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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 computationMon, 27 Dec 2010 13:28:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/27/t12934563622uq3srdzzh03q2w.htm/, Retrieved Mon, 06 May 2024 14:13:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115964, Retrieved Mon, 06 May 2024 14:13:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

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] [] [2010-12-14 13:47:21] [acfa3f91ce5598ec4ba98aad4cfba2f0]
- RMPD    [Variance Reduction Matrix] [] [2010-12-27 13:28:24] [c474a97a96075919a678ad3d2290b00b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35.36
31.19
35.29
33.80
36.38
37.77
34.88
37.07
35.56
34.18
32.05
32.35
34.79
33.75
33.76
36.80
36.57
34.14
33.85
35.10
33.92
33.34
30.69
32.32
32.47
34.71
37.19
35.58
36.04
35.63
32.74
33.31
28.40
27.37
28.20
29.23
28.05
27.70
28.05
28.01
30.73
30.82
30.48
30.92
31.20
31.41
31.96
36.95
35.64
37.18
38.69
39.97
40.36
40.79
42.92
41.21
44.15
44.70
47.42
45.14
46.08
50.59
48.63
47.46
47.30
49.02
51.77
54.15
56.10
52.58
52.56
51.27
57.72
53.46
55.48
59.33
57.32
56.44
58.80
55.64
53.62
54.87
56.15
55.35
52.38
51.27
53.95
56.09
56.34
60.65
58.35
57.18
58.87
66.20
62.25
62.62
54.73
56.20
52.54
63.06
63.53
60.95
53.83
51.20
44.57
44.15
44.04
42.28
38.42
35.41
37.01
39.19
46.50
44.79
47.01
49.15
50.85
54.09
55.40
56.16
54.37
52.34
56.13
51.29
42.95
28.88
38.47
34.83
41.17
40.80
40.00
44.00

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115964&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]2 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=115964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115964&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)109.820028915105Range38.83Trim Var.86.2186199333623
V(Y[t],d=1,D=0)10.7554827363476Range24.59Trim Var.4.39210271146478
V(Y[t],d=2,D=0)23.4862577280859Range36.89Trim Var.10.1946163118441
V(Y[t],d=3,D=0)74.3228543725776Range66.28Trim Var.30.3139943249428
V(Y[t],d=0,D=1)86.903994222689Range42.99Trim Var.58.1875927570093
V(Y[t],d=1,D=1)18.6900872240422Range24.99Trim Var.10.7480636924705
V(Y[t],d=2,D=1)39.1001521150225Range34.01Trim Var.22.8243223450135
V(Y[t],d=3,D=1)122.748938196287Range61.66Trim Var.71.1835768864469
V(Y[t],d=0,D=2)206.051794080997Range71.1Trim Var.105.061338771930
V(Y[t],d=1,D=2)47.5929098395345Range39.14Trim Var.27.0532736170213
V(Y[t],d=2,D=2)95.8833831895778Range55.17Trim Var.53.085951132464
V(Y[t],d=3,D=2)296.706266978022Range98.64Trim Var.158.03824399252

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 109.820028915105 & Range & 38.83 & Trim Var. & 86.2186199333623 \tabularnewline
V(Y[t],d=1,D=0) & 10.7554827363476 & Range & 24.59 & Trim Var. & 4.39210271146478 \tabularnewline
V(Y[t],d=2,D=0) & 23.4862577280859 & Range & 36.89 & Trim Var. & 10.1946163118441 \tabularnewline
V(Y[t],d=3,D=0) & 74.3228543725776 & Range & 66.28 & Trim Var. & 30.3139943249428 \tabularnewline
V(Y[t],d=0,D=1) & 86.903994222689 & Range & 42.99 & Trim Var. & 58.1875927570093 \tabularnewline
V(Y[t],d=1,D=1) & 18.6900872240422 & Range & 24.99 & Trim Var. & 10.7480636924705 \tabularnewline
V(Y[t],d=2,D=1) & 39.1001521150225 & Range & 34.01 & Trim Var. & 22.8243223450135 \tabularnewline
V(Y[t],d=3,D=1) & 122.748938196287 & Range & 61.66 & Trim Var. & 71.1835768864469 \tabularnewline
V(Y[t],d=0,D=2) & 206.051794080997 & Range & 71.1 & Trim Var. & 105.061338771930 \tabularnewline
V(Y[t],d=1,D=2) & 47.5929098395345 & Range & 39.14 & Trim Var. & 27.0532736170213 \tabularnewline
V(Y[t],d=2,D=2) & 95.8833831895778 & Range & 55.17 & Trim Var. & 53.085951132464 \tabularnewline
V(Y[t],d=3,D=2) & 296.706266978022 & Range & 98.64 & Trim Var. & 158.03824399252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115964&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]109.820028915105[/C][C]Range[/C][C]38.83[/C][C]Trim Var.[/C][C]86.2186199333623[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]10.7554827363476[/C][C]Range[/C][C]24.59[/C][C]Trim Var.[/C][C]4.39210271146478[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]23.4862577280859[/C][C]Range[/C][C]36.89[/C][C]Trim Var.[/C][C]10.1946163118441[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]74.3228543725776[/C][C]Range[/C][C]66.28[/C][C]Trim Var.[/C][C]30.3139943249428[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]86.903994222689[/C][C]Range[/C][C]42.99[/C][C]Trim Var.[/C][C]58.1875927570093[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]18.6900872240422[/C][C]Range[/C][C]24.99[/C][C]Trim Var.[/C][C]10.7480636924705[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]39.1001521150225[/C][C]Range[/C][C]34.01[/C][C]Trim Var.[/C][C]22.8243223450135[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]122.748938196287[/C][C]Range[/C][C]61.66[/C][C]Trim Var.[/C][C]71.1835768864469[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]206.051794080997[/C][C]Range[/C][C]71.1[/C][C]Trim Var.[/C][C]105.061338771930[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]47.5929098395345[/C][C]Range[/C][C]39.14[/C][C]Trim Var.[/C][C]27.0532736170213[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]95.8833831895778[/C][C]Range[/C][C]55.17[/C][C]Trim Var.[/C][C]53.085951132464[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]296.706266978022[/C][C]Range[/C][C]98.64[/C][C]Trim Var.[/C][C]158.03824399252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115964&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)109.820028915105Range38.83Trim Var.86.2186199333623
V(Y[t],d=1,D=0)10.7554827363476Range24.59Trim Var.4.39210271146478
V(Y[t],d=2,D=0)23.4862577280859Range36.89Trim Var.10.1946163118441
V(Y[t],d=3,D=0)74.3228543725776Range66.28Trim Var.30.3139943249428
V(Y[t],d=0,D=1)86.903994222689Range42.99Trim Var.58.1875927570093
V(Y[t],d=1,D=1)18.6900872240422Range24.99Trim Var.10.7480636924705
V(Y[t],d=2,D=1)39.1001521150225Range34.01Trim Var.22.8243223450135
V(Y[t],d=3,D=1)122.748938196287Range61.66Trim Var.71.1835768864469
V(Y[t],d=0,D=2)206.051794080997Range71.1Trim Var.105.061338771930
V(Y[t],d=1,D=2)47.5929098395345Range39.14Trim Var.27.0532736170213
V(Y[t],d=2,D=2)95.8833831895778Range55.17Trim Var.53.085951132464
V(Y[t],d=3,D=2)296.706266978022Range98.64Trim Var.158.03824399252


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(myx,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')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()