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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, 30 Nov 2008 15:00:21 -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/30/t1228082452fha6i8yql6h7eld.htm/, Retrieved Mon, 20 May 2024 03:48:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26757, Retrieved Mon, 20 May 2024 03:48:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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]
- RM D    [Variance Reduction Matrix] [Q8 Non Stationary...] [2008-11-30 22:00:21] [5e9e099b83e50415d7642e10d74756e4] [Current]
- RM        [Standard Deviation-Mean Plot] [Q8 Non Stationary...] [2008-11-30 22:03:26] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
308347
298427
289231
291975
294912
293488
290555
284736
281818
287854
316263
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
301631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257
270976

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26757&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26757&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)545645515.709836Range93895Trim Var.349747190.910015
V(Y[t],d=1,D=0)121664761.282203Range52013Trim Var.63902717.650594
V(Y[t],d=2,D=0)162149124.492694Range61931Trim Var.94410612.1386067
V(Y[t],d=3,D=0)347764857.171506Range91364Trim Var.171691991.961916
V(Y[t],d=0,D=1)377992977.677721Range70477Trim Var.277094047.58361
V(Y[t],d=1,D=1)20894033.0620567Range26463Trim Var.8752714.87804878
V(Y[t],d=2,D=1)39390553.1720629Range30864Trim Var.17390984.3756098
V(Y[t],d=3,D=1)111944698.699517Range50518Trim Var.54153789.5871795
V(Y[t],d=0,D=2)280941659.187688Range61729Trim Var.192379823.359848
V(Y[t],d=1,D=2)56073301.7420635Range40889Trim Var.24695770.8346774
V(Y[t],d=2,D=2)92343387.7865546Range51589Trim Var.45074328.5591398
V(Y[t],d=3,D=2)217258267.031194Range59463Trim Var.142915122.529885

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 545645515.709836 & Range & 93895 & Trim Var. & 349747190.910015 \tabularnewline
V(Y[t],d=1,D=0) & 121664761.282203 & Range & 52013 & Trim Var. & 63902717.650594 \tabularnewline
V(Y[t],d=2,D=0) & 162149124.492694 & Range & 61931 & Trim Var. & 94410612.1386067 \tabularnewline
V(Y[t],d=3,D=0) & 347764857.171506 & Range & 91364 & Trim Var. & 171691991.961916 \tabularnewline
V(Y[t],d=0,D=1) & 377992977.677721 & Range & 70477 & Trim Var. & 277094047.58361 \tabularnewline
V(Y[t],d=1,D=1) & 20894033.0620567 & Range & 26463 & Trim Var. & 8752714.87804878 \tabularnewline
V(Y[t],d=2,D=1) & 39390553.1720629 & Range & 30864 & Trim Var. & 17390984.3756098 \tabularnewline
V(Y[t],d=3,D=1) & 111944698.699517 & Range & 50518 & Trim Var. & 54153789.5871795 \tabularnewline
V(Y[t],d=0,D=2) & 280941659.187688 & Range & 61729 & Trim Var. & 192379823.359848 \tabularnewline
V(Y[t],d=1,D=2) & 56073301.7420635 & Range & 40889 & Trim Var. & 24695770.8346774 \tabularnewline
V(Y[t],d=2,D=2) & 92343387.7865546 & Range & 51589 & Trim Var. & 45074328.5591398 \tabularnewline
V(Y[t],d=3,D=2) & 217258267.031194 & Range & 59463 & Trim Var. & 142915122.529885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26757&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]545645515.709836[/C][C]Range[/C][C]93895[/C][C]Trim Var.[/C][C]349747190.910015[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]121664761.282203[/C][C]Range[/C][C]52013[/C][C]Trim Var.[/C][C]63902717.650594[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]162149124.492694[/C][C]Range[/C][C]61931[/C][C]Trim Var.[/C][C]94410612.1386067[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]347764857.171506[/C][C]Range[/C][C]91364[/C][C]Trim Var.[/C][C]171691991.961916[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]377992977.677721[/C][C]Range[/C][C]70477[/C][C]Trim Var.[/C][C]277094047.58361[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]20894033.0620567[/C][C]Range[/C][C]26463[/C][C]Trim Var.[/C][C]8752714.87804878[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]39390553.1720629[/C][C]Range[/C][C]30864[/C][C]Trim Var.[/C][C]17390984.3756098[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]111944698.699517[/C][C]Range[/C][C]50518[/C][C]Trim Var.[/C][C]54153789.5871795[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]280941659.187688[/C][C]Range[/C][C]61729[/C][C]Trim Var.[/C][C]192379823.359848[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]56073301.7420635[/C][C]Range[/C][C]40889[/C][C]Trim Var.[/C][C]24695770.8346774[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]92343387.7865546[/C][C]Range[/C][C]51589[/C][C]Trim Var.[/C][C]45074328.5591398[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]217258267.031194[/C][C]Range[/C][C]59463[/C][C]Trim Var.[/C][C]142915122.529885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26757&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)545645515.709836Range93895Trim Var.349747190.910015
V(Y[t],d=1,D=0)121664761.282203Range52013Trim Var.63902717.650594
V(Y[t],d=2,D=0)162149124.492694Range61931Trim Var.94410612.1386067
V(Y[t],d=3,D=0)347764857.171506Range91364Trim Var.171691991.961916
V(Y[t],d=0,D=1)377992977.677721Range70477Trim Var.277094047.58361
V(Y[t],d=1,D=1)20894033.0620567Range26463Trim Var.8752714.87804878
V(Y[t],d=2,D=1)39390553.1720629Range30864Trim Var.17390984.3756098
V(Y[t],d=3,D=1)111944698.699517Range50518Trim Var.54153789.5871795
V(Y[t],d=0,D=2)280941659.187688Range61729Trim Var.192379823.359848
V(Y[t],d=1,D=2)56073301.7420635Range40889Trim Var.24695770.8346774
V(Y[t],d=2,D=2)92343387.7865546Range51589Trim Var.45074328.5591398
V(Y[t],d=3,D=2)217258267.031194Range59463Trim Var.142915122.529885


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Airline ; par2 = Box-Jenkins ; par3 = Airline Passengers ;
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')