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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareVariance Reduction Matrix
Date of computationThu, 22 Dec 2011 10:48:57 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324569089z4brc92eslzshfy.htm/, Retrieved Fri, 03 May 2024 13:05:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159641, Retrieved Fri, 03 May 2024 13:05:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D    [(Partial) Autocorrelation Function] [] [2011-12-22 15:18:49] [5a05da414fd67612c3b80d44effe0727]
- R         [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [5a05da414fd67612c3b80d44effe0727]
-             [(Partial) Autocorrelation Function] [] [2011-12-22 15:29:46] [5a05da414fd67612c3b80d44effe0727]
- RM              [Variance Reduction Matrix] [] [2011-12-22 15:48:57] [95610e892c4b5c84ff80f4c898567a9d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159641&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159641&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'Herman Ole Andreas Wold' @ wold.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.428279661016949Range2.7Trim Var.0.296516690856314
V(Y[t],d=1,D=0)0.121992986557569Range1.8Trim Var.0.0646666666666667
V(Y[t],d=2,D=0)0.158233514821537Range1.8Trim Var.0.0966628959276018
V(Y[t],d=3,D=0)0.317142857142857Range2.8Trim Var.0.154125490196078
V(Y[t],d=0,D=1)1.02378989361702Range3.1Trim Var.0.851289198606272
V(Y[t],d=1,D=1)0.122710453283996Range1.5Trim Var.0.0590769230769231
V(Y[t],d=2,D=1)0.108444444444445Range1.5Trim Var.0.0665641025641028
V(Y[t],d=3,D=1)0.191464646464648Range1.8Trim Var.0.115681511470986
V(Y[t],d=0,D=2)2.46542063492064Range5.3Trim Var.1.87507056451613
V(Y[t],d=1,D=2)0.325411764705883Range2.4Trim Var.0.196195402298851
V(Y[t],d=2,D=2)0.310989304812836Range2.2Trim Var.0.205057471264369
V(Y[t],d=3,D=2)0.595227272727278Range3.10000000000001Trim Var.0.395049261083747

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.428279661016949 & Range & 2.7 & Trim Var. & 0.296516690856314 \tabularnewline
V(Y[t],d=1,D=0) & 0.121992986557569 & Range & 1.8 & Trim Var. & 0.0646666666666667 \tabularnewline
V(Y[t],d=2,D=0) & 0.158233514821537 & Range & 1.8 & Trim Var. & 0.0966628959276018 \tabularnewline
V(Y[t],d=3,D=0) & 0.317142857142857 & Range & 2.8 & Trim Var. & 0.154125490196078 \tabularnewline
V(Y[t],d=0,D=1) & 1.02378989361702 & Range & 3.1 & Trim Var. & 0.851289198606272 \tabularnewline
V(Y[t],d=1,D=1) & 0.122710453283996 & Range & 1.5 & Trim Var. & 0.0590769230769231 \tabularnewline
V(Y[t],d=2,D=1) & 0.108444444444445 & Range & 1.5 & Trim Var. & 0.0665641025641028 \tabularnewline
V(Y[t],d=3,D=1) & 0.191464646464648 & Range & 1.8 & Trim Var. & 0.115681511470986 \tabularnewline
V(Y[t],d=0,D=2) & 2.46542063492064 & Range & 5.3 & Trim Var. & 1.87507056451613 \tabularnewline
V(Y[t],d=1,D=2) & 0.325411764705883 & Range & 2.4 & Trim Var. & 0.196195402298851 \tabularnewline
V(Y[t],d=2,D=2) & 0.310989304812836 & Range & 2.2 & Trim Var. & 0.205057471264369 \tabularnewline
V(Y[t],d=3,D=2) & 0.595227272727278 & Range & 3.10000000000001 & Trim Var. & 0.395049261083747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159641&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.428279661016949[/C][C]Range[/C][C]2.7[/C][C]Trim Var.[/C][C]0.296516690856314[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.121992986557569[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.0646666666666667[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.158233514821537[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.0966628959276018[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.317142857142857[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.154125490196078[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.02378989361702[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.851289198606272[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.122710453283996[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0590769230769231[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.108444444444445[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0665641025641028[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.191464646464648[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.115681511470986[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2.46542063492064[/C][C]Range[/C][C]5.3[/C][C]Trim Var.[/C][C]1.87507056451613[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.325411764705883[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.196195402298851[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.310989304812836[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.205057471264369[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.595227272727278[/C][C]Range[/C][C]3.10000000000001[/C][C]Trim Var.[/C][C]0.395049261083747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159641&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)0.428279661016949Range2.7Trim Var.0.296516690856314
V(Y[t],d=1,D=0)0.121992986557569Range1.8Trim Var.0.0646666666666667
V(Y[t],d=2,D=0)0.158233514821537Range1.8Trim Var.0.0966628959276018
V(Y[t],d=3,D=0)0.317142857142857Range2.8Trim Var.0.154125490196078
V(Y[t],d=0,D=1)1.02378989361702Range3.1Trim Var.0.851289198606272
V(Y[t],d=1,D=1)0.122710453283996Range1.5Trim Var.0.0590769230769231
V(Y[t],d=2,D=1)0.108444444444445Range1.5Trim Var.0.0665641025641028
V(Y[t],d=3,D=1)0.191464646464648Range1.8Trim Var.0.115681511470986
V(Y[t],d=0,D=2)2.46542063492064Range5.3Trim Var.1.87507056451613
V(Y[t],d=1,D=2)0.325411764705883Range2.4Trim Var.0.196195402298851
V(Y[t],d=2,D=2)0.310989304812836Range2.2Trim Var.0.205057471264369
V(Y[t],d=3,D=2)0.595227272727278Range3.10000000000001Trim Var.0.395049261083747


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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()