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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 computationMon, 20 Dec 2010 12:20:49 +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/2010/Dec/20/t12928475341xh7xbkxgb2senb.htm/, Retrieved Sat, 04 May 2024 03:23:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112869, Retrieved Sat, 04 May 2024 03:23:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- RMPD      [Variance Reduction Matrix] [Olie-VRM] [2010-12-20 12:20:49] [4c7d8c32b2e34fcaa7f14928b91d45ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25.64
27.97
27.62
23.31
29.07
29.58
28.63
29.92
32.68
31.54
32.43
26.54
25.85
27.60
25.71
25.38
28.57
27.64
25.36
25.90
26.29
21.74
19.20
19.32
19.82
20.36
24.31
25.97
25.61
24.67
25.59
26.09
28.37
27.34
24.46
27.46
30.23
32.33
29.87
24.87
25.48
27.28
28.24
29.58
26.95
29.08
28.76
29.59
30.70
30.52
32.67
33.19
37.13
35.54
37.75
41.84
42.94
49.14
44.61
40.22
44.23
45.85
53.38
53.26
51.80
55.30
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.50
55.04
58.34
61.92
67.65
67.68
70.30
75.26
71.44
76.36
81.71
92.60
90.60
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42
75.73
55.48
43.80
45.29
44.01
47.48
51.07
57.84
69.04
65.61
72.87
68.41
73.25
77.43
75.28
77.33
74.31
79.70
85.47
77.98
75.69
75.20
77.21
77.85
83.53
85.99

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112869&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112869&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)691.384218120963Range116.61Trim Var.446.060689581491
V(Y[t],d=1,D=0)29.7688742098986Range40.09Trim Var.9.56438104947527
V(Y[t],d=2,D=0)32.8220169452520Range36.03Trim Var.17.5540264225782
V(Y[t],d=3,D=0)89.6701852116143Range50.3600000000001Trim Var.51.991027984785
V(Y[t],d=0,D=1)549.599722276029Range132.59Trim Var.238.823574977958
V(Y[t],d=1,D=1)67.3559592423584Range61.67Trim Var.20.0168146271339
V(Y[t],d=2,D=1)69.1099663129974Range50.3600000000001Trim Var.34.1629444139194
V(Y[t],d=3,D=1)188.050121139431Range93.02Trim Var.95.399553995519
V(Y[t],d=0,D=2)1854.84819731970Range223.73Trim Var.823.69660530795
V(Y[t],d=1,D=2)222.296695354897Range104.19Trim Var.57.1996289636239
V(Y[t],d=2,D=2)205.903779084249Range89.370Trim Var.96.9744519869098
V(Y[t],d=3,D=2)566.01779005788Range136.180000000000Trim Var.289.785134579551

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 691.384218120963 & Range & 116.61 & Trim Var. & 446.060689581491 \tabularnewline
V(Y[t],d=1,D=0) & 29.7688742098986 & Range & 40.09 & Trim Var. & 9.56438104947527 \tabularnewline
V(Y[t],d=2,D=0) & 32.8220169452520 & Range & 36.03 & Trim Var. & 17.5540264225782 \tabularnewline
V(Y[t],d=3,D=0) & 89.6701852116143 & Range & 50.3600000000001 & Trim Var. & 51.991027984785 \tabularnewline
V(Y[t],d=0,D=1) & 549.599722276029 & Range & 132.59 & Trim Var. & 238.823574977958 \tabularnewline
V(Y[t],d=1,D=1) & 67.3559592423584 & Range & 61.67 & Trim Var. & 20.0168146271339 \tabularnewline
V(Y[t],d=2,D=1) & 69.1099663129974 & Range & 50.3600000000001 & Trim Var. & 34.1629444139194 \tabularnewline
V(Y[t],d=3,D=1) & 188.050121139431 & Range & 93.02 & Trim Var. & 95.399553995519 \tabularnewline
V(Y[t],d=0,D=2) & 1854.84819731970 & Range & 223.73 & Trim Var. & 823.69660530795 \tabularnewline
V(Y[t],d=1,D=2) & 222.296695354897 & Range & 104.19 & Trim Var. & 57.1996289636239 \tabularnewline
V(Y[t],d=2,D=2) & 205.903779084249 & Range & 89.370 & Trim Var. & 96.9744519869098 \tabularnewline
V(Y[t],d=3,D=2) & 566.01779005788 & Range & 136.180000000000 & Trim Var. & 289.785134579551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112869&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]691.384218120963[/C][C]Range[/C][C]116.61[/C][C]Trim Var.[/C][C]446.060689581491[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]29.7688742098986[/C][C]Range[/C][C]40.09[/C][C]Trim Var.[/C][C]9.56438104947527[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]32.8220169452520[/C][C]Range[/C][C]36.03[/C][C]Trim Var.[/C][C]17.5540264225782[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]89.6701852116143[/C][C]Range[/C][C]50.3600000000001[/C][C]Trim Var.[/C][C]51.991027984785[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]549.599722276029[/C][C]Range[/C][C]132.59[/C][C]Trim Var.[/C][C]238.823574977958[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]67.3559592423584[/C][C]Range[/C][C]61.67[/C][C]Trim Var.[/C][C]20.0168146271339[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]69.1099663129974[/C][C]Range[/C][C]50.3600000000001[/C][C]Trim Var.[/C][C]34.1629444139194[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]188.050121139431[/C][C]Range[/C][C]93.02[/C][C]Trim Var.[/C][C]95.399553995519[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1854.84819731970[/C][C]Range[/C][C]223.73[/C][C]Trim Var.[/C][C]823.69660530795[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]222.296695354897[/C][C]Range[/C][C]104.19[/C][C]Trim Var.[/C][C]57.1996289636239[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]205.903779084249[/C][C]Range[/C][C]89.370[/C][C]Trim Var.[/C][C]96.9744519869098[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]566.01779005788[/C][C]Range[/C][C]136.180000000000[/C][C]Trim Var.[/C][C]289.785134579551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112869&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)691.384218120963Range116.61Trim Var.446.060689581491
V(Y[t],d=1,D=0)29.7688742098986Range40.09Trim Var.9.56438104947527
V(Y[t],d=2,D=0)32.8220169452520Range36.03Trim Var.17.5540264225782
V(Y[t],d=3,D=0)89.6701852116143Range50.3600000000001Trim Var.51.991027984785
V(Y[t],d=0,D=1)549.599722276029Range132.59Trim Var.238.823574977958
V(Y[t],d=1,D=1)67.3559592423584Range61.67Trim Var.20.0168146271339
V(Y[t],d=2,D=1)69.1099663129974Range50.3600000000001Trim Var.34.1629444139194
V(Y[t],d=3,D=1)188.050121139431Range93.02Trim Var.95.399553995519
V(Y[t],d=0,D=2)1854.84819731970Range223.73Trim Var.823.69660530795
V(Y[t],d=1,D=2)222.296695354897Range104.19Trim Var.57.1996289636239
V(Y[t],d=2,D=2)205.903779084249Range89.370Trim Var.96.9744519869098
V(Y[t],d=3,D=2)566.01779005788Range136.180000000000Trim Var.289.785134579551


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,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()