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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, 02 Dec 2008 11:13:31 -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/Dec/02/t12282416996ygwyzbynv8i9mi.htm/, Retrieved Fri, 17 May 2024 03:42:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28190, Retrieved Fri, 17 May 2024 03:42:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [(Partial) Autocorrelation Function] [nonstationaryques...] [2008-12-01 19:09:36] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMPD    [Cross Correlation Function] [nonstationaryques...] [2008-12-02 17:59:36] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMPD        [Variance Reduction Matrix] [nonstationaryques...] [2008-12-02 18:13:31] [89a49ebb3ece8e9a225c7f9f53a14c57] [Current]
F    D          [Variance Reduction Matrix] [nonstationaryques...] [2008-12-02 18:23:40] [922d8ae7bd2fd460a62d9020ccd4931a]
Feedback Forum
2008-12-07 10:26:48 [6066575aa30c0611e452e930b1dff53d] [reply] 
Hier werd er enkel gewerkt met de variance reduction matrix om de waarden voor d, D en lambda te vinden. Men had beter ook nog gewerkt met de autocorrelatie functie en met de spectrum analyse. Uit de variance reduction matrix heeft men afgeleid dat de kleinste variantie bereikt wordt bij d=0 en D=2. Dit is niet correct. De kleinste variantie wordt bereikt bij d=0 en D=1. Dit is dus bij 1 keer seizoenaal differentiëren. Men had ook nog de standard deviation-mean plot moeten gebruiken om lambda te vinden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97,8
107,4
117,5
105,6
97,4
99,5
98
104,3
100,6
101,1
103,9
96,9
95,5
108,4
117
103,8
100,8
110,6
104
112,6
107,3
98,9
109,8
104,9
102,2
123,9
124,9
112,7
121,9
100,6
104,3
120,4
107,5
102,9
125,6
107,5
108,8
128,4
121,1
119,5
128,7
108,7
105,5
119,8
111,3
110,6
120,1
97,5
107,7
127,3
117,2
119,8
116,2
111
112,4
130,6
109,1
118,8
123,9
101,6
112,8
128
129,6
125,8
119,5
115,7
113,6
129,7
112
116,8
127
112,1
114,2
121,1
131,6
125
120,4
117,7
117,5
120,6
127,5
112,3
124,5
115,2
105,4

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'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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28190&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28190&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28190&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)95.2122633053221Range36.1Trim Var.71.1241513513514
V(Y[t],d=1,D=0)119.782799770511Range45.3Trim Var.75.7598241392077
V(Y[t],d=2,D=0)328.117140758155Range74.3Trim Var.220.810350076104
V(Y[t],d=3,D=0)1004.95738030714Range139Trim Var.648.207198748044
V(Y[t],d=0,D=1)40.1340943683409Range33.6Trim Var.21.2510336538462
V(Y[t],d=1,D=1)75.0755379499217Range55.7Trim Var.39.7155158730159
V(Y[t],d=2,D=1)226.253513078471Range86Trim Var.106.195151049667
V(Y[t],d=3,D=1)741.842113871635Range166.9Trim Var.355.179153886832
V(Y[t],d=0,D=2)92.817Range39.4Trim Var.56.6287590711176
V(Y[t],d=1,D=2)143.775864406780Range71.2Trim Var.80.9414116002795
V(Y[t],d=2,D=2)415.207627118644Range103.8Trim Var.234.084753265602
V(Y[t],d=3,D=2)1354.69443436177Range194.2Trim Var.818.819064856712

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 95.2122633053221 & Range & 36.1 & Trim Var. & 71.1241513513514 \tabularnewline
V(Y[t],d=1,D=0) & 119.782799770511 & Range & 45.3 & Trim Var. & 75.7598241392077 \tabularnewline
V(Y[t],d=2,D=0) & 328.117140758155 & Range & 74.3 & Trim Var. & 220.810350076104 \tabularnewline
V(Y[t],d=3,D=0) & 1004.95738030714 & Range & 139 & Trim Var. & 648.207198748044 \tabularnewline
V(Y[t],d=0,D=1) & 40.1340943683409 & Range & 33.6 & Trim Var. & 21.2510336538462 \tabularnewline
V(Y[t],d=1,D=1) & 75.0755379499217 & Range & 55.7 & Trim Var. & 39.7155158730159 \tabularnewline
V(Y[t],d=2,D=1) & 226.253513078471 & Range & 86 & Trim Var. & 106.195151049667 \tabularnewline
V(Y[t],d=3,D=1) & 741.842113871635 & Range & 166.9 & Trim Var. & 355.179153886832 \tabularnewline
V(Y[t],d=0,D=2) & 92.817 & Range & 39.4 & Trim Var. & 56.6287590711176 \tabularnewline
V(Y[t],d=1,D=2) & 143.775864406780 & Range & 71.2 & Trim Var. & 80.9414116002795 \tabularnewline
V(Y[t],d=2,D=2) & 415.207627118644 & Range & 103.8 & Trim Var. & 234.084753265602 \tabularnewline
V(Y[t],d=3,D=2) & 1354.69443436177 & Range & 194.2 & Trim Var. & 818.819064856712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28190&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]95.2122633053221[/C][C]Range[/C][C]36.1[/C][C]Trim Var.[/C][C]71.1241513513514[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]119.782799770511[/C][C]Range[/C][C]45.3[/C][C]Trim Var.[/C][C]75.7598241392077[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]328.117140758155[/C][C]Range[/C][C]74.3[/C][C]Trim Var.[/C][C]220.810350076104[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1004.95738030714[/C][C]Range[/C][C]139[/C][C]Trim Var.[/C][C]648.207198748044[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]40.1340943683409[/C][C]Range[/C][C]33.6[/C][C]Trim Var.[/C][C]21.2510336538462[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]75.0755379499217[/C][C]Range[/C][C]55.7[/C][C]Trim Var.[/C][C]39.7155158730159[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]226.253513078471[/C][C]Range[/C][C]86[/C][C]Trim Var.[/C][C]106.195151049667[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]741.842113871635[/C][C]Range[/C][C]166.9[/C][C]Trim Var.[/C][C]355.179153886832[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]92.817[/C][C]Range[/C][C]39.4[/C][C]Trim Var.[/C][C]56.6287590711176[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]143.775864406780[/C][C]Range[/C][C]71.2[/C][C]Trim Var.[/C][C]80.9414116002795[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]415.207627118644[/C][C]Range[/C][C]103.8[/C][C]Trim Var.[/C][C]234.084753265602[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1354.69443436177[/C][C]Range[/C][C]194.2[/C][C]Trim Var.[/C][C]818.819064856712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28190&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28190&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)95.2122633053221Range36.1Trim Var.71.1241513513514
V(Y[t],d=1,D=0)119.782799770511Range45.3Trim Var.75.7598241392077
V(Y[t],d=2,D=0)328.117140758155Range74.3Trim Var.220.810350076104
V(Y[t],d=3,D=0)1004.95738030714Range139Trim Var.648.207198748044
V(Y[t],d=0,D=1)40.1340943683409Range33.6Trim Var.21.2510336538462
V(Y[t],d=1,D=1)75.0755379499217Range55.7Trim Var.39.7155158730159
V(Y[t],d=2,D=1)226.253513078471Range86Trim Var.106.195151049667
V(Y[t],d=3,D=1)741.842113871635Range166.9Trim Var.355.179153886832
V(Y[t],d=0,D=2)92.817Range39.4Trim Var.56.6287590711176
V(Y[t],d=1,D=2)143.775864406780Range71.2Trim Var.80.9414116002795
V(Y[t],d=2,D=2)415.207627118644Range103.8Trim Var.234.084753265602
V(Y[t],d=3,D=2)1354.69443436177Range194.2Trim Var.818.819064856712


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 <- 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')