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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 08:18:35 -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/t1228663145lldygj75gaqj3ep.htm/, Retrieved Sun, 19 May 2024 10:19:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30067, Retrieved Sun, 19 May 2024 10:19:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207

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]
- RMPD  [Spectral Analysis] [Q6 non statistica...] [2008-12-01 11:41:39] [7d3039e6253bb5fb3b26df1537d500b4]
F RMPD    [Cross Correlation Function] [Q7 Cross Correlat...] [2008-12-01 20:49:08] [7d3039e6253bb5fb3b26df1537d500b4]
- RMPD        [Variance Reduction Matrix] [Q8 Variance reduc...] [2008-12-07 15:18:35] [35348cd8592af0baf5f138bd59921307] [Current]
- RM            [Standard Deviation-Mean Plot] [Q8 standard devia...] [2008-12-07 15:23:44] [7d3039e6253bb5fb3b26df1537d500b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.0
9.1
8.7
8.2
7.9
7.9
9.1
9.4
9.5
9.1
9.0
9.3
9.9
9.8
9.4
8.3
8.0
8.5
10.4
11.1
10.9
9.9
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9.0
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9.0
9.0
9.0
9.8
10.0
9.9
9.3
9.0
9.0
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.8
7.9
7.9
8.0
7.9
7.5
7.2
6.9
6.6
6.7
7.3
7.5

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=30067&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=30067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30067&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)0.895206321334504Range4.5Trim Var.0.505793785310734
V(Y[t],d=1,D=0)0.224491180461330Range3Trim Var.0.077583182093164
V(Y[t],d=2,D=0)0.264459207459207Range2.6Trim Var.0.135977443609023
V(Y[t],d=3,D=0)0.505778846153846Range4.1Trim Var.0.180350649350649
V(Y[t],d=0,D=1)0.81635064935065Range4Trim Var.0.502024489795918
V(Y[t],d=1,D=1)0.142390572390572Range1.50000000000000Trim Var.0.0984183673469387
V(Y[t],d=2,D=1)0.121526904262753Range1.60000000000000Trim Var.0.0760106382978725
V(Y[t],d=3,D=1)0.203447024673439Range2.50000000000000Trim Var.0.107752081406105
V(Y[t],d=0,D=2)0.789994714587738Range3.8Trim Var.0.465689900426743
V(Y[t],d=1,D=2)0.373399778516058Range2.8Trim Var.0.207972972972973
V(Y[t],d=2,D=2)0.285644599303135Range2.49999999999999Trim Var.0.133142857142857
V(Y[t],d=3,D=2)0.456743902439021Range3.59999999999999Trim Var.0.187142857142855

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.895206321334504 & Range & 4.5 & Trim Var. & 0.505793785310734 \tabularnewline
V(Y[t],d=1,D=0) & 0.224491180461330 & Range & 3 & Trim Var. & 0.077583182093164 \tabularnewline
V(Y[t],d=2,D=0) & 0.264459207459207 & Range & 2.6 & Trim Var. & 0.135977443609023 \tabularnewline
V(Y[t],d=3,D=0) & 0.505778846153846 & Range & 4.1 & Trim Var. & 0.180350649350649 \tabularnewline
V(Y[t],d=0,D=1) & 0.81635064935065 & Range & 4 & Trim Var. & 0.502024489795918 \tabularnewline
V(Y[t],d=1,D=1) & 0.142390572390572 & Range & 1.50000000000000 & Trim Var. & 0.0984183673469387 \tabularnewline
V(Y[t],d=2,D=1) & 0.121526904262753 & Range & 1.60000000000000 & Trim Var. & 0.0760106382978725 \tabularnewline
V(Y[t],d=3,D=1) & 0.203447024673439 & Range & 2.50000000000000 & Trim Var. & 0.107752081406105 \tabularnewline
V(Y[t],d=0,D=2) & 0.789994714587738 & Range & 3.8 & Trim Var. & 0.465689900426743 \tabularnewline
V(Y[t],d=1,D=2) & 0.373399778516058 & Range & 2.8 & Trim Var. & 0.207972972972973 \tabularnewline
V(Y[t],d=2,D=2) & 0.285644599303135 & Range & 2.49999999999999 & Trim Var. & 0.133142857142857 \tabularnewline
V(Y[t],d=3,D=2) & 0.456743902439021 & Range & 3.59999999999999 & Trim Var. & 0.187142857142855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30067&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.895206321334504[/C][C]Range[/C][C]4.5[/C][C]Trim Var.[/C][C]0.505793785310734[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.224491180461330[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.077583182093164[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.264459207459207[/C][C]Range[/C][C]2.6[/C][C]Trim Var.[/C][C]0.135977443609023[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.505778846153846[/C][C]Range[/C][C]4.1[/C][C]Trim Var.[/C][C]0.180350649350649[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.81635064935065[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0.502024489795918[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.142390572390572[/C][C]Range[/C][C]1.50000000000000[/C][C]Trim Var.[/C][C]0.0984183673469387[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.121526904262753[/C][C]Range[/C][C]1.60000000000000[/C][C]Trim Var.[/C][C]0.0760106382978725[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.203447024673439[/C][C]Range[/C][C]2.50000000000000[/C][C]Trim Var.[/C][C]0.107752081406105[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.789994714587738[/C][C]Range[/C][C]3.8[/C][C]Trim Var.[/C][C]0.465689900426743[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.373399778516058[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.207972972972973[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.285644599303135[/C][C]Range[/C][C]2.49999999999999[/C][C]Trim Var.[/C][C]0.133142857142857[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.456743902439021[/C][C]Range[/C][C]3.59999999999999[/C][C]Trim Var.[/C][C]0.187142857142855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30067&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)0.895206321334504Range4.5Trim Var.0.505793785310734
V(Y[t],d=1,D=0)0.224491180461330Range3Trim Var.0.077583182093164
V(Y[t],d=2,D=0)0.264459207459207Range2.6Trim Var.0.135977443609023
V(Y[t],d=3,D=0)0.505778846153846Range4.1Trim Var.0.180350649350649
V(Y[t],d=0,D=1)0.81635064935065Range4Trim Var.0.502024489795918
V(Y[t],d=1,D=1)0.142390572390572Range1.50000000000000Trim Var.0.0984183673469387
V(Y[t],d=2,D=1)0.121526904262753Range1.60000000000000Trim Var.0.0760106382978725
V(Y[t],d=3,D=1)0.203447024673439Range2.50000000000000Trim Var.0.107752081406105
V(Y[t],d=0,D=2)0.789994714587738Range3.8Trim Var.0.465689900426743
V(Y[t],d=1,D=2)0.373399778516058Range2.8Trim Var.0.207972972972973
V(Y[t],d=2,D=2)0.285644599303135Range2.49999999999999Trim Var.0.133142857142857
V(Y[t],d=3,D=2)0.456743902439021Range3.59999999999999Trim Var.0.187142857142855


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')