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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 computationTue, 02 Dec 2008 00:32:20 -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/02/t1228203177zab1baynqlba48a.htm/, Retrieved Sun, 19 May 2024 09:26:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27567, Retrieved Sun, 19 May 2024 09:26:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact265

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  [Variance Reduction Matrix] [Non Stationary Ti...] [2008-12-01 17:48:47] [b943bd7078334192ff8343563ee31113]
- RMP     [Spectral Analysis] [Non Stationary Ti...] [2008-12-01 19:56:04] [b943bd7078334192ff8343563ee31113]
- RMPD      [Cross Correlation Function] [Non Stationary Ti...] [2008-12-01 20:13:53] [b943bd7078334192ff8343563ee31113]
- RMPD        [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-01 20:27:10] [b943bd7078334192ff8343563ee31113]
-   PD          [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-01 20:29:06] [b943bd7078334192ff8343563ee31113]
-   P             [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-01 20:31:48] [b943bd7078334192ff8343563ee31113]
- RMP               [Variance Reduction Matrix] [Non Stationary Ti...] [2008-12-01 20:34:07] [b943bd7078334192ff8343563ee31113]
- RMP                 [Spectral Analysis] [Non Stationary Ti...] [2008-12-01 20:37:58] [b943bd7078334192ff8343563ee31113]
- RMP                   [Standard Deviation-Mean Plot] [Non Stationary Ti...] [2008-12-01 20:41:45] [b943bd7078334192ff8343563ee31113]
- RMPD                    [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-02 07:15:23] [b943bd7078334192ff8343563ee31113]
-   PD                      [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-02 07:17:05] [b943bd7078334192ff8343563ee31113]
-   P                         [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-02 07:19:06] [b943bd7078334192ff8343563ee31113]
- RMP                           [Variance Reduction Matrix] [Non Stationary Ti...] [2008-12-02 07:22:03] [b943bd7078334192ff8343563ee31113]
- RMP                             [Spectral Analysis] [Non Stationary Ti...] [2008-12-02 07:25:43] [b943bd7078334192ff8343563ee31113]
- RMP                                 [Standard Deviation-Mean Plot] [Non Stationary Ti...] [2008-12-02 07:32:20] [620b6ad5c4696049e39cb73ce029682c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.8721
0.8552
0.8564
0.8973
0.9383
0.9217
0.9095
0.892
0.8742
0.8532
0.8607
0.9005
0.9111
0.9059
0.8883
0.8924
0.8833
0.87
0.8758
0.8858
0.917
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.457
1.4718
1.4748
1.5527
1.575
1.5557
1.5553
1.577
1.4975
1.4369

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27567&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27567&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27567&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.8859250.02829886361354780.0851
20.9129166666666670.04070804774875790.1222
31.071850.06546426506117670.1855
41.208291666666670.04012508755772570.1424
51.271391666666670.04606458822000680.1371
61.226333333333330.03728795402206340.102500000000000
71.321091666666670.03590478464781620.110500000000000
81.499791666666670.06247827925597720.1874

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.885925 & 0.0282988636135478 & 0.0851 \tabularnewline
2 & 0.912916666666667 & 0.0407080477487579 & 0.1222 \tabularnewline
3 & 1.07185 & 0.0654642650611767 & 0.1855 \tabularnewline
4 & 1.20829166666667 & 0.0401250875577257 & 0.1424 \tabularnewline
5 & 1.27139166666667 & 0.0460645882200068 & 0.1371 \tabularnewline
6 & 1.22633333333333 & 0.0372879540220634 & 0.102500000000000 \tabularnewline
7 & 1.32109166666667 & 0.0359047846478162 & 0.110500000000000 \tabularnewline
8 & 1.49979166666667 & 0.0624782792559772 & 0.1874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27567&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]0.885925[/C][C]0.0282988636135478[/C][C]0.0851[/C][/ROW]
[ROW][C]2[/C][C]0.912916666666667[/C][C]0.0407080477487579[/C][C]0.1222[/C][/ROW]
[ROW][C]3[/C][C]1.07185[/C][C]0.0654642650611767[/C][C]0.1855[/C][/ROW]
[ROW][C]4[/C][C]1.20829166666667[/C][C]0.0401250875577257[/C][C]0.1424[/C][/ROW]
[ROW][C]5[/C][C]1.27139166666667[/C][C]0.0460645882200068[/C][C]0.1371[/C][/ROW]
[ROW][C]6[/C][C]1.22633333333333[/C][C]0.0372879540220634[/C][C]0.102500000000000[/C][/ROW]
[ROW][C]7[/C][C]1.32109166666667[/C][C]0.0359047846478162[/C][C]0.110500000000000[/C][/ROW]
[ROW][C]8[/C][C]1.49979166666667[/C][C]0.0624782792559772[/C][C]0.1874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27567&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27567&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
10.8859250.02829886361354780.0851
20.9129166666666670.04070804774875790.1222
31.071850.06546426506117670.1855
41.208291666666670.04012508755772570.1424
51.271391666666670.04606458822000680.1371
61.226333333333330.03728795402206340.102500000000000
71.321091666666670.03590478464781620.110500000000000
81.499791666666670.06247827925597720.1874






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0145366094116559
beta0.0255426074411431
S.D.0.0233392548919482
T-STAT1.09440543665150
p-value0.315754255702695

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0145366094116559 \tabularnewline
beta & 0.0255426074411431 \tabularnewline
S.D. & 0.0233392548919482 \tabularnewline
T-STAT & 1.09440543665150 \tabularnewline
p-value & 0.315754255702695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27567&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0145366094116559[/C][/ROW]
[ROW][C]beta[/C][C]0.0255426074411431[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0233392548919482[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.09440543665150[/C][/ROW]
[ROW][C]p-value[/C][C]0.315754255702695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27567&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27567&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)
alpha0.0145366094116559
beta0.0255426074411431
S.D.0.0233392548919482
T-STAT1.09440543665150
p-value0.315754255702695






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.24843468987199
beta0.691989602305032
S.D.0.565260067565705
T-STAT1.22419686443638
p-value0.266761863248653
Lambda0.308010397694968

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.24843468987199 \tabularnewline
beta & 0.691989602305032 \tabularnewline
S.D. & 0.565260067565705 \tabularnewline
T-STAT & 1.22419686443638 \tabularnewline
p-value & 0.266761863248653 \tabularnewline
Lambda & 0.308010397694968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27567&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.24843468987199[/C][/ROW]
[ROW][C]beta[/C][C]0.691989602305032[/C][/ROW]
[ROW][C]S.D.[/C][C]0.565260067565705[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.22419686443638[/C][/ROW]
[ROW][C]p-value[/C][C]0.266761863248653[/C][/ROW]
[ROW][C]Lambda[/C][C]0.308010397694968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27567&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27567&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-3.24843468987199
beta0.691989602305032
S.D.0.565260067565705
T-STAT1.22419686443638
p-value0.266761863248653
Lambda0.308010397694968


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')