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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationTue, 16 Dec 2008 16:32:22 -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/17/t1229470438xqiqknsf1y3jnw8.htm/, Retrieved Mon, 03 Nov 2025 04:32:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34251, Retrieved Mon, 03 Nov 2025 04:32:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact461

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] [Arabica Price in ...] [2008-01-05 23:14:31] [74be16979710d4c4e7c6647856088456]
- RMPD    [Variance Reduction Matrix] [Paper ARIMA Forec...] [2008-12-16 23:32:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.2
100.5
98
106.6
90.1
96.9
125.9
112
100
123.9
79.8
83.4
113.6
112.9
104
109.9
99
106.3
128.9
111.1
102.9
130
87
87.5
117.6
103.4
110.8
112.6
102.5
112.4
135.6
105.1
127.7
137
91
90.5
122.4
123.3
124.3
120
118.1
119
142.7
123.6
129.6
151.6
110.4
99.2
130.5
136.2
129.7
128
121.6
135.8
143.8
147.5
136.2
156.6
123.3
100.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34251&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]6 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=34251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34251&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)312.916734463277Range76.8Trim Var.213.700017470300
V(Y[t],d=1,D=0)382.718088836937Range77.9Trim Var.256.729978229318
V(Y[t],d=2,D=0)999.917592256503Range123.2Trim Var.711.484524886878
V(Y[t],d=3,D=0)2978.35872807018Range221.1Trim Var.1997.57523137255
V(Y[t],d=0,D=1)46.5112721631206Range34.3Trim Var.22.5480429732869
V(Y[t],d=1,D=1)104.161544865865Range48.6Trim Var.53.6789512195122
V(Y[t],d=2,D=1)337.017202898551Range92.1Trim Var.156.266641025641
V(Y[t],d=3,D=1)1162.59245454545Range159.6Trim Var.581.807368421052
V(Y[t],d=0,D=2)122.339142857143Range52.3Trim Var.58.8646673387097
V(Y[t],d=1,D=2)263.024907563025Range77.9Trim Var.147.601397849462
V(Y[t],d=2,D=2)846.848921568627Range149.4Trim Var.441.822022988505
V(Y[t],d=3,D=2)2884.88609848485Range250Trim Var.1622.67399014778

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 312.916734463277 & Range & 76.8 & Trim Var. & 213.700017470300 \tabularnewline
V(Y[t],d=1,D=0) & 382.718088836937 & Range & 77.9 & Trim Var. & 256.729978229318 \tabularnewline
V(Y[t],d=2,D=0) & 999.917592256503 & Range & 123.2 & Trim Var. & 711.484524886878 \tabularnewline
V(Y[t],d=3,D=0) & 2978.35872807018 & Range & 221.1 & Trim Var. & 1997.57523137255 \tabularnewline
V(Y[t],d=0,D=1) & 46.5112721631206 & Range & 34.3 & Trim Var. & 22.5480429732869 \tabularnewline
V(Y[t],d=1,D=1) & 104.161544865865 & Range & 48.6 & Trim Var. & 53.6789512195122 \tabularnewline
V(Y[t],d=2,D=1) & 337.017202898551 & Range & 92.1 & Trim Var. & 156.266641025641 \tabularnewline
V(Y[t],d=3,D=1) & 1162.59245454545 & Range & 159.6 & Trim Var. & 581.807368421052 \tabularnewline
V(Y[t],d=0,D=2) & 122.339142857143 & Range & 52.3 & Trim Var. & 58.8646673387097 \tabularnewline
V(Y[t],d=1,D=2) & 263.024907563025 & Range & 77.9 & Trim Var. & 147.601397849462 \tabularnewline
V(Y[t],d=2,D=2) & 846.848921568627 & Range & 149.4 & Trim Var. & 441.822022988505 \tabularnewline
V(Y[t],d=3,D=2) & 2884.88609848485 & Range & 250 & Trim Var. & 1622.67399014778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34251&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]312.916734463277[/C][C]Range[/C][C]76.8[/C][C]Trim Var.[/C][C]213.700017470300[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]382.718088836937[/C][C]Range[/C][C]77.9[/C][C]Trim Var.[/C][C]256.729978229318[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]999.917592256503[/C][C]Range[/C][C]123.2[/C][C]Trim Var.[/C][C]711.484524886878[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2978.35872807018[/C][C]Range[/C][C]221.1[/C][C]Trim Var.[/C][C]1997.57523137255[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]46.5112721631206[/C][C]Range[/C][C]34.3[/C][C]Trim Var.[/C][C]22.5480429732869[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]104.161544865865[/C][C]Range[/C][C]48.6[/C][C]Trim Var.[/C][C]53.6789512195122[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]337.017202898551[/C][C]Range[/C][C]92.1[/C][C]Trim Var.[/C][C]156.266641025641[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1162.59245454545[/C][C]Range[/C][C]159.6[/C][C]Trim Var.[/C][C]581.807368421052[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]122.339142857143[/C][C]Range[/C][C]52.3[/C][C]Trim Var.[/C][C]58.8646673387097[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]263.024907563025[/C][C]Range[/C][C]77.9[/C][C]Trim Var.[/C][C]147.601397849462[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]846.848921568627[/C][C]Range[/C][C]149.4[/C][C]Trim Var.[/C][C]441.822022988505[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2884.88609848485[/C][C]Range[/C][C]250[/C][C]Trim Var.[/C][C]1622.67399014778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34251&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)312.916734463277Range76.8Trim Var.213.700017470300
V(Y[t],d=1,D=0)382.718088836937Range77.9Trim Var.256.729978229318
V(Y[t],d=2,D=0)999.917592256503Range123.2Trim Var.711.484524886878
V(Y[t],d=3,D=0)2978.35872807018Range221.1Trim Var.1997.57523137255
V(Y[t],d=0,D=1)46.5112721631206Range34.3Trim Var.22.5480429732869
V(Y[t],d=1,D=1)104.161544865865Range48.6Trim Var.53.6789512195122
V(Y[t],d=2,D=1)337.017202898551Range92.1Trim Var.156.266641025641
V(Y[t],d=3,D=1)1162.59245454545Range159.6Trim Var.581.807368421052
V(Y[t],d=0,D=2)122.339142857143Range52.3Trim Var.58.8646673387097
V(Y[t],d=1,D=2)263.024907563025Range77.9Trim Var.147.601397849462
V(Y[t],d=2,D=2)846.848921568627Range149.4Trim Var.441.822022988505
V(Y[t],d=3,D=2)2884.88609848485Range250Trim Var.1622.67399014778


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')