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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 17:12:14 +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/t1513699954bevsmbmjoj4wbpq.htm/, Retrieved Wed, 15 May 2024 09:01:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310369, Retrieved Wed, 15 May 2024 09:01:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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] [Non-durable consu...] [2017-12-19 16:12:14] [a98cfedcb2213d624216c666f97af8d4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
50
52.4
57.5
52.5
57.5
57.6
48.3
52
62.1
59.1
62.6
57.9
59.3
61.5
66
61.1
63.8
69.6
57
59.9
63.8
69.8
64.6
60.8
64.7
63.6
68.8
66.4
64.4
65.3
63
61.1
67.7
72.3
65.4
63.2
69.4
62.3
71
68.6
62
68.2
66.8
65.5
76.9
78.1
67.6
80.1
64.7
70.4
84.6
75.1
69.6
81.8
74.2
72.9
84.9
80.5
79.6
90.8
76.5
70.9
82.3
77.8
75.6
81.3
71
75.1
89.2
84.1
82.7
82.4
78.2
78.5
91.5
76.6
80.6
85.9
74.5
79.4
89.7
92.7
89.6
87
80.9
76.2
89.7
79.1
82.4
90.3
85.8
83.5
85.1
90.6
87.7
86
89.7
86.2
91.1
91.3
85.5
92
91.5
80
100.9
97.3
89.1
104
80.2
83.3
97.5
86.8
84.3
93.4
90.2
82.5
93.7
93.9
91.1
96.9
88.2
100.9
109.5
91
89.5
109.6
97.9
94.9
103.5
100
107.1
108
95
102.2
131.4
104.5
105.6
106.1
98
113
113.2
105.4
100.1
100.7
96.1
98.2
123.5
93.9
94.8
103.5
105.3
105.8
112
114.5
108.3
103.8
103
97.7
118.7
115.1
110
117.3
119.1
105.9
114.1
124.6
117.3
115
103.6
113.4
122
122.5
119.6
132.6
113
107.5
139.3
134.6
125.6
124
111.9
101.5
130.2
121.9
111.3
122
116.4
119.1
133
128.9
126.1
122.3
110.2
113.6
131
123.2
120.7
142.8
131.7
131.6
139
128.5
122.7
148.4
118.6
126.3
141
120.9
127
138.5
131.9
136.3

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=310369&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=310369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310369&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)545.405Range100.1Trim Var.403.716
V(Y[t],d=1,D=0)97.4532Range61.6Trim Var.48.8066
V(Y[t],d=2,D=0)272.447Range95.2Trim Var.147.015
V(Y[t],d=3,D=0)828.748Range180Trim Var.426.471
V(Y[t],d=0,D=1)50.4047Range38Trim Var.30.3765
V(Y[t],d=1,D=1)75.3608Range57Trim Var.38.3381
V(Y[t],d=2,D=1)211.852Range87.5Trim Var.114.138
V(Y[t],d=3,D=1)673.042Range157.9Trim Var.354.222
V(Y[t],d=0,D=2)142.076Range63.3Trim Var.80.4819
V(Y[t],d=1,D=2)197.421Range84.1Trim Var.101.4
V(Y[t],d=2,D=2)539.915Range133.7Trim Var.310.753
V(Y[t],d=3,D=2)1677.35Range226.2Trim Var.899.271

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 545.405 & Range & 100.1 & Trim Var. & 403.716 \tabularnewline
V(Y[t],d=1,D=0) & 97.4532 & Range & 61.6 & Trim Var. & 48.8066 \tabularnewline
V(Y[t],d=2,D=0) & 272.447 & Range & 95.2 & Trim Var. & 147.015 \tabularnewline
V(Y[t],d=3,D=0) & 828.748 & Range & 180 & Trim Var. & 426.471 \tabularnewline
V(Y[t],d=0,D=1) & 50.4047 & Range & 38 & Trim Var. & 30.3765 \tabularnewline
V(Y[t],d=1,D=1) & 75.3608 & Range & 57 & Trim Var. & 38.3381 \tabularnewline
V(Y[t],d=2,D=1) & 211.852 & Range & 87.5 & Trim Var. & 114.138 \tabularnewline
V(Y[t],d=3,D=1) & 673.042 & Range & 157.9 & Trim Var. & 354.222 \tabularnewline
V(Y[t],d=0,D=2) & 142.076 & Range & 63.3 & Trim Var. & 80.4819 \tabularnewline
V(Y[t],d=1,D=2) & 197.421 & Range & 84.1 & Trim Var. & 101.4 \tabularnewline
V(Y[t],d=2,D=2) & 539.915 & Range & 133.7 & Trim Var. & 310.753 \tabularnewline
V(Y[t],d=3,D=2) & 1677.35 & Range & 226.2 & Trim Var. & 899.271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310369&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]545.405[/C][C]Range[/C][C]100.1[/C][C]Trim Var.[/C][C]403.716[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]97.4532[/C][C]Range[/C][C]61.6[/C][C]Trim Var.[/C][C]48.8066[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]272.447[/C][C]Range[/C][C]95.2[/C][C]Trim Var.[/C][C]147.015[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]828.748[/C][C]Range[/C][C]180[/C][C]Trim Var.[/C][C]426.471[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]50.4047[/C][C]Range[/C][C]38[/C][C]Trim Var.[/C][C]30.3765[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]75.3608[/C][C]Range[/C][C]57[/C][C]Trim Var.[/C][C]38.3381[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]211.852[/C][C]Range[/C][C]87.5[/C][C]Trim Var.[/C][C]114.138[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]673.042[/C][C]Range[/C][C]157.9[/C][C]Trim Var.[/C][C]354.222[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]142.076[/C][C]Range[/C][C]63.3[/C][C]Trim Var.[/C][C]80.4819[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]197.421[/C][C]Range[/C][C]84.1[/C][C]Trim Var.[/C][C]101.4[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]539.915[/C][C]Range[/C][C]133.7[/C][C]Trim Var.[/C][C]310.753[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1677.35[/C][C]Range[/C][C]226.2[/C][C]Trim Var.[/C][C]899.271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310369&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)545.405Range100.1Trim Var.403.716
V(Y[t],d=1,D=0)97.4532Range61.6Trim Var.48.8066
V(Y[t],d=2,D=0)272.447Range95.2Trim Var.147.015
V(Y[t],d=3,D=0)828.748Range180Trim Var.426.471
V(Y[t],d=0,D=1)50.4047Range38Trim Var.30.3765
V(Y[t],d=1,D=1)75.3608Range57Trim Var.38.3381
V(Y[t],d=2,D=1)211.852Range87.5Trim Var.114.138
V(Y[t],d=3,D=1)673.042Range157.9Trim Var.354.222
V(Y[t],d=0,D=2)142.076Range63.3Trim Var.80.4819
V(Y[t],d=1,D=2)197.421Range84.1Trim Var.101.4
V(Y[t],d=2,D=2)539.915Range133.7Trim Var.310.753
V(Y[t],d=3,D=2)1677.35Range226.2Trim Var.899.271


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()