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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 03:07:54 -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/t1228730961kkns7vt93i07srl.htm/, Retrieved Thu, 16 May 2024 16:05:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30357, Retrieved Thu, 16 May 2024 16:05:30 +0000

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Original text written by user:

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)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [Standard Deviation-Mean Plot] [SMP Analysis] [2008-12-08 10:07:54] [63302faa1e3976bf98d1de42298c0b24] [Current]
F           [Standard Deviation-Mean Plot] [Step 1] [2008-12-08 18:24:00] [5faef9c71125a233e2c8b38f64296883] 
F    D      [Standard Deviation-Mean Plot] [SMP Aankoop wagens] [2008-12-08 21:36:21] [23bfa928dab4b48567707937094f7011] 
F RMPD      [(Partial) Autocorrelation Function] [ACF] [2008-12-08 21:39:21] [23bfa928dab4b48567707937094f7011] 
F RM D      [Variance Reduction Matrix] [VRM] [2008-12-08 21:41:24] [23bfa928dab4b48567707937094f7011] 
- RMPD      [Spectral Analysis] [Cumulative Period...] [2008-12-08 21:43:31] [23bfa928dab4b48567707937094f7011] 

Feedback Forum

2008-12-14 22:18:30 [df2ed12c9b09685cd516719b004050c5] [reply] 
We gebruiken de SMP om de variantie gelijk te maken en om de transformatie toe te passen. 
Standard deviation meanplot: bij een scatterplot weet je niet wanneer in de tijdreeks een outlier zich voordoet. Wat wel belangrijk is of deze outlier  helemaal links of rechts ligt. Want deze kan dan de helling van de regressierechte beïnvloeden ( die door de punten van de scatterplot wordt getrokken ). Hier zien we dat deze outlier zich meer in de midden bevindt, dus deze outlier is niet zo een probleem.  
 
2de tabel: de p-waarde heeft betrekking op de beta (helling van de regressielijn). De beta wordt hier dus getoetst. Hier is de beta significant verschillend van 0. (p-waarde 0.0038 is kleiner dan 5% (alpha bij 95% betrouwbaarheid)) Er is dus een verband tussen de SE en het gemiddelde. 
 
3de tabel: Hier lezen we de lambda af ALS de beta uit de 2de tabel significant verschillend is van 0 en als in de scatterplot geen outliers zijn die de regressievergelijking beïnvloeden. We mogen hier dus de lambdawaarde gebruiken.
2008-12-15 22:22:23 [Bonifer Spillemaeckers] [reply] 
De student maakt hier een goede reproductie, maar trekt hier geen conclusie. Hier volgt wat meer uitleg.  
 
Als we naar het plot kijken, zien we hier bovenaan een outlier. Deze zal echter de regressierechte niet sterk beïnvloeden. Bovendien kunnen we hier een stijgende lijn waarnemen.  
 
De beta-waarde die we hier vaststellen is 0,049. Deze beta-waarde duidt de positieve helling in het plot aan. We kunnen dus afleiden dat de stijgende lijn beduidend verschillend is van 0. Als we naar de p-waarde kijken, stellen we een waarde vast van 0,004. De kans dat deze stijgende lijn op toeval berust is dus zeer klein.  
 
De lambda-waarde is hier 0,47. We gebruiken deze waarde als er geen al te grote outliers in het plot te zien zijn en als de beta-waarde beduidend verschillend is van 0. In de volgende stappen van het ARMA-proces werken we dus verder met deze lambda-waarde. 
 

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Dataseries X:

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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	1 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=30357&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=30357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30357&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227.733333333333 & 29.1940010442162 & 106 \tabularnewline
2 & 363.65 & 36.3267119348834 & 139.3 \tabularnewline
3 & 328.916666666667 & 93.5458451857438 & 273.6 \tabularnewline
4 & 205.45 & 30.3247123946491 & 89.5 \tabularnewline
5 & 188.333333333333 & 27.3773739803621 & 86 \tabularnewline
6 & 181.25 & 26.1571995999016 & 85.2 \tabularnewline
7 & 353.341666666667 & 36.2089506346236 & 110.8 \tabularnewline
8 & 285.308333333333 & 46.6051783766048 & 138.5 \tabularnewline
9 & 275.125 & 35.0509272345255 & 108.8 \tabularnewline
10 & 285.85 & 30.7409262296136 & 86.7 \tabularnewline
11 & 460.166666666667 & 56.0969831198748 & 147.3 \tabularnewline
12 & 373.95 & 53.1021228817215 & 150.3 \tabularnewline
13 & 385.1 & 35.1442999387072 & 115.5 \tabularnewline
14 & 471.358333333333 & 64.2130184808676 & 179.1 \tabularnewline
15 & 394.208333333333 & 40.6847628018454 & 138.7 \tabularnewline
16 & 407 & 46.6030432092544 & 147.6 \tabularnewline
17 & 378.575 & 49.9696839912143 & 132 \tabularnewline
18 & 336.633333333333 & 51.5290973993129 & 146.3 \tabularnewline
19 & 287.841666666667 & 33.2699826033054 & 112.7 \tabularnewline
20 & 297.566666666667 & 30.476438987082 & 117 \tabularnewline
21 & 281.666666666667 & 40.7140434412173 & 131.1 \tabularnewline
22 & 283.033333333333 & 28.4860837901065 & 109 \tabularnewline
23 & 408.85 & 48.934882520271 & 128.5 \tabularnewline
24 & 499.333333333333 & 37.5159925494408 & 109.6 \tabularnewline
25 & 484.008333333333 & 48.4390236808249 & 133.1 \tabularnewline
26 & 430.433333333333 & 37.4665022103584 & 108.4 \tabularnewline
27 & 507.583333333333 & 53.8722703730919 & 196.2 \tabularnewline
28 & 782.975 & 48.4555489832973 & 137.4 \tabularnewline
29 & 728.8 & 53.3077684940777 & 187 \tabularnewline
30 & 685.558333333333 & 72.5442618285032 & 222.9 \tabularnewline
31 & 604.716666666667 & 50.4040372360882 & 144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30357&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]227.733333333333[/C][C]29.1940010442162[/C][C]106[/C][/ROW]
[ROW][C]2[/C][C]363.65[/C][C]36.3267119348834[/C][C]139.3[/C][/ROW]
[ROW][C]3[/C][C]328.916666666667[/C][C]93.5458451857438[/C][C]273.6[/C][/ROW]
[ROW][C]4[/C][C]205.45[/C][C]30.3247123946491[/C][C]89.5[/C][/ROW]
[ROW][C]5[/C][C]188.333333333333[/C][C]27.3773739803621[/C][C]86[/C][/ROW]
[ROW][C]6[/C][C]181.25[/C][C]26.1571995999016[/C][C]85.2[/C][/ROW]
[ROW][C]7[/C][C]353.341666666667[/C][C]36.2089506346236[/C][C]110.8[/C][/ROW]
[ROW][C]8[/C][C]285.308333333333[/C][C]46.6051783766048[/C][C]138.5[/C][/ROW]
[ROW][C]9[/C][C]275.125[/C][C]35.0509272345255[/C][C]108.8[/C][/ROW]
[ROW][C]10[/C][C]285.85[/C][C]30.7409262296136[/C][C]86.7[/C][/ROW]
[ROW][C]11[/C][C]460.166666666667[/C][C]56.0969831198748[/C][C]147.3[/C][/ROW]
[ROW][C]12[/C][C]373.95[/C][C]53.1021228817215[/C][C]150.3[/C][/ROW]
[ROW][C]13[/C][C]385.1[/C][C]35.1442999387072[/C][C]115.5[/C][/ROW]
[ROW][C]14[/C][C]471.358333333333[/C][C]64.2130184808676[/C][C]179.1[/C][/ROW]
[ROW][C]15[/C][C]394.208333333333[/C][C]40.6847628018454[/C][C]138.7[/C][/ROW]
[ROW][C]16[/C][C]407[/C][C]46.6030432092544[/C][C]147.6[/C][/ROW]
[ROW][C]17[/C][C]378.575[/C][C]49.9696839912143[/C][C]132[/C][/ROW]
[ROW][C]18[/C][C]336.633333333333[/C][C]51.5290973993129[/C][C]146.3[/C][/ROW]
[ROW][C]19[/C][C]287.841666666667[/C][C]33.2699826033054[/C][C]112.7[/C][/ROW]
[ROW][C]20[/C][C]297.566666666667[/C][C]30.476438987082[/C][C]117[/C][/ROW]
[ROW][C]21[/C][C]281.666666666667[/C][C]40.7140434412173[/C][C]131.1[/C][/ROW]
[ROW][C]22[/C][C]283.033333333333[/C][C]28.4860837901065[/C][C]109[/C][/ROW]
[ROW][C]23[/C][C]408.85[/C][C]48.934882520271[/C][C]128.5[/C][/ROW]
[ROW][C]24[/C][C]499.333333333333[/C][C]37.5159925494408[/C][C]109.6[/C][/ROW]
[ROW][C]25[/C][C]484.008333333333[/C][C]48.4390236808249[/C][C]133.1[/C][/ROW]
[ROW][C]26[/C][C]430.433333333333[/C][C]37.4665022103584[/C][C]108.4[/C][/ROW]
[ROW][C]27[/C][C]507.583333333333[/C][C]53.8722703730919[/C][C]196.2[/C][/ROW]
[ROW][C]28[/C][C]782.975[/C][C]48.4555489832973[/C][C]137.4[/C][/ROW]
[ROW][C]29[/C][C]728.8[/C][C]53.3077684940777[/C][C]187[/C][/ROW]
[ROW][C]30[/C][C]685.558333333333[/C][C]72.5442618285032[/C][C]222.9[/C][/ROW]
[ROW][C]31[/C][C]604.716666666667[/C][C]50.4040372360882[/C][C]144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30357&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	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820021

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 25.0818554501784 \tabularnewline
beta & 0.0488516650103526 \tabularnewline
S.D. & 0.0155384837695400 \tabularnewline
T-STAT & 3.14391453728042 \tabularnewline
p-value & 0.00382792717820021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30357&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]25.0818554501784[/C][/ROW]
[ROW][C]beta[/C][C]0.0488516650103526[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0155384837695400[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14391453728042[/C][/ROW]
[ROW][C]p-value[/C][C]0.00382792717820021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30357&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	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820021

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.596066412617842
beta	0.532942026074986
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336408e-05
Lambda	0.467057973925014

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.596066412617842 \tabularnewline
beta & 0.532942026074986 \tabularnewline
S.D. & 0.115396834084912 \tabularnewline
T-STAT & 4.61834183148243 \tabularnewline
p-value & 7.31833172336408e-05 \tabularnewline
Lambda & 0.467057973925014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30357&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.596066412617842[/C][/ROW]
[ROW][C]beta[/C][C]0.532942026074986[/C][/ROW]
[ROW][C]S.D.[/C][C]0.115396834084912[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.61834183148243[/C][/ROW]
[ROW][C]p-value[/C][C]7.31833172336408e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]0.467057973925014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30357&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30357&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	0.596066412617842
beta	0.532942026074986
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336408e-05
Lambda	0.467057973925014

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code