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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 01 Dec 2008 09:36:24 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/01/t1228149455b0tuepdsy03fcda.htm/, Retrieved Sun, 05 May 2024 13:41:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26979, Retrieved Sun, 05 May 2024 13:41:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

225

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]
F RMPD    [Standard Deviation-Mean Plot] [] [2008-12-01 16:36:24] [cdc575afe547a0c8f1ab59a46ec2fd93] [Current]

Feedback Forum

2008-12-04 11:59:33 [Glenn Maras] [reply] 
De student zegt hier duidelijk dat er een trendmatig, seizoenaal verloop is en dat het de bedoeling is om deze er uit te halen om de tijdreeks stationair te maken.
2008-12-06 13:18:37 [Maarten Van Gucht] [reply] 
De student heeft inderdaad duidelijk gezegd dat we de reeks stationair moeten maken, en er is sprake van een trend en seizoenaliteit.  
de lamba berekenen doen we door de standard deviation plot. deze verdeelt de reeks onder in perioden. in de grafiek zie je punten die de jaren voorstellen.  
x-as = het gemiddelde  
y-as = standard deviation  
 
Door een lambda toe te voegen kan men de tijdreeks transformeren waardoor de spreiding harder naar een diagonaal zal deinen. Een lambda van 1 geeft bijvoorbeeld een perfecte rechte. De bedoeling van deze transformatie is om de tijdreeks stationair proberen te krijgen. Hier voor moet je zien dat de spreiding gelijk loopt door de tijd en hierdoor wordt de trend eruit gehaald.  
de optimale lambda is -0.312592539725757  
We hebben gezien op de run sequence plot dat er sprake was van heteroskedasticiteit : de variantie werd groter naarmate de tijd vordert. De gegevens in de standard deviation mean plot bevestigden dit. Ook de p value (6.19…e-11) is kleiner dan 0.05 wat de heteroskedasticiteit bevestigt. We gaan de tijdreeks tot de 0.3e macht vereffenen om deze heteroskedastische trend weg te werken.
2008-12-10 09:31:26 [Peter Van Doninck] [reply] 
De student heeft de correcte berekeningen gemaakt. Hij heeft ze echter niet geïnterpreteerd! In de tabel zien we dat de p-waarde zeer klein is, waardoor de kans dat we de nul hypothese foutief verwerpen zeer klein is. Hierdoor kunnen we besluiten dat de optimale lambda gelijk dient de zijn aan -0,31. Hoeveel keer we dienen te differentiëren, kunnen we dan weer afleiden door gebruik te maken van de ACF.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26979&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26979&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	126.666666666667	13.7201466552812	44
2	139.666666666667	19.0708408230201	56
3	170.166666666667	18.4382671899964	54
4	197	22.9663785881568	71
5	225	28.4668866643972	92
6	238.916666666667	34.9244856364370	114
7	284	42.1404577789347	131
8	328.25	47.8617801591207	142
9	368.416666666667	57.8908979081	166
10	381	64.5304720126997	195
11	428.333333333333	69.8300968368398	217
12	476.166666666667	77.7371250179771	232

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 126.666666666667 & 13.7201466552812 & 44 \tabularnewline
2 & 139.666666666667 & 19.0708408230201 & 56 \tabularnewline
3 & 170.166666666667 & 18.4382671899964 & 54 \tabularnewline
4 & 197 & 22.9663785881568 & 71 \tabularnewline
5 & 225 & 28.4668866643972 & 92 \tabularnewline
6 & 238.916666666667 & 34.9244856364370 & 114 \tabularnewline
7 & 284 & 42.1404577789347 & 131 \tabularnewline
8 & 328.25 & 47.8617801591207 & 142 \tabularnewline
9 & 368.416666666667 & 57.8908979081 & 166 \tabularnewline
10 & 381 & 64.5304720126997 & 195 \tabularnewline
11 & 428.333333333333 & 69.8300968368398 & 217 \tabularnewline
12 & 476.166666666667 & 77.7371250179771 & 232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26979&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]126.666666666667[/C][C]13.7201466552812[/C][C]44[/C][/ROW]
[ROW][C]2[/C][C]139.666666666667[/C][C]19.0708408230201[/C][C]56[/C][/ROW]
[ROW][C]3[/C][C]170.166666666667[/C][C]18.4382671899964[/C][C]54[/C][/ROW]
[ROW][C]4[/C][C]197[/C][C]22.9663785881568[/C][C]71[/C][/ROW]
[ROW][C]5[/C][C]225[/C][C]28.4668866643972[/C][C]92[/C][/ROW]
[ROW][C]6[/C][C]238.916666666667[/C][C]34.9244856364370[/C][C]114[/C][/ROW]
[ROW][C]7[/C][C]284[/C][C]42.1404577789347[/C][C]131[/C][/ROW]
[ROW][C]8[/C][C]328.25[/C][C]47.8617801591207[/C][C]142[/C][/ROW]
[ROW][C]9[/C][C]368.416666666667[/C][C]57.8908979081[/C][C]166[/C][/ROW]
[ROW][C]10[/C][C]381[/C][C]64.5304720126997[/C][C]195[/C][/ROW]
[ROW][C]11[/C][C]428.333333333333[/C][C]69.8300968368398[/C][C]217[/C][/ROW]
[ROW][C]12[/C][C]476.166666666667[/C][C]77.7371250179771[/C][C]232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26979&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	126.666666666667	13.7201466552812	44
2	139.666666666667	19.0708408230201	56
3	170.166666666667	18.4382671899964	54
4	197	22.9663785881568	71
5	225	28.4668866643972	92
6	238.916666666667	34.9244856364370	114
7	284	42.1404577789347	131
8	328.25	47.8617801591207	142
9	368.416666666667	57.8908979081	166
10	381	64.5304720126997	195
11	428.333333333333	69.8300968368398	217
12	476.166666666667	77.7371250179771	232

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-11.4032541425579
beta	0.188613398899484
S.D.	0.00657733180244678
T-STAT	28.6762785525460
p-value	6.1917170560278e-11

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.4032541425579 \tabularnewline
beta & 0.188613398899484 \tabularnewline
S.D. & 0.00657733180244678 \tabularnewline
T-STAT & 28.6762785525460 \tabularnewline
p-value & 6.1917170560278e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26979&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4032541425579[/C][/ROW]
[ROW][C]beta[/C][C]0.188613398899484[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00657733180244678[/C][/ROW]
[ROW][C]T-STAT[/C][C]28.6762785525460[/C][/ROW]
[ROW][C]p-value[/C][C]6.1917170560278e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26979&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-11.4032541425579
beta	0.188613398899484
S.D.	0.00657733180244678
T-STAT	28.6762785525460
p-value	6.1917170560278e-11

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.70703989322047
beta	1.31259253972576
S.D.	0.0574958902763329
T-STAT	22.8293280340083
p-value	5.8658934502009e-10
Lambda	-0.312592539725755

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70703989322047 \tabularnewline
beta & 1.31259253972576 \tabularnewline
S.D. & 0.0574958902763329 \tabularnewline
T-STAT & 22.8293280340083 \tabularnewline
p-value & 5.8658934502009e-10 \tabularnewline
Lambda & -0.312592539725755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26979&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70703989322047[/C][/ROW]
[ROW][C]beta[/C][C]1.31259253972576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0574958902763329[/C][/ROW]
[ROW][C]T-STAT[/C][C]22.8293280340083[/C][/ROW]
[ROW][C]p-value[/C][C]5.8658934502009e-10[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.312592539725755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26979&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.70703989322047
beta	1.31259253972576
S.D.	0.0574958902763329
T-STAT	22.8293280340083
p-value	5.8658934502009e-10
Lambda	-0.312592539725755

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code