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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 computationMon, 29 Nov 2010 11:02:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/29/t1291028445m7xuo9au9zen2sg.htm/, Retrieved Sat, 27 Apr 2024 06:15:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102829, Retrieved Sat, 27 Apr 2024 06:15:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact490

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Soldiers] [2010-11-29 09:51:25] [b98453cac15ba1066b407e146608df68]
- RM        [Standard Deviation-Mean Plot] [Soldiers] [2010-11-29 11:02:42] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- RMP         [ARIMA Backward Selection] [Soldiers] [2010-11-29 17:56:11] [b98453cac15ba1066b407e146608df68]
-   PD          [ARIMA Backward Selection] [Aantal faillissem...] [2010-12-04 15:51:53] [d6a5e6c1b0014d57cedb2bdfb4a7099f]
-                 [ARIMA Backward Selection] [] [2010-12-07 22:36:55] [afdb2fc47981b6a655b732edc8065db9]
-   PD            [ARIMA Backward Selection] [Verbetering Peer] [2010-12-10 20:50:43] [d6a5e6c1b0014d57cedb2bdfb4a7099f]
- R PD          [ARIMA Backward Selection] [WS9 4 Foutmelding] [2010-12-07 15:26:08] [afe9379cca749d06b3d6872e02cc47ed]
-   P             [ARIMA Backward Selection] [WS9 4 AR MA] [2010-12-07 15:33:10] [afe9379cca749d06b3d6872e02cc47ed]
-    D              [ARIMA Backward Selection] [] [2010-12-16 15:02:15] [69c775ce4d55db2aa75a88e773e8d700]
- R PD              [ARIMA Backward Selection] [] [2011-12-03 13:58:43] [74be16979710d4c4e7c6647856088456]
-   P                 [ARIMA Backward Selection] [Paper: ARMA] [2011-12-17 16:17:34] [54b1f171ce7a12209ffa11b565e1dcf5]
-   PD                  [ARIMA Backward Selection] [Paper: ARMA] [2011-12-17 16:36:06] [54b1f171ce7a12209ffa11b565e1dcf5]
- R PD              [ARIMA Backward Selection] [ARIMA] [2011-12-04 14:15:32] [74be16979710d4c4e7c6647856088456]
- R P               [ARIMA Backward Selection] [Workshop 9 - ARIMA] [2011-12-06 18:06:12] [f0855b2dc4da686ca3c0ae4fedd71fda]
-   P                 [ARIMA Backward Selection] [] [2012-12-04 03:05:25] [74be16979710d4c4e7c6647856088456]
- R P               [ARIMA Backward Selection] [WS9 ARIMA Backwar...] [2012-11-29 14:42:51] [617a576b3e2f0c57f6da5ea5fef54049]
-   P                 [ARIMA Backward Selection] [Arima backward se...] [2012-12-07 09:43:48] [57fcaae991493f873bcb4ee93ca06ef0]
- R PD              [ARIMA Backward Selection] [WS 9 ARIMA Backwa...] [2012-12-03 19:03:37] [8c30f4dd45e15fd207e4faf2fdf6253e]
- R P               [ARIMA Backward Selection] [] [2012-12-04 16:26:05] [74be16979710d4c4e7c6647856088456]
- R P               [ARIMA Backward Selection] [workshop 9: AR MA...] [2012-12-04 18:23:48] [74be16979710d4c4e7c6647856088456]
- RMP               [ARIMA Backward Selection] [WS 9 - ARIMA] [2012-12-04 18:58:07] [74be16979710d4c4e7c6647856088456]
-    D          [ARIMA Backward Selection] [WS9] [2010-12-07 21:01:45] [87116ee6ef949037dfa02b8eb1a3bf97]
-   PD            [ARIMA Backward Selection] [Correctie WS9] [2010-12-13 20:14:37] [87116ee6ef949037dfa02b8eb1a3bf97]
-   PD          [ARIMA Backward Selection] [ARIMA ] [2010-12-15 12:36:54] [0ed8ad64bdfc801eaa95d5097964fc04]
-               [ARIMA Backward Selection] [Workshop 9 (ARIMA)] [2010-12-15 16:00:56] [845827b7f02503df17c96f445745fee7]
-                 [ARIMA Backward Selection] [] [2010-12-16 16:59:52] [24bb5b06bd1854f48aebec8f44957ed0]
-   P           [ARIMA Backward Selection] [ARIMA Backward Se...] [2010-12-16 14:05:46] [9f313cc7203314d73bf17d2b325aee79]
- RMP           [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-16 14:17:27] [9f313cc7203314d73bf17d2b325aee79]
-   PD          [ARIMA Backward Selection] [estimating arma p...] [2010-12-22 16:03:39] [a8a0ff0853b70f438be515083758c362]
-   PD          [ARIMA Backward Selection] [WS 9: ARIMA backw...] [2011-12-01 13:47:14] [10b12745961ee885a66356b3bf31ed40]
-               [ARIMA Backward Selection] [WS 9 - ARIMA ] [2011-12-02 13:57:49] [6a3e51c0c7ab195427042dfaef1df5a0]
-   PD          [ARIMA Backward Selection] [Model 1] [2011-12-05 11:47:38] [c035d973aa8488be257660c2dc4ec375]
- R  D          [ARIMA Backward Selection] [Workshop 9 (5)] [2011-12-06 09:02:52] [74be16979710d4c4e7c6647856088456]
-   PD          [ARIMA Backward Selection] [Workshop 9: ARIMA...] [2011-12-06 09:56:00] [21b3d52ef28595defb5676e0f3570994]
- R PD          [ARIMA Backward Selection] [WS IX-aantal over...] [2011-12-06 20:15:53] [74be16979710d4c4e7c6647856088456]
-   P             [ARIMA Backward Selection] [WS IX-aantal over...] [2011-12-06 20:44:23] [74be16979710d4c4e7c6647856088456]
-    D            [ARIMA Backward Selection] [Paper arima foutm...] [2011-12-20 16:15:18] [7c680a04865e75aa8ab422cdbfd97ac3]
-   P               [ARIMA Backward Selection] [Paper arima corre...] [2011-12-22 11:17:52] [7c680a04865e75aa8ab422cdbfd97ac3]
- RMPD          [Variance Reduction Matrix] [Variance reductio...] [2011-12-07 09:43:44] [71fa56397b79b6f4596b21687a2f6e82]
- RMPD          [(Partial) Autocorrelation Function] [ACF d=0 en D=1] [2011-12-07 09:58:09] [71fa56397b79b6f4596b21687a2f6e82]
- RMP             [Spectral Analysis] [spectraalanalyse] [2011-12-08 21:23:11] [71fa56397b79b6f4596b21687a2f6e82]
- RMPD          [(Partial) Autocorrelation Function] [ACF d=0 en D=0] [2011-12-07 10:03:24] [71fa56397b79b6f4596b21687a2f6e82]
- RMPD          [(Partial) Autocorrelation Function] [ACF d=1 en D=0] [2011-12-07 10:04:06] [71fa56397b79b6f4596b21687a2f6e82]
- RMPD          [(Partial) Autocorrelation Function] [ACF d=1 en D=1] [2011-12-07 10:04:53] [71fa56397b79b6f4596b21687a2f6e82]
-    D          [ARIMA Backward Selection] [ARIMA Backward Se...] [2011-12-07 12:35:23] [933c43040ae019b88c07d6cc7db3263c]
- RMPD          [(Partial) Autocorrelation Function] [] [2011-12-07 18:04:11] [5b1044653d12da6c563533920760fdbb]
- RMPD          [(Partial) Autocorrelation Function] [] [2011-12-07 18:10:28] [5b1044653d12da6c563533920760fdbb]
- RMP             [Stem-and-leaf Plot] [] [2011-12-07 18:11:06] [5b1044653d12da6c563533920760fdbb]
- RMP             [Spectral Analysis] [] [2011-12-07 18:16:08] [5b1044653d12da6c563533920760fdbb]
- RMP             [Variance Reduction Matrix] [] [2011-12-07 18:18:13] [5b1044653d12da6c563533920760fdbb]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102829&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102829&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
149.833333333333331.2550601963712117
270.666666666666728.2949829582218101
367.083333333333318.613085979948966
476.083333333333319.009367706635163
557.2530.334873420776798
617.41666666666675.4848275573014419

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 49.8333333333333 & 31.2550601963712 & 117 \tabularnewline
2 & 70.6666666666667 & 28.2949829582218 & 101 \tabularnewline
3 & 67.0833333333333 & 18.6130859799489 & 66 \tabularnewline
4 & 76.0833333333333 & 19.0093677066351 & 63 \tabularnewline
5 & 57.25 & 30.3348734207767 & 98 \tabularnewline
6 & 17.4166666666667 & 5.48482755730144 & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102829&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]49.8333333333333[/C][C]31.2550601963712[/C][C]117[/C][/ROW]
[ROW][C]2[/C][C]70.6666666666667[/C][C]28.2949829582218[/C][C]101[/C][/ROW]
[ROW][C]3[/C][C]67.0833333333333[/C][C]18.6130859799489[/C][C]66[/C][/ROW]
[ROW][C]4[/C][C]76.0833333333333[/C][C]19.0093677066351[/C][C]63[/C][/ROW]
[ROW][C]5[/C][C]57.25[/C][C]30.3348734207767[/C][C]98[/C][/ROW]
[ROW][C]6[/C][C]17.4166666666667[/C][C]5.48482755730144[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102829&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
149.833333333333331.2550601963712117
270.666666666666728.2949829582218101
367.083333333333318.613085979948966
476.083333333333319.009367706635163
557.2530.334873420776798
617.41666666666675.4848275573014419






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha7.62734060098987
beta0.257817204571377
S.D.0.192696886862756
T-STAT1.33794172167919
p-value0.251913511181569

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.62734060098987 \tabularnewline
beta & 0.257817204571377 \tabularnewline
S.D. & 0.192696886862756 \tabularnewline
T-STAT & 1.33794172167919 \tabularnewline
p-value & 0.251913511181569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102829&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.62734060098987[/C][/ROW]
[ROW][C]beta[/C][C]0.257817204571377[/C][/ROW]
[ROW][C]S.D.[/C][C]0.192696886862756[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.33794172167919[/C][/ROW]
[ROW][C]p-value[/C][C]0.251913511181569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102829&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)
alpha7.62734060098987
beta0.257817204571377
S.D.0.192696886862756
T-STAT1.33794172167919
p-value0.251913511181569






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.952456878721548
beta0.994638095085676
S.D.0.334109924590222
T-STAT2.97697859860217
p-value0.0408608743220421
Lambda0.00536190491432365

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.952456878721548 \tabularnewline
beta & 0.994638095085676 \tabularnewline
S.D. & 0.334109924590222 \tabularnewline
T-STAT & 2.97697859860217 \tabularnewline
p-value & 0.0408608743220421 \tabularnewline
Lambda & 0.00536190491432365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102829&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.952456878721548[/C][/ROW]
[ROW][C]beta[/C][C]0.994638095085676[/C][/ROW]
[ROW][C]S.D.[/C][C]0.334109924590222[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.97697859860217[/C][/ROW]
[ROW][C]p-value[/C][C]0.0408608743220421[/C][/ROW]
[ROW][C]Lambda[/C][C]0.00536190491432365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102829&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102829&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-0.952456878721548
beta0.994638095085676
S.D.0.334109924590222
T-STAT2.97697859860217
p-value0.0408608743220421
Lambda0.00536190491432365


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 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')