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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 computationSat, 06 Dec 2008 04:59:34 -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/06/t12285648301xkm3ecq46z0p3a.htm/, Retrieved Fri, 04 Apr 2025 23:05:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29529, Retrieved Fri, 04 Apr 2025 23:05:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact260

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  [Cross Correlation Function] [question 8] [2008-12-02 14:53:11] [31c9f333c18b3396ccf9d2485dd39c8a]
- RMPD      [Variance Reduction Matrix] [] [2008-12-06 11:59:34] [86e877ba38171644c8ca01af8044e645] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
123.28
133.52
153.20
163.63
168.45
166.26
162.31
161.56
156.59
157.97
158.68
163.55
162.89
164.95
159.82
159.05
166.76
164.55
163.22
160.68
155.24
157.60
156.56
154.82
151.11
149.65
148.99
148.53
146.70
145.11
142.70
143.59
140.96
140.77
139.81
140.58
139.59
138.05
136.06
135.98
134.75
132.22
135.37
138.84
138.83
136.55
135.63
139.14
136.09
135.97
134.51
134.54
134.08
132.86
134.48
129.08
133.13
134.78
134.13
132.43
127.84
128.12
128.94
132.38
134.99
138.05
135.83
130.12
128.16
128.60
126.12
124.20
121.65
121.57
118.38
116.31
117.11
117.80
115.86
115.81
114.75
116.23
117.12
113.38
108.68
109.86
108.20
109.34
107.21
104.30
106.50
110.36
110.33
107.08
109.57
100.61
93.26
92.74
93.11
97.76
101.39
100.71
98.09
99.92
102.59
107.64
106.53
103.72
108.25
113.52
112.39
120.10
123.71
125.32
129.71
128.16
130.20
130.78
131.35

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=29529&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=29529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29529&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)386.658115624555Range75.71Trim Var.291.322675630400
V(Y[t],d=1,D=0)13.6286238809213Range28.64Trim Var.5.65142109613656
V(Y[t],d=2,D=0)16.5035265399351Range20.8999999999999Trim Var.9.67336543956043
V(Y[t],d=3,D=0)44.3970021814092Range35.1599999999999Trim Var.25.7383073935773
V(Y[t],d=0,D=1)158.836639252336Range60.13Trim Var.84.72349462486
V(Y[t],d=1,D=1)19.8693112039532Range36.69Trim Var.7.55287441088994
V(Y[t],d=2,D=1)26.6234471062270Range30.7199999999999Trim Var.13.1892086489013
V(Y[t],d=3,D=1)65.9953874159819Range47.7399999999999Trim Var.32.6822244027710
V(Y[t],d=0,D=2)256.168852698768Range91.42Trim Var.128.192558543417
V(Y[t],d=1,D=2)40.9985075840768Range42.0500000000000Trim Var.20.517764242685
V(Y[t],d=2,D=2)67.2653507246375Range48.5599999999999Trim Var.34.8408344401998
V(Y[t],d=3,D=2)165.510783695652Range79.3999999999999Trim Var.75.7432781240587

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 386.658115624555 & Range & 75.71 & Trim Var. & 291.322675630400 \tabularnewline
V(Y[t],d=1,D=0) & 13.6286238809213 & Range & 28.64 & Trim Var. & 5.65142109613656 \tabularnewline
V(Y[t],d=2,D=0) & 16.5035265399351 & Range & 20.8999999999999 & Trim Var. & 9.67336543956043 \tabularnewline
V(Y[t],d=3,D=0) & 44.3970021814092 & Range & 35.1599999999999 & Trim Var. & 25.7383073935773 \tabularnewline
V(Y[t],d=0,D=1) & 158.836639252336 & Range & 60.13 & Trim Var. & 84.72349462486 \tabularnewline
V(Y[t],d=1,D=1) & 19.8693112039532 & Range & 36.69 & Trim Var. & 7.55287441088994 \tabularnewline
V(Y[t],d=2,D=1) & 26.6234471062270 & Range & 30.7199999999999 & Trim Var. & 13.1892086489013 \tabularnewline
V(Y[t],d=3,D=1) & 65.9953874159819 & Range & 47.7399999999999 & Trim Var. & 32.6822244027710 \tabularnewline
V(Y[t],d=0,D=2) & 256.168852698768 & Range & 91.42 & Trim Var. & 128.192558543417 \tabularnewline
V(Y[t],d=1,D=2) & 40.9985075840768 & Range & 42.0500000000000 & Trim Var. & 20.517764242685 \tabularnewline
V(Y[t],d=2,D=2) & 67.2653507246375 & Range & 48.5599999999999 & Trim Var. & 34.8408344401998 \tabularnewline
V(Y[t],d=3,D=2) & 165.510783695652 & Range & 79.3999999999999 & Trim Var. & 75.7432781240587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29529&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]386.658115624555[/C][C]Range[/C][C]75.71[/C][C]Trim Var.[/C][C]291.322675630400[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]13.6286238809213[/C][C]Range[/C][C]28.64[/C][C]Trim Var.[/C][C]5.65142109613656[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]16.5035265399351[/C][C]Range[/C][C]20.8999999999999[/C][C]Trim Var.[/C][C]9.67336543956043[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]44.3970021814092[/C][C]Range[/C][C]35.1599999999999[/C][C]Trim Var.[/C][C]25.7383073935773[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]158.836639252336[/C][C]Range[/C][C]60.13[/C][C]Trim Var.[/C][C]84.72349462486[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]19.8693112039532[/C][C]Range[/C][C]36.69[/C][C]Trim Var.[/C][C]7.55287441088994[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]26.6234471062270[/C][C]Range[/C][C]30.7199999999999[/C][C]Trim Var.[/C][C]13.1892086489013[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]65.9953874159819[/C][C]Range[/C][C]47.7399999999999[/C][C]Trim Var.[/C][C]32.6822244027710[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]256.168852698768[/C][C]Range[/C][C]91.42[/C][C]Trim Var.[/C][C]128.192558543417[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]40.9985075840768[/C][C]Range[/C][C]42.0500000000000[/C][C]Trim Var.[/C][C]20.517764242685[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]67.2653507246375[/C][C]Range[/C][C]48.5599999999999[/C][C]Trim Var.[/C][C]34.8408344401998[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]165.510783695652[/C][C]Range[/C][C]79.3999999999999[/C][C]Trim Var.[/C][C]75.7432781240587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29529&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)386.658115624555Range75.71Trim Var.291.322675630400
V(Y[t],d=1,D=0)13.6286238809213Range28.64Trim Var.5.65142109613656
V(Y[t],d=2,D=0)16.5035265399351Range20.8999999999999Trim Var.9.67336543956043
V(Y[t],d=3,D=0)44.3970021814092Range35.1599999999999Trim Var.25.7383073935773
V(Y[t],d=0,D=1)158.836639252336Range60.13Trim Var.84.72349462486
V(Y[t],d=1,D=1)19.8693112039532Range36.69Trim Var.7.55287441088994
V(Y[t],d=2,D=1)26.6234471062270Range30.7199999999999Trim Var.13.1892086489013
V(Y[t],d=3,D=1)65.9953874159819Range47.7399999999999Trim Var.32.6822244027710
V(Y[t],d=0,D=2)256.168852698768Range91.42Trim Var.128.192558543417
V(Y[t],d=1,D=2)40.9985075840768Range42.0500000000000Trim Var.20.517764242685
V(Y[t],d=2,D=2)67.2653507246375Range48.5599999999999Trim Var.34.8408344401998
V(Y[t],d=3,D=2)165.510783695652Range79.3999999999999Trim Var.75.7432781240587


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')