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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 computationSun, 07 Dec 2008 09:10:52 -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/07/t122866631782jwfrcvyk70y3o.htm/, Retrieved Wed, 22 May 2024 07:24:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30134, Retrieved Wed, 22 May 2024 07:24:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

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]
F RMPD    [Variance Reduction Matrix] [workshop8, step 2...] [2008-12-07 16:10:52] [a16dfd7e948381d8b6391003c5d09447] [Current]
Feedback Forum
2008-12-15 18:43:33 [Peter Van Doninck] [reply] 
De studente heeft de juiste waarde voor d en D gevonden. Indien ze echter rekening zou houden met de outliers, die zich voordoen zoals ze vermeld heeft in vraag 1, dan zou ze moeten opteren voor de getrimde variantie! Deze waarde is het kleinste bij d=1 en D=0. We dienen dus enkel niet-seizoenaal te differentiëren!
2008-12-15 19:24:21 [Lana Van Wesemael] [reply] 
Dit is vrij lastig. De kleinste variantie vinden we inderdaad bij een maal gewoon en een keer seizoenaal differentiëren. Deze variantie van een maal gewoon differentiëren is echter net ietsje groter. De getrimde variantie vertelt ons dat we best seizoenaal differentiëren. We kunnen dus best gewoon beide mogelijkheden uiproberen in de ACF en spectraalanalyse en dan besluiten welke differentiaties in dit geval het beste resultaat geven.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.5
7.2
6.9
6.7
6.4
6.3
6.8
7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8
6.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30134&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30134&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.668819407008086Range3.3Trim Var.0.488754289636239
V(Y[t],d=1,D=0)0.0895567765567766Range2.1Trim Var.0.039315100514259
V(Y[t],d=2,D=0)0.112229275578790Range1.8Trim Var.0.0559101123595505
V(Y[t],d=3,D=0)0.252156862745098Range2.8Trim Var.0.118417582417583
V(Y[t],d=0,D=1)0.510853351635781Range2.8Trim Var.0.379374641422834
V(Y[t],d=1,D=1)0.0837096774193549Range1.40000000000000Trim Var.0.044
V(Y[t],d=2,D=1)0.0892259913999045Range1.5Trim Var.0.0539777175549534
V(Y[t],d=3,D=1)0.174747252747253Range2.00000000000000Trim Var.0.106799382716050
V(Y[t],d=0,D=2)0.696370069256248Range4.1Trim Var.0.324505086071987
V(Y[t],d=1,D=2)0.209567901234568Range2.50000000000000Trim Var.0.097606625258799
V(Y[t],d=2,D=2)0.229613924050633Range2Trim Var.0.148945674044266
V(Y[t],d=3,D=2)0.440344044141513Range3Trim Var.0.280378269617707

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.668819407008086 & Range & 3.3 & Trim Var. & 0.488754289636239 \tabularnewline
V(Y[t],d=1,D=0) & 0.0895567765567766 & Range & 2.1 & Trim Var. & 0.039315100514259 \tabularnewline
V(Y[t],d=2,D=0) & 0.112229275578790 & Range & 1.8 & Trim Var. & 0.0559101123595505 \tabularnewline
V(Y[t],d=3,D=0) & 0.252156862745098 & Range & 2.8 & Trim Var. & 0.118417582417583 \tabularnewline
V(Y[t],d=0,D=1) & 0.510853351635781 & Range & 2.8 & Trim Var. & 0.379374641422834 \tabularnewline
V(Y[t],d=1,D=1) & 0.0837096774193549 & Range & 1.40000000000000 & Trim Var. & 0.044 \tabularnewline
V(Y[t],d=2,D=1) & 0.0892259913999045 & Range & 1.5 & Trim Var. & 0.0539777175549534 \tabularnewline
V(Y[t],d=3,D=1) & 0.174747252747253 & Range & 2.00000000000000 & Trim Var. & 0.106799382716050 \tabularnewline
V(Y[t],d=0,D=2) & 0.696370069256248 & Range & 4.1 & Trim Var. & 0.324505086071987 \tabularnewline
V(Y[t],d=1,D=2) & 0.209567901234568 & Range & 2.50000000000000 & Trim Var. & 0.097606625258799 \tabularnewline
V(Y[t],d=2,D=2) & 0.229613924050633 & Range & 2 & Trim Var. & 0.148945674044266 \tabularnewline
V(Y[t],d=3,D=2) & 0.440344044141513 & Range & 3 & Trim Var. & 0.280378269617707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30134&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.668819407008086[/C][C]Range[/C][C]3.3[/C][C]Trim Var.[/C][C]0.488754289636239[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0895567765567766[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.039315100514259[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.112229275578790[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.0559101123595505[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.252156862745098[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.118417582417583[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.510853351635781[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.379374641422834[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0837096774193549[/C][C]Range[/C][C]1.40000000000000[/C][C]Trim Var.[/C][C]0.044[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0892259913999045[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0539777175549534[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.174747252747253[/C][C]Range[/C][C]2.00000000000000[/C][C]Trim Var.[/C][C]0.106799382716050[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.696370069256248[/C][C]Range[/C][C]4.1[/C][C]Trim Var.[/C][C]0.324505086071987[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.209567901234568[/C][C]Range[/C][C]2.50000000000000[/C][C]Trim Var.[/C][C]0.097606625258799[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.229613924050633[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]0.148945674044266[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.440344044141513[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.280378269617707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30134&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)0.668819407008086Range3.3Trim Var.0.488754289636239
V(Y[t],d=1,D=0)0.0895567765567766Range2.1Trim Var.0.039315100514259
V(Y[t],d=2,D=0)0.112229275578790Range1.8Trim Var.0.0559101123595505
V(Y[t],d=3,D=0)0.252156862745098Range2.8Trim Var.0.118417582417583
V(Y[t],d=0,D=1)0.510853351635781Range2.8Trim Var.0.379374641422834
V(Y[t],d=1,D=1)0.0837096774193549Range1.40000000000000Trim Var.0.044
V(Y[t],d=2,D=1)0.0892259913999045Range1.5Trim Var.0.0539777175549534
V(Y[t],d=3,D=1)0.174747252747253Range2.00000000000000Trim Var.0.106799382716050
V(Y[t],d=0,D=2)0.696370069256248Range4.1Trim Var.0.324505086071987
V(Y[t],d=1,D=2)0.209567901234568Range2.50000000000000Trim Var.0.097606625258799
V(Y[t],d=2,D=2)0.229613924050633Range2Trim Var.0.148945674044266
V(Y[t],d=3,D=2)0.440344044141513Range3Trim Var.0.280378269617707


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')