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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 26 Nov 2008 10:17:59 -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/26/t12277199848bn418e5fjlnaum.htm/, Retrieved Tue, 14 May 2024 13:57:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25668, Retrieved Tue, 14 May 2024 13:57:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224

Tree of Dependent Computations

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] [] [2008-11-26 17:17:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-03 10:29:31 [Romina Machiels] [reply] 
Q3 werd correct beantwoord.
Q4 werd niet opgelost.
Q5 werd correct beantwoord,maar er mocht wat meer uitleg bij staan.
Naarmate de populatie stijgt (dus het aantal mensen dat een vlucht kan betalen neemt toe), zijn er meer reizigers en is er dus een stijgende trend.
De meerderheid van deze reizigers gaan echter op reis gedurende de vakantiemaanden. Hierdoor worden deze maanden nog extremer.
Er is dus een toename van de populatie die een toename van seizonaliteit veroorzaakt en dus ook een toename van de standaard fout.
Om de spreiding te stabiliseren (en dus de standaard fout te stabiliseren) gebruiken we de Lambda.
2008-12-05 15:40:42 [Nick Wuyts] [reply] 
Bij destandard deviation mean plot moet de spreiding door heel de tijd constant zijn. Dit is conform het concept heteroskedasticity. We bemerken dat het gemiddelde per jaar toeneemt, hetzelfde kan gezegd worden over de standaardfout.
Een economische verantwoording kan zijn dat naarmate de kapitaalkrachtige populatie stijgt, er meer reizigers zullen zijn. De pieken zullen de vakantieperiodes zijn.

We berekenen de regressie die de standaardfout verklaart dmv het gemiddelde. Is de helling van de regressierechte significant? We kijken hiervoor naar de optimale lambda die nodig is om de spreiding te stabiliseren.
2008-12-08 19:42:20 [Kim De Vos] [reply] 
Bij deze vraag dien je de tijdreeks te interpreteren met de grafiek Box Jenkins maar ook opnieuw te reproducen en dit model te analyseren, nl. het Standard Deviation-Mean Plot]. Zie link :http://www.freestatistics.org/blog/date/2008/Dec/08/t1228763486b4hk3amupw7hvsp.htm
Het gemiddelde neemt jaar na jaar toe, dit is logisch want er is een lange termijn trend, de standaard fout neemt dan ook jaar na jaar toe. Naarmate het niveau stijgt, stijgt ook de volatiliteit. Dit kan je zien omdat de spreiding vergroot. (grafiek Box Jenkins)

Bij het standard deviation – Mean Plot is de gevonden lambda waarde dan gelijk aan -0.31… We kunnen de Lambda coëfficiënt berekenen wanneer we 1 verminderen met de beta coëfficiënt. Hier is dat 1 – 1.31 en dit geeft een optimale Lambda van-0.31. M.a.w. bij een transformatie met -0.31 krijg je een optimale variantie. Deze transformatie moeten we enkel uitvoeren als om de spreiding optimaal te stabiliseren.


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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25668&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25668&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25668&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1126.66666666666713.720146655281244
2139.66666666666719.070840823020156
3170.16666666666718.438267189996454
419722.966378588156871
522528.466886664397292
6238.91666666666734.9244856364370114
728442.1404577789347131
8328.2547.8617801591207142
9368.41666666666757.8908979081166
1038164.5304720126997195
11428.33333333333369.8300968368398217
12476.16666666666777.7371250179771232

\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=25668&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=25668&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25668&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:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1126.66666666666713.720146655281244
2139.66666666666719.070840823020156
3170.16666666666718.438267189996454
419722.966378588156871
522528.466886664397292
6238.91666666666734.9244856364370114
728442.1404577789347131
8328.2547.8617801591207142
9368.41666666666757.8908979081166
1038164.5304720126997195
11428.33333333333369.8300968368398217
12476.16666666666777.7371250179771232






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.4032541425579
beta0.188613398899484
S.D.0.00657733180244678
T-STAT28.6762785525460
p-value6.19171705602778e-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 & 6.19171705602778e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25668&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]6.19171705602778e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25668&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25668&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.4032541425579
beta0.188613398899484
S.D.0.00657733180244678
T-STAT28.6762785525460
p-value6.19171705602778e-11






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.70703989322048
beta1.31259253972576
S.D.0.0574958902763332
T-STAT22.8293280340083
p-value5.8658934502011e-10
Lambda-0.312592539725757

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70703989322048 \tabularnewline
beta & 1.31259253972576 \tabularnewline
S.D. & 0.0574958902763332 \tabularnewline
T-STAT & 22.8293280340083 \tabularnewline
p-value & 5.8658934502011e-10 \tabularnewline
Lambda & -0.312592539725757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25668&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70703989322048[/C][/ROW]
[ROW][C]beta[/C][C]1.31259253972576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0574958902763332[/C][/ROW]
[ROW][C]T-STAT[/C][C]22.8293280340083[/C][/ROW]
[ROW][C]p-value[/C][C]5.8658934502011e-10[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.312592539725757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25668&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25668&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.70703989322048
beta1.31259253972576
S.D.0.0574958902763332
T-STAT22.8293280340083
p-value5.8658934502011e-10
Lambda-0.312592539725757


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))
(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')