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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationSat, 29 Nov 2008 09:21:11 -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/Nov/29/t1227975700agoq6bmwmvy87ia.htm/, Retrieved Mon, 27 May 2024 18:01:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26329, Retrieved Mon, 27 May 2024 18:01:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F         [Law of Averages] [s0700274] [2008-11-29 16:21:11] [c00776cbed2786c9c4960950021bd861] [Current]
Feedback Forum
2008-12-03 19:00:10 [407693b66d7f2e0b350979005057872d] [reply] 
Dit antwoord is volledig correct omdat: We zien hier een tabel met varianties. We moeten eerst de tijdreeksen differentiëren. We hebben het liefste een zo klein mogelijke variantie hoe kleiner de variantie hoe meer je kan verklaren
2008-12-04 14:07:24 [c97d2ae59c98cf77a04815c1edffab5a] [reply] 
deze conclusie was correct.
je kan misschien nog vermelden dat bij d=0 en D=0 de ruwe variantie wordt berekend van de oorspronkelijke tijdsreeks, die nog niet gedifferentieerd is.
2008-12-07 18:06:07 [Sandra Hofmans] [reply] 
Goede conclusie.
Als we de tijdreeks het best willen verklaren, moeten we kijken naar de kleinste variantie. Ik kan hier nog bij vermelden dat als we kiezen voor d=1 dit betekent dat we 1 periode terug in de tijdreeks zullen gaan.
2008-12-08 12:49:40 [Dave Bellekens] [reply] 
Als we zoveel mogelijk willen verklaren van onze tijdreeks moeten we inderdaad op zoek naar de laagst mogelijk variantie.
Hier wordt die variantie inderdaad bereikt bij d=1 en D=0, wat betekent dat we éénmaal moeten differentiëren om de lange termijn trend weg te zuiveren.

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Dataset

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=26329&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=26329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26329&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)42.6941723446894Range27Trim Var.31.6593582346391
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)6.00804828973843Range8Trim Var.2.56884201274445
V(Y[t],d=0,D=1)14.3768808698287Range18Trim Var.6.73209741912032
V(Y[t],d=1,D=1)1.97524104072131Range4Trim Var.0
V(Y[t],d=2,D=1)4.12371134020619Range8Trim Var.2.31828978622328
V(Y[t],d=3,D=1)12.5371730425151Range16Trim Var.7.13572079198428
V(Y[t],d=0,D=2)25.0680406899602Range30Trim Var.14.1702970297030
V(Y[t],d=1,D=2)5.9071019320453Range8Trim Var.2.63674701607507
V(Y[t],d=2,D=2)12.6173361522199Range16Trim Var.6.09910791993037
V(Y[t],d=3,D=2)38.0588741176049Range28Trim Var.21.4474330142003

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 42.6941723446894 & Range & 27 & Trim Var. & 31.6593582346391 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97987927565392 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.00804828973843 & Range & 8 & Trim Var. & 2.56884201274445 \tabularnewline
V(Y[t],d=0,D=1) & 14.3768808698287 & Range & 18 & Trim Var. & 6.73209741912032 \tabularnewline
V(Y[t],d=1,D=1) & 1.97524104072131 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.12371134020619 & Range & 8 & Trim Var. & 2.31828978622328 \tabularnewline
V(Y[t],d=3,D=1) & 12.5371730425151 & Range & 16 & Trim Var. & 7.13572079198428 \tabularnewline
V(Y[t],d=0,D=2) & 25.0680406899602 & Range & 30 & Trim Var. & 14.1702970297030 \tabularnewline
V(Y[t],d=1,D=2) & 5.9071019320453 & Range & 8 & Trim Var. & 2.63674701607507 \tabularnewline
V(Y[t],d=2,D=2) & 12.6173361522199 & Range & 16 & Trim Var. & 6.09910791993037 \tabularnewline
V(Y[t],d=3,D=2) & 38.0588741176049 & Range & 28 & Trim Var. & 21.4474330142003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26329&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]42.6941723446894[/C][C]Range[/C][C]27[/C][C]Trim Var.[/C][C]31.6593582346391[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00181085061690[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.97987927565392[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6.00804828973843[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.56884201274445[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.3768808698287[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.73209741912032[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.97524104072131[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4.12371134020619[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.31828978622328[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.5371730425151[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.13572079198428[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.0680406899602[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]14.1702970297030[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.9071019320453[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63674701607507[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.6173361522199[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.09910791993037[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.0588741176049[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.4474330142003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26329&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)42.6941723446894Range27Trim Var.31.6593582346391
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)6.00804828973843Range8Trim Var.2.56884201274445
V(Y[t],d=0,D=1)14.3768808698287Range18Trim Var.6.73209741912032
V(Y[t],d=1,D=1)1.97524104072131Range4Trim Var.0
V(Y[t],d=2,D=1)4.12371134020619Range8Trim Var.2.31828978622328
V(Y[t],d=3,D=1)12.5371730425151Range16Trim Var.7.13572079198428
V(Y[t],d=0,D=2)25.0680406899602Range30Trim Var.14.1702970297030
V(Y[t],d=1,D=2)5.9071019320453Range8Trim Var.2.63674701607507
V(Y[t],d=2,D=2)12.6173361522199Range16Trim Var.6.09910791993037
V(Y[t],d=3,D=2)38.0588741176049Range28Trim Var.21.4474330142003


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
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')