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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 computationSun, 07 Dec 2008 04:33:42 -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/Dec/07/t1228649646uizgjroopgyei6z.htm/, Retrieved Sun, 19 May 2024 10:51:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29876, Retrieved Sun, 19 May 2024 10:51:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact245

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  [Spectral Analysis] [q6] [2008-12-02 13:19:49] [74be16979710d4c4e7c6647856088456]
F RMPD    [Cross Correlation Function] [q7] [2008-12-02 13:34:43] [7ab42b4673454531c59df48fbb842b60]
F   PD      [Cross Correlation Function] [q8] [2008-12-02 13:49:39] [7ab42b4673454531c59df48fbb842b60]
F RM D        [Variance Reduction Matrix] [q8] [2008-12-02 13:55:29] [7ab42b4673454531c59df48fbb842b60]
- RMP             [Standard Deviation-Mean Plot] [q9] [2008-12-07 11:33:42] [607bd9e9685911f7e343f7bc0bf7bdf9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9762.12
10124.63
10540.05
10601.61
10323.73
10418.4
10092.96
10364.91
10152.09
10032.8
10204.59
10001.6
10411.75
10673.38
10539.51
10723.78
10682.06
10283.19
10377.18
10486.64
10545.38
10554.27
10532.54
10324.31
10695.25
10827.81
10872.48
10971.19
11145.65
11234.68
11333.88
10997.97
11036.89
11257.35
11533.59
11963.12
12185.15
12377.62
12512.89
12631.48
12268.53
12754.8
13407.75
13480.21
13673.28
13239.71
13557.69
13901.28
13200.58
13406.97
12538.12
12419.57
12193.88
12656.63
12812.48
12056.67
11322.38
11530.75
11114.08

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=29876&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=29876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29876&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
110257.1025392.131501699366839.49
210300143.364968524393325.440000000001
310097.7796.3170884803593202.990000000000
410587.105140.401912736259312.030000000001
510457.2675171.378135006579398.869999999999
610489.125110.238139951652229.960000000001
710841.6825114.536168777960275.940000000001
811178.045142.558189405824335.91
911447.7375399.179509107954926.230000000001
1012426.785191.588782291657446.33
1112977.8225574.4753378736111211.68000000000
1213592.99275.403980000290661.570000000002
1312891.31486.084688163150987.4
1412429.915361.837911087271755.81

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10257.1025 & 392.131501699366 & 839.49 \tabularnewline
2 & 10300 & 143.364968524393 & 325.440000000001 \tabularnewline
3 & 10097.77 & 96.3170884803593 & 202.990000000000 \tabularnewline
4 & 10587.105 & 140.401912736259 & 312.030000000001 \tabularnewline
5 & 10457.2675 & 171.378135006579 & 398.869999999999 \tabularnewline
6 & 10489.125 & 110.238139951652 & 229.960000000001 \tabularnewline
7 & 10841.6825 & 114.536168777960 & 275.940000000001 \tabularnewline
8 & 11178.045 & 142.558189405824 & 335.91 \tabularnewline
9 & 11447.7375 & 399.179509107954 & 926.230000000001 \tabularnewline
10 & 12426.785 & 191.588782291657 & 446.33 \tabularnewline
11 & 12977.8225 & 574.475337873611 & 1211.68000000000 \tabularnewline
12 & 13592.99 & 275.403980000290 & 661.570000000002 \tabularnewline
13 & 12891.31 & 486.084688163150 & 987.4 \tabularnewline
14 & 12429.915 & 361.837911087271 & 755.81 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29876&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]10257.1025[/C][C]392.131501699366[/C][C]839.49[/C][/ROW]
[ROW][C]2[/C][C]10300[/C][C]143.364968524393[/C][C]325.440000000001[/C][/ROW]
[ROW][C]3[/C][C]10097.77[/C][C]96.3170884803593[/C][C]202.990000000000[/C][/ROW]
[ROW][C]4[/C][C]10587.105[/C][C]140.401912736259[/C][C]312.030000000001[/C][/ROW]
[ROW][C]5[/C][C]10457.2675[/C][C]171.378135006579[/C][C]398.869999999999[/C][/ROW]
[ROW][C]6[/C][C]10489.125[/C][C]110.238139951652[/C][C]229.960000000001[/C][/ROW]
[ROW][C]7[/C][C]10841.6825[/C][C]114.536168777960[/C][C]275.940000000001[/C][/ROW]
[ROW][C]8[/C][C]11178.045[/C][C]142.558189405824[/C][C]335.91[/C][/ROW]
[ROW][C]9[/C][C]11447.7375[/C][C]399.179509107954[/C][C]926.230000000001[/C][/ROW]
[ROW][C]10[/C][C]12426.785[/C][C]191.588782291657[/C][C]446.33[/C][/ROW]
[ROW][C]11[/C][C]12977.8225[/C][C]574.475337873611[/C][C]1211.68000000000[/C][/ROW]
[ROW][C]12[/C][C]13592.99[/C][C]275.403980000290[/C][C]661.570000000002[/C][/ROW]
[ROW][C]13[/C][C]12891.31[/C][C]486.084688163150[/C][C]987.4[/C][/ROW]
[ROW][C]14[/C][C]12429.915[/C][C]361.837911087271[/C][C]755.81[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29876&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
110257.1025392.131501699366839.49
210300143.364968524393325.440000000001
310097.7796.3170884803593202.990000000000
410587.105140.401912736259312.030000000001
510457.2675171.378135006579398.869999999999
610489.125110.238139951652229.960000000001
710841.6825114.536168777960275.940000000001
811178.045142.558189405824335.91
911447.7375399.179509107954926.230000000001
1012426.785191.588782291657446.33
1112977.8225574.4753378736111211.68000000000
1213592.99275.403980000290661.570000000002
1312891.31486.084688163150987.4
1412429.915361.837911087271755.81






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-680.29153043526
beta0.0820353545010713
S.D.0.0297147156841391
T-STAT2.76076525089754
p-value0.0172546780128477

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -680.29153043526 \tabularnewline
beta & 0.0820353545010713 \tabularnewline
S.D. & 0.0297147156841391 \tabularnewline
T-STAT & 2.76076525089754 \tabularnewline
p-value & 0.0172546780128477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29876&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-680.29153043526[/C][/ROW]
[ROW][C]beta[/C][C]0.0820353545010713[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0297147156841391[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.76076525089754[/C][/ROW]
[ROW][C]p-value[/C][C]0.0172546780128477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29876&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29876&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-680.29153043526
beta0.0820353545010713
S.D.0.0297147156841391
T-STAT2.76076525089754
p-value0.0172546780128477






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-30.8868174504947
beta3.88324302118657
S.D.1.28633029678678
T-STAT3.01885373522401
p-value0.0106856566417955
Lambda-2.88324302118657

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -30.8868174504947 \tabularnewline
beta & 3.88324302118657 \tabularnewline
S.D. & 1.28633029678678 \tabularnewline
T-STAT & 3.01885373522401 \tabularnewline
p-value & 0.0106856566417955 \tabularnewline
Lambda & -2.88324302118657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29876&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-30.8868174504947[/C][/ROW]
[ROW][C]beta[/C][C]3.88324302118657[/C][/ROW]
[ROW][C]S.D.[/C][C]1.28633029678678[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.01885373522401[/C][/ROW]
[ROW][C]p-value[/C][C]0.0106856566417955[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.88324302118657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29876&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29876&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-30.8868174504947
beta3.88324302118657
S.D.1.28633029678678
T-STAT3.01885373522401
p-value0.0106856566417955
Lambda-2.88324302118657


Figures (Output of Computation)

Input Parameters & R Code

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')