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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 29 Nov 2008 14:03:17 -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/t1227992660x9qocjaqliottj8.htm/, Retrieved Sun, 19 May 2024 04:28:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26378, Retrieved Sun, 19 May 2024 04:28:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236

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]
- RMPD  [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:10:39] [57fa5e3679c393aa19449b2f1be9928b]
-   P     [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:18:39] [57fa5e3679c393aa19449b2f1be9928b]
- RM        [Variance Reduction Matrix] [Q6 Variance] [2008-11-29 20:25:29] [57fa5e3679c393aa19449b2f1be9928b]
- RM          [(Partial) Autocorrelation Function] [Q6 ACF] [2008-11-29 20:35:57] [57fa5e3679c393aa19449b2f1be9928b]
-               [(Partial) Autocorrelation Function] [Q6 aangepaste ACF] [2008-11-29 20:44:03] [57fa5e3679c393aa19449b2f1be9928b]
- RM D            [Cross Correlation Function] [Q7] [2008-11-29 20:55:14] [57fa5e3679c393aa19449b2f1be9928b]
F RM D                [Standard Deviation-Mean Plot] [Q8 Mean plot insc...] [2008-11-29 21:03:17] [270782e2502ae87124d0ebdcd1862d6a] [Current]
F RM                    [Variance Reduction Matrix] [Q8 VRM Inschrijvi...] [2008-11-29 21:06:11] [57fa5e3679c393aa19449b2f1be9928b]
-                         [Variance Reduction Matrix] [] [2008-11-30 11:19:07] [ffbe22449df335faef31f462015daa42]
-   P                     [Variance Reduction Matrix] [] [2008-11-30 11:22:31] [a4ee3bef49b119f4bd2e925060c84f5e]
- RM                      [(Partial) Autocorrelation Function] [Q2 inschrijvingen...] [2008-12-07 14:47:46] [57fa5e3679c393aa19449b2f1be9928b]
- RM                        [Spectral Analysis] [Q2 inschrijvingen...] [2008-12-07 14:51:43] [57fa5e3679c393aa19449b2f1be9928b]
-                             [Spectral Analysis] [Q3 Spec analyse] [2008-12-07 14:56:15] [57fa5e3679c393aa19449b2f1be9928b]
-   P                           [Spectral Analysis] [Q3 Spec analyse] [2008-12-08 19:19:32] [57fa5e3679c393aa19449b2f1be9928b]
-   P                         [Spectral Analysis] [Q2 inschrijvingen...] [2008-12-08 19:15:44] [57fa5e3679c393aa19449b2f1be9928b]
-                           [(Partial) Autocorrelation Function] [Q3] [2008-12-07 14:59:20] [57fa5e3679c393aa19449b2f1be9928b]
- RM                          [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-07 15:06:11] [57fa5e3679c393aa19449b2f1be9928b]
F   P                           [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-08 19:21:54] [57fa5e3679c393aa19449b2f1be9928b]
-   P                             [ARIMA Backward Selection] [] [2008-12-11 16:10:37] [d134696a922d84037f02d49ded84b0bd]
-   P                         [(Partial) Autocorrelation Function] [Q3] [2008-12-08 19:17:56] [57fa5e3679c393aa19449b2f1be9928b]
-   P                       [(Partial) Autocorrelation Function] [Q2 inschrijvingen...] [2008-12-08 19:13:41] [57fa5e3679c393aa19449b2f1be9928b]
-    D                  [Standard Deviation-Mean Plot] [Q8 Mean plot bouw...] [2008-11-29 21:08:55] [57fa5e3679c393aa19449b2f1be9928b]
- RM                      [Variance Reduction Matrix] [Q8 VRM Bouwvergun...] [2008-11-29 21:11:38] [57fa5e3679c393aa19449b2f1be9928b]
-                           [Variance Reduction Matrix] [] [2008-11-30 11:21:50] [ffbe22449df335faef31f462015daa42]
-                             [Variance Reduction Matrix] [] [2008-11-30 11:22:57] [ffbe22449df335faef31f462015daa42]
-   P                       [Variance Reduction Matrix] [] [2008-11-30 11:25:19] [a4ee3bef49b119f4bd2e925060c84f5e]
-                         [Standard Deviation-Mean Plot] [] [2008-11-30 11:20:10] [ffbe22449df335faef31f462015daa42]
-   P                     [Standard Deviation-Mean Plot] [] [2008-11-30 11:23:30] [a4ee3bef49b119f4bd2e925060c84f5e]
-                       [Standard Deviation-Mean Plot] [] [2008-11-30 11:16:46] [ffbe22449df335faef31f462015daa42]
-   P                   [Standard Deviation-Mean Plot] [] [2008-11-30 11:21:31] [a4ee3bef49b119f4bd2e925060c84f5e]
F    D                    [Standard Deviation-Mean Plot] [] [2008-12-01 19:27:47] [d134696a922d84037f02d49ded84b0bd]
F                         [Standard Deviation-Mean Plot] [] [2008-12-01 19:29:03] [d134696a922d84037f02d49ded84b0bd]
Feedback Forum
2008-12-13 11:05:07 [Ruben Jacobs] [reply] 
Als je naar de p-waarde kijkt bij Beta, zie je dat deze 0,70 is en dus groter dan 5%. De Beta-parameter is dus niet significant verschillend van 0. Er is geen verband tussen het gemiddelde en de standaardfout. Het is dus het beste om als lambda-waarde 1 te nemen. Met lambda-waarde 1 gebeurt er eigenlijk niets met de observaties.
Op de grafiek kan je ook zien dat verband tussen het gemiddelde en de standaardfout klein is.
2008-12-13 23:07:30 [df2ed12c9b09685cd516719b004050c5] [reply] 
de student hierboven heeft gelijk.
in de 2de tabel zie je de p-waarde staan, deze heeft betrekking op de beta (helling van de regressievergelijking). Hier zien we dat de p-waarde 0.70981 groter is dan 5% (bij 95% betrouwbaarheid). Dus het de beta is niet significant verschillend van 0.
De voorwaarden om de gegeven lambda uit de 3de tabel te gebruiken zijn: beta uit de 2de tabel moet significant verschillend zijn van 0 en er mogen ook geen outliers zijn die de regressielijn beïnvloeden. Aan de eerste voorwaarde is dus niet voldaan, we mogen de lambda al niet gebruiken. Wanneer we de lambda=1 gebruiken verandert dit echter niets aan de tijdreeks, dit gaat ze niet transformeren. Dus we kiezen deze lambdawaarde.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26378&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26378&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
122949.08333333335573.513474189320000
2243346241.015928371120890
322668.83333333335025.7197554784215936
423242.16666666676893.0083132156923808
522208.08333333336395.8882737744921757
624429.08333333336043.1840261771319196

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22949.0833333333 & 5573.5134741893 & 20000 \tabularnewline
2 & 24334 & 6241.0159283711 & 20890 \tabularnewline
3 & 22668.8333333333 & 5025.71975547842 & 15936 \tabularnewline
4 & 23242.1666666667 & 6893.00831321569 & 23808 \tabularnewline
5 & 22208.0833333333 & 6395.88827377449 & 21757 \tabularnewline
6 & 24429.0833333333 & 6043.18402617713 & 19196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26378&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]22949.0833333333[/C][C]5573.5134741893[/C][C]20000[/C][/ROW]
[ROW][C]2[/C][C]24334[/C][C]6241.0159283711[/C][C]20890[/C][/ROW]
[ROW][C]3[/C][C]22668.8333333333[/C][C]5025.71975547842[/C][C]15936[/C][/ROW]
[ROW][C]4[/C][C]23242.1666666667[/C][C]6893.00831321569[/C][C]23808[/C][/ROW]
[ROW][C]5[/C][C]22208.0833333333[/C][C]6395.88827377449[/C][C]21757[/C][/ROW]
[ROW][C]6[/C][C]24429.0833333333[/C][C]6043.18402617713[/C][C]19196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26378&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
122949.08333333335573.513474189320000
2243346241.015928371120890
322668.83333333335025.7197554784215936
423242.16666666676893.0083132156923808
522208.08333333336395.8882737744921757
624429.08333333336043.1840261771319196






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2713.14775985542
beta0.142267506098055
S.D.0.355950988081975
T-STAT0.399682852025939
p-value0.70981292309731

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2713.14775985542 \tabularnewline
beta & 0.142267506098055 \tabularnewline
S.D. & 0.355950988081975 \tabularnewline
T-STAT & 0.399682852025939 \tabularnewline
p-value & 0.70981292309731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26378&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2713.14775985542[/C][/ROW]
[ROW][C]beta[/C][C]0.142267506098055[/C][/ROW]
[ROW][C]S.D.[/C][C]0.355950988081975[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.399682852025939[/C][/ROW]
[ROW][C]p-value[/C][C]0.70981292309731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26378&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26378&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)
alpha2713.14775985542
beta0.142267506098055
S.D.0.355950988081975
T-STAT0.399682852025939
p-value0.70981292309731






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.43354478273827
beta0.623090622428469
S.D.1.40877183777369
T-STAT0.442293496875371
p-value0.681139439478773
Lambda0.376909377571531

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.43354478273827 \tabularnewline
beta & 0.623090622428469 \tabularnewline
S.D. & 1.40877183777369 \tabularnewline
T-STAT & 0.442293496875371 \tabularnewline
p-value & 0.681139439478773 \tabularnewline
Lambda & 0.376909377571531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26378&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.43354478273827[/C][/ROW]
[ROW][C]beta[/C][C]0.623090622428469[/C][/ROW]
[ROW][C]S.D.[/C][C]1.40877183777369[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.442293496875371[/C][/ROW]
[ROW][C]p-value[/C][C]0.681139439478773[/C][/ROW]
[ROW][C]Lambda[/C][C]0.376909377571531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26378&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26378&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)
alpha2.43354478273827
beta0.623090622428469
S.D.1.40877183777369
T-STAT0.442293496875371
p-value0.681139439478773
Lambda0.376909377571531


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')