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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 computationWed, 23 Dec 2009 03:57:13 -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/2009/Dec/23/t1261565892weetjvkwsjh7q22.htm/, Retrieved Mon, 29 Apr 2024 14:31:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70497, Retrieved Mon, 29 Apr 2024 14:31:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper
Estimated Impact175

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [VRM] [2009-12-23 10:57:13] [b08f24ccf7d7e0757793cda532be96b3] [Current]
- RMP     [Standard Deviation-Mean Plot] [SMP s=4] [2009-12-23 11:23:21] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Standard Deviation-Mean Plot] [SMP s=12] [2009-12-23 11:27:41] [5e6d255681a7853beaa91b62357037a7]
-   P     [Variance Reduction Matrix] [VRM s=12] [2009-12-27 09:43:09] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=1] [2009-12-27 09:50:20] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=1 d=1 D=0] [2009-12-27 10:11:29] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=1 d=1 D=1] [2009-12-27 10:17:26] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=1 d=2 D=1] [2009-12-27 10:20:21] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=-3 d=1 D=1] [2009-12-27 10:35:05] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=-2 d=1 D=1] [2009-12-27 10:34:06] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=-2 d=1 D=1] [2009-12-27 10:32:54] [5e6d255681a7853beaa91b62357037a7]
- RMP     [Spectral Analysis] [SA Lambda=-2 d=1 D=1] [2009-12-27 10:32:20] [5e6d255681a7853beaa91b62357037a7]
- RMP     [(Partial) Autocorrelation Function] [ACF, PACF d=1 D=1...] [2009-12-27 11:04:14] [5e6d255681a7853beaa91b62357037a7]
-   P       [(Partial) Autocorrelation Function] [ACF, PACF d=1 D=1...] [2009-12-27 13:55:39] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [Backward ARIMA] [2009-12-27 13:15:47] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [Backward ARIMA p=...] [2009-12-27 14:39:45] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [Backward ARIMA 2 ...] [2009-12-27 15:00:30] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [Backward ARIMA la...] [2009-12-27 15:27:49] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [Backward ARIMA la...] [2009-12-27 15:30:59] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Backward Selection] [ARIMA lambda = -3] [2009-12-27 15:43:31] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Forecasting] [ARIMA forecast L=...] [2009-12-28 14:16:29] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Forecasting] [ARIMA forecast L=...] [2009-12-28 14:31:03] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Forecasting] [ARIMA forecast L=...] [2009-12-28 14:34:54] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Forecasting] [ARIMA forecast L=...] [2009-12-28 15:34:08] [5e6d255681a7853beaa91b62357037a7]
- RMP     [ARIMA Forecasting] [ARIMA forecast L=...] [2009-12-28 15:38:28] [5e6d255681a7853beaa91b62357037a7]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.87
84.23
84.61
84.82
85.04
85.06
84.93
84.98
85.23
85.30
85.33
85.55
85.70
85.88
86.04
86.07
86.31
86.38
86.35
86.55
86.70
86.74
86.85
86.95
86.80
87.01
87.17
87.43
87.66
87.68
87.59
87.65
87.72
87.70
87.71
87.80
87.62
87.84
88.17
88.47
88.58
88.57
88.55
88.68
88.79
88.85
88.95
89.27
89.09
89.42
89.72
89.85
89.96
90.25
90.20
90.27
90.78
90.79
90.98
91.25
90.75
91.01
91.50
92.09
92.56
92.66
92.38
92.38
92.66
92.69
92.59
92.98
92.98
93.15
93.65
94.06
94.24
94.24
94.11
94.16
94.43
94.67
94.60
95.00
94.84
95.26
95.81
95.92
95.85
95.90
95.80
96.00
96.34
96.43
96.48
96.75
96.51
96.69
97.28
97.69
98.08
98.09
97.92
98.06
98.23
98.57
98.53
98.92
98.42
98.73
99.32
99.73
100.00
100.08
100.02
100.26
100.71
100.95
100.75
101.03
100.64
100.93
101.41
102.07
102.42
102.53
102.43
102.60
102.65
102.74
102.82
103.21
102.75
103.09
103.71
104.30
104.58
104.71
104.44
104.57
104.95
105.49
106.03
106.48
106.25
106.70
107.60
108.05
108.72
109.17
109.08
109.04
109.34
109.37
108.96
108.77
108.11
108.67
109.05
109.43
109.62
109.85
109.34
109.65
109.69
109.91
110.09

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=70497&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=70497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70497&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)61.5677913931174Range26.22Trim Var.48.9561070187534
V(Y[t],d=1,D=0)0.064901234027017Range1.55999999999999Trim Var.0.0350605396212539
V(Y[t],d=2,D=0)0.111758558758315Range2.11Trim Var.0.0570987233249463
V(Y[t],d=3,D=0)0.312347104593745Range3.10000000000001Trim Var.0.141523703353803
V(Y[t],d=0,D=1)0.33619373447205Range3.8Trim Var.0.148229045602285
V(Y[t],d=1,D=1)0.0826309709119494Range1.68000000000002Trim Var.0.0508963820901319
V(Y[t],d=2,D=1)0.119238189634582Range1.89Trim Var.0.0732370826356738
V(Y[t],d=3,D=1)0.348855377731192Range3.05999999999997Trim Var.0.222624278293874
V(Y[t],d=0,D=2)0.769854310850439Range6Trim Var.0.372599353560627
V(Y[t],d=1,D=2)0.28492637297343Range2.89000000000003Trim Var.0.188990711943297
V(Y[t],d=2,D=2)0.423779566563464Range3.36999999999998Trim Var.0.258484478316872
V(Y[t],d=3,D=2)1.26313912513070Range5.45999999999997Trim Var.0.822924771241823

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 61.5677913931174 & Range & 26.22 & Trim Var. & 48.9561070187534 \tabularnewline
V(Y[t],d=1,D=0) & 0.064901234027017 & Range & 1.55999999999999 & Trim Var. & 0.0350605396212539 \tabularnewline
V(Y[t],d=2,D=0) & 0.111758558758315 & Range & 2.11 & Trim Var. & 0.0570987233249463 \tabularnewline
V(Y[t],d=3,D=0) & 0.312347104593745 & Range & 3.10000000000001 & Trim Var. & 0.141523703353803 \tabularnewline
V(Y[t],d=0,D=1) & 0.33619373447205 & Range & 3.8 & Trim Var. & 0.148229045602285 \tabularnewline
V(Y[t],d=1,D=1) & 0.0826309709119494 & Range & 1.68000000000002 & Trim Var. & 0.0508963820901319 \tabularnewline
V(Y[t],d=2,D=1) & 0.119238189634582 & Range & 1.89 & Trim Var. & 0.0732370826356738 \tabularnewline
V(Y[t],d=3,D=1) & 0.348855377731192 & Range & 3.05999999999997 & Trim Var. & 0.222624278293874 \tabularnewline
V(Y[t],d=0,D=2) & 0.769854310850439 & Range & 6 & Trim Var. & 0.372599353560627 \tabularnewline
V(Y[t],d=1,D=2) & 0.28492637297343 & Range & 2.89000000000003 & Trim Var. & 0.188990711943297 \tabularnewline
V(Y[t],d=2,D=2) & 0.423779566563464 & Range & 3.36999999999998 & Trim Var. & 0.258484478316872 \tabularnewline
V(Y[t],d=3,D=2) & 1.26313912513070 & Range & 5.45999999999997 & Trim Var. & 0.822924771241823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70497&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]61.5677913931174[/C][C]Range[/C][C]26.22[/C][C]Trim Var.[/C][C]48.9561070187534[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.064901234027017[/C][C]Range[/C][C]1.55999999999999[/C][C]Trim Var.[/C][C]0.0350605396212539[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.111758558758315[/C][C]Range[/C][C]2.11[/C][C]Trim Var.[/C][C]0.0570987233249463[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.312347104593745[/C][C]Range[/C][C]3.10000000000001[/C][C]Trim Var.[/C][C]0.141523703353803[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.33619373447205[/C][C]Range[/C][C]3.8[/C][C]Trim Var.[/C][C]0.148229045602285[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0826309709119494[/C][C]Range[/C][C]1.68000000000002[/C][C]Trim Var.[/C][C]0.0508963820901319[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.119238189634582[/C][C]Range[/C][C]1.89[/C][C]Trim Var.[/C][C]0.0732370826356738[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.348855377731192[/C][C]Range[/C][C]3.05999999999997[/C][C]Trim Var.[/C][C]0.222624278293874[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.769854310850439[/C][C]Range[/C][C]6[/C][C]Trim Var.[/C][C]0.372599353560627[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.28492637297343[/C][C]Range[/C][C]2.89000000000003[/C][C]Trim Var.[/C][C]0.188990711943297[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.423779566563464[/C][C]Range[/C][C]3.36999999999998[/C][C]Trim Var.[/C][C]0.258484478316872[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.26313912513070[/C][C]Range[/C][C]5.45999999999997[/C][C]Trim Var.[/C][C]0.822924771241823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70497&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)61.5677913931174Range26.22Trim Var.48.9561070187534
V(Y[t],d=1,D=0)0.064901234027017Range1.55999999999999Trim Var.0.0350605396212539
V(Y[t],d=2,D=0)0.111758558758315Range2.11Trim Var.0.0570987233249463
V(Y[t],d=3,D=0)0.312347104593745Range3.10000000000001Trim Var.0.141523703353803
V(Y[t],d=0,D=1)0.33619373447205Range3.8Trim Var.0.148229045602285
V(Y[t],d=1,D=1)0.0826309709119494Range1.68000000000002Trim Var.0.0508963820901319
V(Y[t],d=2,D=1)0.119238189634582Range1.89Trim Var.0.0732370826356738
V(Y[t],d=3,D=1)0.348855377731192Range3.05999999999997Trim Var.0.222624278293874
V(Y[t],d=0,D=2)0.769854310850439Range6Trim Var.0.372599353560627
V(Y[t],d=1,D=2)0.28492637297343Range2.89000000000003Trim Var.0.188990711943297
V(Y[t],d=2,D=2)0.423779566563464Range3.36999999999998Trim Var.0.258484478316872
V(Y[t],d=3,D=2)1.26313912513070Range5.45999999999997Trim Var.0.822924771241823


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 6 ;
Parameters (R input):
par1 = 6 ;
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')