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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 computationWed, 21 Dec 2011 04:54:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t132446131297vnyvlq5kgdfh7.htm/, Retrieved Tue, 07 May 2024 08:04:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158406, Retrieved Tue, 07 May 2024 08:04:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [web traffic] [2010-10-19 15:13:07] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Traffic] [2010-11-29 09:57:15] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Traffic] [2010-11-29 11:05:08] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Forecasting] [Traffic] [2010-11-29 21:10:32] [b98453cac15ba1066b407e146608df68]
- R PD        [ARIMA Forecasting] [] [2011-12-06 10:39:07] [aba4febe8a2e49e81bdc61a6c01f5c21]
-   PD          [ARIMA Forecasting] [] [2011-12-20 15:47:34] [aba4febe8a2e49e81bdc61a6c01f5c21]
- R               [ARIMA Forecasting] [ARIMA Forecasting CV] [2011-12-20 15:48:10] [aba4febe8a2e49e81bdc61a6c01f5c21]
- RMPD                [Standard Deviation-Mean Plot] [Paper standard de...] [2011-12-21 09:54:23] [3627de22d386f4cb93d383ef7c1ade7f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
492
436
694
1137
380
179
2354
111
740
595
809
693
738
1184
713
1729
844
1298
514
689
837
1330
491
622
1332
1043
1082
636
586
1170
973
721
863
343
1278
1186
1334
652
284
1273
1518
715
671
486
1022
2084
330
658
1385
930
620
218
840
255
454
1149
684
1190
1079
883
1331
1159
1217
946
579
474
626
843
893
633
873
385
729
774
769
996
1194
575
725
706
665
1259
653
694
437
822
458
1545
987
1051
838
703
613
1128
967
617
654
805
1355
1456
878
887
663
214
733
830
1174
1068
413
946
657
690
156
779
192
461
1213
146
866
200
1290
715
514
697
276
752
1021
481
1626
884
1187
488
403
977
1525
551
1807
723
632
898
621
1606
811
716
1001
732
1024
831
0
85
0
0
0
0
773
1128
0
0
74
259
69
301
0
668

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158406&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158406&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1718.333333333333586.2798483711182243
2915.75383.1240304748231238
3934.416666666667307.607027444649989
4918.916666666667539.7255966664631800
5807.25371.7338062744261167
6829.916666666667301.004517735149946
7811.583333333333218.581567189806684
8847.166666666667314.8303535479891108
9893.083333333333336.9158131514681242
10559.916666666667353.4707029992551067
11827.583333333333392.4893648433691350
12939.166666666667456.3507091009831404
13464.5482.8868679853771128

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 718.333333333333 & 586.279848371118 & 2243 \tabularnewline
2 & 915.75 & 383.124030474823 & 1238 \tabularnewline
3 & 934.416666666667 & 307.607027444649 & 989 \tabularnewline
4 & 918.916666666667 & 539.725596666463 & 1800 \tabularnewline
5 & 807.25 & 371.733806274426 & 1167 \tabularnewline
6 & 829.916666666667 & 301.004517735149 & 946 \tabularnewline
7 & 811.583333333333 & 218.581567189806 & 684 \tabularnewline
8 & 847.166666666667 & 314.830353547989 & 1108 \tabularnewline
9 & 893.083333333333 & 336.915813151468 & 1242 \tabularnewline
10 & 559.916666666667 & 353.470702999255 & 1067 \tabularnewline
11 & 827.583333333333 & 392.489364843369 & 1350 \tabularnewline
12 & 939.166666666667 & 456.350709100983 & 1404 \tabularnewline
13 & 464.5 & 482.886867985377 & 1128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158406&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]718.333333333333[/C][C]586.279848371118[/C][C]2243[/C][/ROW]
[ROW][C]2[/C][C]915.75[/C][C]383.124030474823[/C][C]1238[/C][/ROW]
[ROW][C]3[/C][C]934.416666666667[/C][C]307.607027444649[/C][C]989[/C][/ROW]
[ROW][C]4[/C][C]918.916666666667[/C][C]539.725596666463[/C][C]1800[/C][/ROW]
[ROW][C]5[/C][C]807.25[/C][C]371.733806274426[/C][C]1167[/C][/ROW]
[ROW][C]6[/C][C]829.916666666667[/C][C]301.004517735149[/C][C]946[/C][/ROW]
[ROW][C]7[/C][C]811.583333333333[/C][C]218.581567189806[/C][C]684[/C][/ROW]
[ROW][C]8[/C][C]847.166666666667[/C][C]314.830353547989[/C][C]1108[/C][/ROW]
[ROW][C]9[/C][C]893.083333333333[/C][C]336.915813151468[/C][C]1242[/C][/ROW]
[ROW][C]10[/C][C]559.916666666667[/C][C]353.470702999255[/C][C]1067[/C][/ROW]
[ROW][C]11[/C][C]827.583333333333[/C][C]392.489364843369[/C][C]1350[/C][/ROW]
[ROW][C]12[/C][C]939.166666666667[/C][C]456.350709100983[/C][C]1404[/C][/ROW]
[ROW][C]13[/C][C]464.5[/C][C]482.886867985377[/C][C]1128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158406&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
1718.333333333333586.2798483711182243
2915.75383.1240304748231238
3934.416666666667307.607027444649989
4918.916666666667539.7255966664631800
5807.25371.7338062744261167
6829.916666666667301.004517735149946
7811.583333333333218.581567189806684
8847.166666666667314.8303535479891108
9893.083333333333336.9158131514681242
10559.916666666667353.4707029992551067
11827.583333333333392.4893648433691350
12939.166666666667456.3507091009831404
13464.5482.8868679853771128






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha503.124321854601
beta-0.142880732896794
S.D.0.209739761014183
T-STAT-0.681228643562401
p-value0.509813885478937

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 503.124321854601 \tabularnewline
beta & -0.142880732896794 \tabularnewline
S.D. & 0.209739761014183 \tabularnewline
T-STAT & -0.681228643562401 \tabularnewline
p-value & 0.509813885478937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158406&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]503.124321854601[/C][/ROW]
[ROW][C]beta[/C][C]-0.142880732896794[/C][/ROW]
[ROW][C]S.D.[/C][C]0.209739761014183[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.681228643562401[/C][/ROW]
[ROW][C]p-value[/C][C]0.509813885478937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158406&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)
alpha503.124321854601
beta-0.142880732896794
S.D.0.209739761014183
T-STAT-0.681228643562401
p-value0.509813885478937






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.74316942464766
beta-0.271971176740196
S.D.0.372673251998901
T-STAT-0.729784537209014
p-value0.480774400040406
Lambda1.2719711767402

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.74316942464766 \tabularnewline
beta & -0.271971176740196 \tabularnewline
S.D. & 0.372673251998901 \tabularnewline
T-STAT & -0.729784537209014 \tabularnewline
p-value & 0.480774400040406 \tabularnewline
Lambda & 1.2719711767402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158406&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.74316942464766[/C][/ROW]
[ROW][C]beta[/C][C]-0.271971176740196[/C][/ROW]
[ROW][C]S.D.[/C][C]0.372673251998901[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.729784537209014[/C][/ROW]
[ROW][C]p-value[/C][C]0.480774400040406[/C][/ROW]
[ROW][C]Lambda[/C][C]1.2719711767402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158406&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158406&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)
alpha7.74316942464766
beta-0.271971176740196
S.D.0.372673251998901
T-STAT-0.729784537209014
p-value0.480774400040406
Lambda1.2719711767402


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')