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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, 02 Dec 2008 15:48:32 -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/02/t1228258166f23v67rjoknzxsy.htm/, Retrieved Sun, 19 May 2024 12:39:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28521, Retrieved Sun, 19 May 2024 12:39:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192

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]
- RM D  [(Partial) Autocorrelation Function] [Non stationary ti...] [2008-12-02 22:44:03] [1a689e9ccc515e1757f0522229a687e9]
- RM        [Variance Reduction Matrix] [Non stationary ti...] [2008-12-02 22:48:32] [74a138e5b32af267311b5ad4cd13bf7e] [Current]
-    D        [Variance Reduction Matrix] [Non stationary ti...] [2008-12-02 23:03:57] [1a689e9ccc515e1757f0522229a687e9]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,7
105,7
109,5
105,3
102,8
100,6
97,6
110,3
107,2
107,2
108,1
97,1
92,2
112,2
111,6
115,7
111,3
104,2
103,2
112,7
106,4
102,6
110,6
95,2
89
112,5
116,8
107,2
113,6
101,8
102,6
122,7
110,3
110,5
121,6
100,3
100,7
123,4
127,1
124,1
131,2
111,6
114,2
130,1
125,9
119
133,8
107,5
113,5
134,4
126,8
135,6
139,9
129,8
131
153,1
134,1
144,1
155,9
123,3
128,1
144,3
153
149,9
150,9
141
138,9
157,4
142,9
151,7
161
138,5
135,9
151,5
164
159,1
157
142,1
144,8
152,1
154,6
148,7
157,7
146,4
136,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28521&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28521&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28521&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)407.024201680672Range75Trim Var.311.658025225225
V(Y[t],d=1,D=0)136.061353987378Range56.1Trim Var.79.143887449093
V(Y[t],d=2,D=0)346.525263003233Range81.8Trim Var.224.121632420091
V(Y[t],d=3,D=0)1019.95797651310Range144.6Trim Var.616.372949921753
V(Y[t],d=0,D=1)51.4686111111111Range34.7Trim Var.29.9337884615385
V(Y[t],d=1,D=1)52.4153345070423Range31.8Trim Var.31.3844444444445
V(Y[t],d=2,D=1)167.022185110664Range63.4Trim Var.98.6457654889914
V(Y[t],d=3,D=1)572.791861283644Range112.6Trim Var.336.672863564252
V(Y[t],d=0,D=2)104.155240437158Range45.4Trim Var.59.3238679245283
V(Y[t],d=1,D=2)123.384505649718Range51.3Trim Var.74.608459119497
V(Y[t],d=2,D=2)400.473471654004Range98.3Trim Var.264.125058055153
V(Y[t],d=3,D=2)1425.95620084695Range162.2Trim Var.936.47608974359

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 407.024201680672 & Range & 75 & Trim Var. & 311.658025225225 \tabularnewline
V(Y[t],d=1,D=0) & 136.061353987378 & Range & 56.1 & Trim Var. & 79.143887449093 \tabularnewline
V(Y[t],d=2,D=0) & 346.525263003233 & Range & 81.8 & Trim Var. & 224.121632420091 \tabularnewline
V(Y[t],d=3,D=0) & 1019.95797651310 & Range & 144.6 & Trim Var. & 616.372949921753 \tabularnewline
V(Y[t],d=0,D=1) & 51.4686111111111 & Range & 34.7 & Trim Var. & 29.9337884615385 \tabularnewline
V(Y[t],d=1,D=1) & 52.4153345070423 & Range & 31.8 & Trim Var. & 31.3844444444445 \tabularnewline
V(Y[t],d=2,D=1) & 167.022185110664 & Range & 63.4 & Trim Var. & 98.6457654889914 \tabularnewline
V(Y[t],d=3,D=1) & 572.791861283644 & Range & 112.6 & Trim Var. & 336.672863564252 \tabularnewline
V(Y[t],d=0,D=2) & 104.155240437158 & Range & 45.4 & Trim Var. & 59.3238679245283 \tabularnewline
V(Y[t],d=1,D=2) & 123.384505649718 & Range & 51.3 & Trim Var. & 74.608459119497 \tabularnewline
V(Y[t],d=2,D=2) & 400.473471654004 & Range & 98.3 & Trim Var. & 264.125058055153 \tabularnewline
V(Y[t],d=3,D=2) & 1425.95620084695 & Range & 162.2 & Trim Var. & 936.47608974359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28521&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]407.024201680672[/C][C]Range[/C][C]75[/C][C]Trim Var.[/C][C]311.658025225225[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]136.061353987378[/C][C]Range[/C][C]56.1[/C][C]Trim Var.[/C][C]79.143887449093[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]346.525263003233[/C][C]Range[/C][C]81.8[/C][C]Trim Var.[/C][C]224.121632420091[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1019.95797651310[/C][C]Range[/C][C]144.6[/C][C]Trim Var.[/C][C]616.372949921753[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]51.4686111111111[/C][C]Range[/C][C]34.7[/C][C]Trim Var.[/C][C]29.9337884615385[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]52.4153345070423[/C][C]Range[/C][C]31.8[/C][C]Trim Var.[/C][C]31.3844444444445[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]167.022185110664[/C][C]Range[/C][C]63.4[/C][C]Trim Var.[/C][C]98.6457654889914[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]572.791861283644[/C][C]Range[/C][C]112.6[/C][C]Trim Var.[/C][C]336.672863564252[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]104.155240437158[/C][C]Range[/C][C]45.4[/C][C]Trim Var.[/C][C]59.3238679245283[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]123.384505649718[/C][C]Range[/C][C]51.3[/C][C]Trim Var.[/C][C]74.608459119497[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]400.473471654004[/C][C]Range[/C][C]98.3[/C][C]Trim Var.[/C][C]264.125058055153[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1425.95620084695[/C][C]Range[/C][C]162.2[/C][C]Trim Var.[/C][C]936.47608974359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28521&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28521&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)407.024201680672Range75Trim Var.311.658025225225
V(Y[t],d=1,D=0)136.061353987378Range56.1Trim Var.79.143887449093
V(Y[t],d=2,D=0)346.525263003233Range81.8Trim Var.224.121632420091
V(Y[t],d=3,D=0)1019.95797651310Range144.6Trim Var.616.372949921753
V(Y[t],d=0,D=1)51.4686111111111Range34.7Trim Var.29.9337884615385
V(Y[t],d=1,D=1)52.4153345070423Range31.8Trim Var.31.3844444444445
V(Y[t],d=2,D=1)167.022185110664Range63.4Trim Var.98.6457654889914
V(Y[t],d=3,D=1)572.791861283644Range112.6Trim Var.336.672863564252
V(Y[t],d=0,D=2)104.155240437158Range45.4Trim Var.59.3238679245283
V(Y[t],d=1,D=2)123.384505649718Range51.3Trim Var.74.608459119497
V(Y[t],d=2,D=2)400.473471654004Range98.3Trim Var.264.125058055153
V(Y[t],d=3,D=2)1425.95620084695Range162.2Trim Var.936.47608974359


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Airline ; par2 = Box-Jenkins ; par3 = Airline Passengers ;
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')