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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 08 Dec 2008 11:35:03 -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/08/t12287613475sh4deuisbas2q5.htm/, Retrieved Thu, 16 May 2024 18:40:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30664, Retrieved Thu, 16 May 2024 18:40:31 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

167

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Standard Deviation-Mean Plot] [Q1 Uitvoer EU - SMP] [2008-12-08 18:21:20] [9e54d1454d464f1bf9ee4a54d5d56945]
F   PD    [Standard Deviation-Mean Plot] [Q1 Uitvoer EU - SMP] [2008-12-08 18:35:03] [8da7502cfecb272886bc60b3f290b8b8] [Current]

Feedback Forum

2008-12-14 14:46:56 [Olivier Uyttendaele] [reply] 
Je schreef in het document:  
'Ik heb de seizonaliteitsparameter eerst ingesteld op 12, aangezien het gaat over maandelijkse gegevens. Ik heb echter niet voldoende observaties om dan een goede evolutie te zien. Daarom heb ik gekozen om de parameter in te stellen op 4, waardoor ik meer punten op de grafiek heb en dus betere conclusies kan trekken.' 
 
Het is inderdaad correct dat je parameter 12 moest instellen aangezien het over maandgegevens gaat. Nu weet ik niet of het correct is om deze parameter zonder aanpassen van de gegevens op 4 te zetten. Ik kan voorlopig enkel aannemen van niet. 
 
Ik kan dus enkel wat theoretische bevestigingen en aanvullingen geven over dit plot. 
 
Je schreef correct in het document dat de outlier rechts de helling van uw regressierechte gaat bepalen. Het is inderdaad zo dat je vooral rekening moet houden met de outliers links en rechts, deze zijn belangrijk, de outliers in het begin en einde niet. 
 
De Beta-coëfficient die je kan aflezen uit de tabel is tevens de helling van de regressierechte, dus de richting van het scatterplot.

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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	4 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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30664&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]4 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=30664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30664&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	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	11446.65	1484.04845720527	3472.6
2	11119.75	623.806297392602	1404.7
3	12125.6	399.651272986838	934.5
4	11511.525	1779.18154849358	3942.7
5	11516	274.893555156658	601.4
6	13055	968.013515745864	2122.9
7	12649.775	1593.80896466086	3256
8	13056.3	542.996642101342	1297.6
9	13935.725	782.70278895206	1895.7
10	12872.95	1395.73958053308	2873
11	13931.525	556.895755505462	1206.4
12	14914.8	1247.54987876237	2909.6
13	14064.925	1387.17494540763	2831.2
14	14357.675	978.617294536872	2322.1
15	15423.825	824.118205012687	1809.8
16	14985.225	1658.00263645749	3927.1
17	16031.975	1829.64662776723	3932.7
18	17690.275	941.758884127637	2224.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11446.65 & 1484.04845720527 & 3472.6 \tabularnewline
2 & 11119.75 & 623.806297392602 & 1404.7 \tabularnewline
3 & 12125.6 & 399.651272986838 & 934.5 \tabularnewline
4 & 11511.525 & 1779.18154849358 & 3942.7 \tabularnewline
5 & 11516 & 274.893555156658 & 601.4 \tabularnewline
6 & 13055 & 968.013515745864 & 2122.9 \tabularnewline
7 & 12649.775 & 1593.80896466086 & 3256 \tabularnewline
8 & 13056.3 & 542.996642101342 & 1297.6 \tabularnewline
9 & 13935.725 & 782.70278895206 & 1895.7 \tabularnewline
10 & 12872.95 & 1395.73958053308 & 2873 \tabularnewline
11 & 13931.525 & 556.895755505462 & 1206.4 \tabularnewline
12 & 14914.8 & 1247.54987876237 & 2909.6 \tabularnewline
13 & 14064.925 & 1387.17494540763 & 2831.2 \tabularnewline
14 & 14357.675 & 978.617294536872 & 2322.1 \tabularnewline
15 & 15423.825 & 824.118205012687 & 1809.8 \tabularnewline
16 & 14985.225 & 1658.00263645749 & 3927.1 \tabularnewline
17 & 16031.975 & 1829.64662776723 & 3932.7 \tabularnewline
18 & 17690.275 & 941.758884127637 & 2224.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30664&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]11446.65[/C][C]1484.04845720527[/C][C]3472.6[/C][/ROW]
[ROW][C]2[/C][C]11119.75[/C][C]623.806297392602[/C][C]1404.7[/C][/ROW]
[ROW][C]3[/C][C]12125.6[/C][C]399.651272986838[/C][C]934.5[/C][/ROW]
[ROW][C]4[/C][C]11511.525[/C][C]1779.18154849358[/C][C]3942.7[/C][/ROW]
[ROW][C]5[/C][C]11516[/C][C]274.893555156658[/C][C]601.4[/C][/ROW]
[ROW][C]6[/C][C]13055[/C][C]968.013515745864[/C][C]2122.9[/C][/ROW]
[ROW][C]7[/C][C]12649.775[/C][C]1593.80896466086[/C][C]3256[/C][/ROW]
[ROW][C]8[/C][C]13056.3[/C][C]542.996642101342[/C][C]1297.6[/C][/ROW]
[ROW][C]9[/C][C]13935.725[/C][C]782.70278895206[/C][C]1895.7[/C][/ROW]
[ROW][C]10[/C][C]12872.95[/C][C]1395.73958053308[/C][C]2873[/C][/ROW]
[ROW][C]11[/C][C]13931.525[/C][C]556.895755505462[/C][C]1206.4[/C][/ROW]
[ROW][C]12[/C][C]14914.8[/C][C]1247.54987876237[/C][C]2909.6[/C][/ROW]
[ROW][C]13[/C][C]14064.925[/C][C]1387.17494540763[/C][C]2831.2[/C][/ROW]
[ROW][C]14[/C][C]14357.675[/C][C]978.617294536872[/C][C]2322.1[/C][/ROW]
[ROW][C]15[/C][C]15423.825[/C][C]824.118205012687[/C][C]1809.8[/C][/ROW]
[ROW][C]16[/C][C]14985.225[/C][C]1658.00263645749[/C][C]3927.1[/C][/ROW]
[ROW][C]17[/C][C]16031.975[/C][C]1829.64662776723[/C][C]3932.7[/C][/ROW]
[ROW][C]18[/C][C]17690.275[/C][C]941.758884127637[/C][C]2224.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30664&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	11446.65	1484.04845720527	3472.6
2	11119.75	623.806297392602	1404.7
3	12125.6	399.651272986838	934.5
4	11511.525	1779.18154849358	3942.7
5	11516	274.893555156658	601.4
6	13055	968.013515745864	2122.9
7	12649.775	1593.80896466086	3256
8	13056.3	542.996642101342	1297.6
9	13935.725	782.70278895206	1895.7
10	12872.95	1395.73958053308	2873
11	13931.525	556.895755505462	1206.4
12	14914.8	1247.54987876237	2909.6
13	14064.925	1387.17494540763	2831.2
14	14357.675	978.617294536872	2322.1
15	15423.825	824.118205012687	1809.8
16	14985.225	1658.00263645749	3927.1
17	16031.975	1829.64662776723	3932.7
18	17690.275	941.758884127637	2224.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	389.558117412748
beta	0.0500902602579027
S.D.	0.0676128414166747
T-STAT	0.740839450145478
p-value	0.469524630721662

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 389.558117412748 \tabularnewline
beta & 0.0500902602579027 \tabularnewline
S.D. & 0.0676128414166747 \tabularnewline
T-STAT & 0.740839450145478 \tabularnewline
p-value & 0.469524630721662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30664&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]389.558117412748[/C][/ROW]
[ROW][C]beta[/C][C]0.0500902602579027[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0676128414166747[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.740839450145478[/C][/ROW]
[ROW][C]p-value[/C][C]0.469524630721662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30664&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	389.558117412748
beta	0.0500902602579027
S.D.	0.0676128414166747
T-STAT	0.740839450145478
p-value	0.469524630721662

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.35388476092078
beta	1.17841997305950
S.D.	1.01540820066770
T-STAT	1.16053816808315
p-value	0.262853614298185
Lambda	-0.178419973059501

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.35388476092078 \tabularnewline
beta & 1.17841997305950 \tabularnewline
S.D. & 1.01540820066770 \tabularnewline
T-STAT & 1.16053816808315 \tabularnewline
p-value & 0.262853614298185 \tabularnewline
Lambda & -0.178419973059501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30664&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.35388476092078[/C][/ROW]
[ROW][C]beta[/C][C]1.17841997305950[/C][/ROW]
[ROW][C]S.D.[/C][C]1.01540820066770[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.16053816808315[/C][/ROW]
[ROW][C]p-value[/C][C]0.262853614298185[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.178419973059501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30664&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30664&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	-4.35388476092078
beta	1.17841997305950
S.D.	1.01540820066770
T-STAT	1.16053816808315
p-value	0.262853614298185
Lambda	-0.178419973059501

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code