
27
39
35
29
28
29
23
27
36
35
30
19
22
23
21
34
32
24
22
17
26
19

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=310518&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=310518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310518&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)516.322Range96Trim Var.338.503
V(Y[t],d=1,D=0)370.117Range119Trim Var.130.589
V(Y[t],d=2,D=0)1099.84Range207Trim Var.381.741
V(Y[t],d=3,D=0)3579.24Range390Trim Var.1298.78
V(Y[t],d=0,D=1)369.1Range121Trim Var.186.828
V(Y[t],d=1,D=1)573.297Range177Trim Var.225.928
V(Y[t],d=2,D=1)1718.71Range307Trim Var.630.206
V(Y[t],d=3,D=1)5800.09Range567Trim Var.2240.55
V(Y[t],d=0,D=2)943.85Range198Trim Var.381.445
V(Y[t],d=1,D=2)1606.79Range243Trim Var.659.542
V(Y[t],d=2,D=2)4851.87Range408Trim Var.1994.67
V(Y[t],d=3,D=2)16610.2Range721Trim Var.8019.52

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 516.322 & Range & 96 & Trim Var. & 338.503 \tabularnewline
V(Y[t],d=1,D=0) & 370.117 & Range & 119 & Trim Var. & 130.589 \tabularnewline
V(Y[t],d=2,D=0) & 1099.84 & Range & 207 & Trim Var. & 381.741 \tabularnewline
V(Y[t],d=3,D=0) & 3579.24 & Range & 390 & Trim Var. & 1298.78 \tabularnewline
V(Y[t],d=0,D=1) & 369.1 & Range & 121 & Trim Var. & 186.828 \tabularnewline
V(Y[t],d=1,D=1) & 573.297 & Range & 177 & Trim Var. & 225.928 \tabularnewline
V(Y[t],d=2,D=1) & 1718.71 & Range & 307 & Trim Var. & 630.206 \tabularnewline
V(Y[t],d=3,D=1) & 5800.09 & Range & 567 & Trim Var. & 2240.55 \tabularnewline
V(Y[t],d=0,D=2) & 943.85 & Range & 198 & Trim Var. & 381.445 \tabularnewline
V(Y[t],d=1,D=2) & 1606.79 & Range & 243 & Trim Var. & 659.542 \tabularnewline
V(Y[t],d=2,D=2) & 4851.87 & Range & 408 & Trim Var. & 1994.67 \tabularnewline
V(Y[t],d=3,D=2) & 16610.2 & Range & 721 & Trim Var. & 8019.52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310518&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]516.322[/C][C]Range[/C][C]96[/C][C]Trim Var.[/C][C]338.503[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]370.117[/C][C]Range[/C][C]119[/C][C]Trim Var.[/C][C]130.589[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1099.84[/C][C]Range[/C][C]207[/C][C]Trim Var.[/C][C]381.741[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3579.24[/C][C]Range[/C][C]390[/C][C]Trim Var.[/C][C]1298.78[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]369.1[/C][C]Range[/C][C]121[/C][C]Trim Var.[/C][C]186.828[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]573.297[/C][C]Range[/C][C]177[/C][C]Trim Var.[/C][C]225.928[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1718.71[/C][C]Range[/C][C]307[/C][C]Trim Var.[/C][C]630.206[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]5800.09[/C][C]Range[/C][C]567[/C][C]Trim Var.[/C][C]2240.55[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]943.85[/C][C]Range[/C][C]198[/C][C]Trim Var.[/C][C]381.445[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1606.79[/C][C]Range[/C][C]243[/C][C]Trim Var.[/C][C]659.542[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]4851.87[/C][C]Range[/C][C]408[/C][C]Trim Var.[/C][C]1994.67[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]16610.2[/C][C]Range[/C][C]721[/C][C]Trim Var.[/C][C]8019.52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310518&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)516.322Range96Trim Var.338.503
V(Y[t],d=1,D=0)370.117Range119Trim Var.130.589
V(Y[t],d=2,D=0)1099.84Range207Trim Var.381.741
V(Y[t],d=3,D=0)3579.24Range390Trim Var.1298.78
V(Y[t],d=0,D=1)369.1Range121Trim Var.186.828
V(Y[t],d=1,D=1)573.297Range177Trim Var.225.928
V(Y[t],d=2,D=1)1718.71Range307Trim Var.630.206
V(Y[t],d=3,D=1)5800.09Range567Trim Var.2240.55
V(Y[t],d=0,D=2)943.85Range198Trim Var.381.445
V(Y[t],d=1,D=2)1606.79Range243Trim Var.659.542
V(Y[t],d=2,D=2)4851.87Range408Trim Var.1994.67
V(Y[t],d=3,D=2)16610.2Range721Trim Var.8019.52


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()