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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 computationThu, 27 Nov 2008 10:18:43 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/27/t1227806487hka7ssmt6wez8iq.htm/, Retrieved Tue, 28 May 2024 00:48:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25863, Retrieved Tue, 28 May 2024 00:48:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F RM D    [Variance Reduction Matrix] [Q8 RVM Aantal ins...] [2008-11-27 17:18:43] [286e96bd53289970f8e5f25a93fb50b3] [Current]
Feedback Forum
2008-12-07 12:07:44 [Kevin Neelen] [reply] 
De variantie is het laagst bij d = 0 en D = 1. Dit betekent dat er origineel gezien seizoensinvloeden in de reeks vervat zaten, maar geen LT-trend.
2008-12-09 01:28:10 [Michael Van Spaandonck] [reply] 
Deze methode wordt gebruikt om te bepalen welke graad van differentiatie het beste is voor d en D.
De variantie is het laagst bij d = 0 en D = 1. Dit betekent dat er origineel gezien seizoensinvloeden in de reeks vervat zaten, maar geen LT-trend.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
54.281
63.654
68.918
58.686
67.074
60.183
54.326
54.085
53.564
60.873
53.398
45.164
59.672
56.298
62.361
56.930
62.954
62.431
52.528
54.060
53.093
52.695
52.333
41.747
58.576
57.851
63.721
63.384
61.141
59.231
63.472
49.214
55.816
61.713
48.664
45.351
57.888
54.091
59.098
58.962
55.433
60.403
60.721
48.440
57.981
60.258
47.312
46.980
54.846
56.824
67.744
62.849
54.691
65.461
53.724
54.560
57.722
55.458
48.490
46.362

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25863&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25863&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)35.8567051073446Range27.171Trim Var.23.6184840251572
V(Y[t],d=1,D=0)54.171091554062Range31.087Trim Var.37.4698841211901
V(Y[t],d=2,D=0)148.716333333636Range49.922Trim Var.108.152090488688
V(Y[t],d=3,D=0)474.998600071429Range84.328Trim Var.340.086323483137
V(Y[t],d=0,D=1)19.1803474782801Range19.122Trim Var.10.9660718815331
V(Y[t],d=1,D=1)42.3621938686402Range29.934Trim Var.23.6814323939024
V(Y[t],d=2,D=1)130.796202551208Range55.106Trim Var.68.4962152923077
V(Y[t],d=3,D=1)436.556334904040Range98.758Trim Var.208.506254414305
V(Y[t],d=0,D=2)50.2925476Range30.891Trim Var.31.9534355120968
V(Y[t],d=1,D=2)99.2694392436975Range37.99Trim Var.66.9818540451613
V(Y[t],d=2,D=2)304.087185316399Range71.587Trim Var.188.540868943678
V(Y[t],d=3,D=2)1018.40910221591Range124.925Trim Var.626.07426643596

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 35.8567051073446 & Range & 27.171 & Trim Var. & 23.6184840251572 \tabularnewline
V(Y[t],d=1,D=0) & 54.171091554062 & Range & 31.087 & Trim Var. & 37.4698841211901 \tabularnewline
V(Y[t],d=2,D=0) & 148.716333333636 & Range & 49.922 & Trim Var. & 108.152090488688 \tabularnewline
V(Y[t],d=3,D=0) & 474.998600071429 & Range & 84.328 & Trim Var. & 340.086323483137 \tabularnewline
V(Y[t],d=0,D=1) & 19.1803474782801 & Range & 19.122 & Trim Var. & 10.9660718815331 \tabularnewline
V(Y[t],d=1,D=1) & 42.3621938686402 & Range & 29.934 & Trim Var. & 23.6814323939024 \tabularnewline
V(Y[t],d=2,D=1) & 130.796202551208 & Range & 55.106 & Trim Var. & 68.4962152923077 \tabularnewline
V(Y[t],d=3,D=1) & 436.556334904040 & Range & 98.758 & Trim Var. & 208.506254414305 \tabularnewline
V(Y[t],d=0,D=2) & 50.2925476 & Range & 30.891 & Trim Var. & 31.9534355120968 \tabularnewline
V(Y[t],d=1,D=2) & 99.2694392436975 & Range & 37.99 & Trim Var. & 66.9818540451613 \tabularnewline
V(Y[t],d=2,D=2) & 304.087185316399 & Range & 71.587 & Trim Var. & 188.540868943678 \tabularnewline
V(Y[t],d=3,D=2) & 1018.40910221591 & Range & 124.925 & Trim Var. & 626.07426643596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25863&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]35.8567051073446[/C][C]Range[/C][C]27.171[/C][C]Trim Var.[/C][C]23.6184840251572[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]54.171091554062[/C][C]Range[/C][C]31.087[/C][C]Trim Var.[/C][C]37.4698841211901[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]148.716333333636[/C][C]Range[/C][C]49.922[/C][C]Trim Var.[/C][C]108.152090488688[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]474.998600071429[/C][C]Range[/C][C]84.328[/C][C]Trim Var.[/C][C]340.086323483137[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]19.1803474782801[/C][C]Range[/C][C]19.122[/C][C]Trim Var.[/C][C]10.9660718815331[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]42.3621938686402[/C][C]Range[/C][C]29.934[/C][C]Trim Var.[/C][C]23.6814323939024[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]130.796202551208[/C][C]Range[/C][C]55.106[/C][C]Trim Var.[/C][C]68.4962152923077[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]436.556334904040[/C][C]Range[/C][C]98.758[/C][C]Trim Var.[/C][C]208.506254414305[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]50.2925476[/C][C]Range[/C][C]30.891[/C][C]Trim Var.[/C][C]31.9534355120968[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]99.2694392436975[/C][C]Range[/C][C]37.99[/C][C]Trim Var.[/C][C]66.9818540451613[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]304.087185316399[/C][C]Range[/C][C]71.587[/C][C]Trim Var.[/C][C]188.540868943678[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1018.40910221591[/C][C]Range[/C][C]124.925[/C][C]Trim Var.[/C][C]626.07426643596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25863&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)35.8567051073446Range27.171Trim Var.23.6184840251572
V(Y[t],d=1,D=0)54.171091554062Range31.087Trim Var.37.4698841211901
V(Y[t],d=2,D=0)148.716333333636Range49.922Trim Var.108.152090488688
V(Y[t],d=3,D=0)474.998600071429Range84.328Trim Var.340.086323483137
V(Y[t],d=0,D=1)19.1803474782801Range19.122Trim Var.10.9660718815331
V(Y[t],d=1,D=1)42.3621938686402Range29.934Trim Var.23.6814323939024
V(Y[t],d=2,D=1)130.796202551208Range55.106Trim Var.68.4962152923077
V(Y[t],d=3,D=1)436.556334904040Range98.758Trim Var.208.506254414305
V(Y[t],d=0,D=2)50.2925476Range30.891Trim Var.31.9534355120968
V(Y[t],d=1,D=2)99.2694392436975Range37.99Trim Var.66.9818540451613
V(Y[t],d=2,D=2)304.087185316399Range71.587Trim Var.188.540868943678
V(Y[t],d=3,D=2)1018.40910221591Range124.925Trim Var.626.07426643596


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
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(x,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')