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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, 08 Dec 2008 14:16:26 -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/08/t1228771018eaw9cnfeotg6s9e.htm/, Retrieved Thu, 16 May 2024 14:10:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31043, Retrieved Thu, 16 May 2024 14:10:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Variance Reduction Matrix] [Unemployment - St...] [2008-12-08 17:18:29] [57850c80fd59ccfb28f882be994e814e]
F    D    [Variance Reduction Matrix] [] [2008-12-08 21:16:26] [6d40a467de0f28bd2350f82ac9522c51] [Current]
Feedback Forum
2008-12-14 08:42:42 [Kristof Van Esbroeck] [reply] 
Om een duidelijk antwoord op de eerste vraagstelling – step – te formuleren dienen we een correcte lamba waarde te berekenen.

De berekening werd opnieuw gemaakt met Unemployment data.

We gebruiken de Standard Deviation – Mean Plot software.


http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229240118n4b6am5ynn7a5bl.htm


Uit de tabel Regression: ln S.E.(k) = alpha + beta * ln Mean(k) kunnen we een lamba waarde van 0.467057973925013 afleiden.

Als we 1 in vermindering hadden gebracht met de Beta waarde had dit ook geresulteerd in de optimale Lamba Coëfficiënt. Nl, (1 - 0.532942026074987) is gelijk aan 0.467057973925013.

Op de grafische weergave van de Standard Deviation – Mean Plot noteren we op de x as het gemiddelde en op y as de standaard fout.
2008-12-14 13:23:02 [a9d641c8b88cd97bdfe55e3671cf3c5a] [reply] 
Je had hier inderdaad moeten werken met de Standard Deviation-Mean Plot software ipv van de VRM.
Je eigen verbetering is correct.
2008-12-14 14:12:33 [Kevin Neelen] [reply] 
De student heeft hier geen correcte methode gebruikt om deze vraagstellin gop te lossen. Hier moest namelijk geen Variance Reduction Matrix gebruikt worden, maar een Standard Deviation Mean Plot.

Deze berekening is wel in de verbetering door de student aangebracht.

De tijdreeks wordt hier opgedeeld in secties van 12 waarnemingen, dus iedere stip op de grafieken representeert 1 jaar. We zien een outlier die voldoende in het midden gelegen is om niet van invloed te zijn op het verloop regressierechte. Deze rechte loopt van linksonder naar rechtsboven, wat wil zeggen dat wanneer de werkloosheid stijgt, de standaardfout stijgt. Er is dus sprake van heteroskedasticiteit. Dit wordt bevestigd door de positieve beta-waarde in de tweede tabel. Deze verschilt significant van 0 vanwege de p-waarde die kleiner is dan 5%.

Het is hier de bedoeling om de optimale Lambdawaarde te bepalen. In de laatste tabel vinden we een lambdawaarde van 0,467. Voor het gemak wordt dit afgerond tot 0,5.
2008-12-14 14:52:20 [Nathalie Koulouris] [reply] 
De student heeft voor deze vraag de verkeerde software gebruikt. De student had hier gebruik moeten maken van de standard deviation mean plot in plaats van de variance reduction matrix.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
299,63
305,945
382,252
348,846
335,367
373,617
312,612
312,232
337,161
331,476
350,103
345,127
297,256
295,979
361,007
321,803
354,937
349,432
290,979
349,576
327,625
349,377
336,777
339,134
323,321
318,86
373,583
333,03
408,556
414,646
291,514
348,857
349,368
375,765
364,136
349,53
348,167
332,856
360,551
346,969
392,815
372,02
371,027
342,672
367,343
390,786
343,785
362,6
349,468
340,624
369,536
407,782
392,239
404,824
373,669
344,902
396,7
398,911
366,009
392,484

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=31043&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=31043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31043&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)947.871032484463Range123.667Trim Var.663.550461775332
V(Y[t],d=1,D=0)1344.72598750964Range199.439Trim Var.765.759477401306
V(Y[t],d=2,D=0)3886.39493449244Range309.697Trim Var.2394.84446411878
V(Y[t],d=3,D=0)12492.6649025006Range547.004Trim Var.7958.0893854902
V(Y[t],d=0,D=1)597.84245041844Range122.139Trim Var.300.405221551684
V(Y[t],d=1,D=1)1272.62243970768Range207.837Trim Var.554.532122339025
V(Y[t],d=2,D=1)4042.76009905121Range356.861Trim Var.1827.05881867692
V(Y[t],d=3,D=1)13829.0529759071Range674.556Trim Var.6612.78562938597
V(Y[t],d=0,D=2)1712.03583230714Range197.239Trim Var.891.201228337702
V(Y[t],d=1,D=2)3331.20981047899Range339.119Trim Var.1356.42448344516
V(Y[t],d=2,D=2)10379.1038867103Range508.849Trim Var.4019.31766377472
V(Y[t],d=3,D=2)35321.2230830928Range946.713Trim Var.16107.5694311084

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 947.871032484463 & Range & 123.667 & Trim Var. & 663.550461775332 \tabularnewline
V(Y[t],d=1,D=0) & 1344.72598750964 & Range & 199.439 & Trim Var. & 765.759477401306 \tabularnewline
V(Y[t],d=2,D=0) & 3886.39493449244 & Range & 309.697 & Trim Var. & 2394.84446411878 \tabularnewline
V(Y[t],d=3,D=0) & 12492.6649025006 & Range & 547.004 & Trim Var. & 7958.0893854902 \tabularnewline
V(Y[t],d=0,D=1) & 597.84245041844 & Range & 122.139 & Trim Var. & 300.405221551684 \tabularnewline
V(Y[t],d=1,D=1) & 1272.62243970768 & Range & 207.837 & Trim Var. & 554.532122339025 \tabularnewline
V(Y[t],d=2,D=1) & 4042.76009905121 & Range & 356.861 & Trim Var. & 1827.05881867692 \tabularnewline
V(Y[t],d=3,D=1) & 13829.0529759071 & Range & 674.556 & Trim Var. & 6612.78562938597 \tabularnewline
V(Y[t],d=0,D=2) & 1712.03583230714 & Range & 197.239 & Trim Var. & 891.201228337702 \tabularnewline
V(Y[t],d=1,D=2) & 3331.20981047899 & Range & 339.119 & Trim Var. & 1356.42448344516 \tabularnewline
V(Y[t],d=2,D=2) & 10379.1038867103 & Range & 508.849 & Trim Var. & 4019.31766377472 \tabularnewline
V(Y[t],d=3,D=2) & 35321.2230830928 & Range & 946.713 & Trim Var. & 16107.5694311084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31043&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]947.871032484463[/C][C]Range[/C][C]123.667[/C][C]Trim Var.[/C][C]663.550461775332[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1344.72598750964[/C][C]Range[/C][C]199.439[/C][C]Trim Var.[/C][C]765.759477401306[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]3886.39493449244[/C][C]Range[/C][C]309.697[/C][C]Trim Var.[/C][C]2394.84446411878[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]12492.6649025006[/C][C]Range[/C][C]547.004[/C][C]Trim Var.[/C][C]7958.0893854902[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]597.84245041844[/C][C]Range[/C][C]122.139[/C][C]Trim Var.[/C][C]300.405221551684[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1272.62243970768[/C][C]Range[/C][C]207.837[/C][C]Trim Var.[/C][C]554.532122339025[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4042.76009905121[/C][C]Range[/C][C]356.861[/C][C]Trim Var.[/C][C]1827.05881867692[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13829.0529759071[/C][C]Range[/C][C]674.556[/C][C]Trim Var.[/C][C]6612.78562938597[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1712.03583230714[/C][C]Range[/C][C]197.239[/C][C]Trim Var.[/C][C]891.201228337702[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]3331.20981047899[/C][C]Range[/C][C]339.119[/C][C]Trim Var.[/C][C]1356.42448344516[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10379.1038867103[/C][C]Range[/C][C]508.849[/C][C]Trim Var.[/C][C]4019.31766377472[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35321.2230830928[/C][C]Range[/C][C]946.713[/C][C]Trim Var.[/C][C]16107.5694311084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31043&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)947.871032484463Range123.667Trim Var.663.550461775332
V(Y[t],d=1,D=0)1344.72598750964Range199.439Trim Var.765.759477401306
V(Y[t],d=2,D=0)3886.39493449244Range309.697Trim Var.2394.84446411878
V(Y[t],d=3,D=0)12492.6649025006Range547.004Trim Var.7958.0893854902
V(Y[t],d=0,D=1)597.84245041844Range122.139Trim Var.300.405221551684
V(Y[t],d=1,D=1)1272.62243970768Range207.837Trim Var.554.532122339025
V(Y[t],d=2,D=1)4042.76009905121Range356.861Trim Var.1827.05881867692
V(Y[t],d=3,D=1)13829.0529759071Range674.556Trim Var.6612.78562938597
V(Y[t],d=0,D=2)1712.03583230714Range197.239Trim Var.891.201228337702
V(Y[t],d=1,D=2)3331.20981047899Range339.119Trim Var.1356.42448344516
V(Y[t],d=2,D=2)10379.1038867103Range508.849Trim Var.4019.31766377472
V(Y[t],d=3,D=2)35321.2230830928Range946.713Trim Var.16107.5694311084


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')