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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, 06 Dec 2008 04:49:39 -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/06/t1228564255gjc04aa6e7sjke4.htm/, Retrieved Sun, 19 May 2024 11:09:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29521, Retrieved Sun, 19 May 2024 11:09:30 +0000
QR Codes:

Original text written by user:Seizonaal op 6 gezet in plaats van 12.
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact289

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] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD    [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [a8228479d4547a92e2d3f176a5299609] [Current]
F RM        [Variance Reduction Matrix] [variance reduction] [2008-12-06 12:44:59] [ed2ba3b6182103c15c0ab511ae4e6284]
F    D        [Variance Reduction Matrix] [VRM Vlaanderen] [2008-12-08 18:29:56] [077ffec662d24c06be4c491541a44245]
- RMPD        [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:32:31] [077ffec662d24c06be4c491541a44245]
-   P           [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:34:40] [077ffec662d24c06be4c491541a44245]
-   P             [(Partial) Autocorrelation Function] [ACF] [2008-12-08 18:36:48] [077ffec662d24c06be4c491541a44245]
-   P         [Variance Reduction Matrix] [variance reduction] [2008-12-08 19:33:22] [4ad596f10399a71ad29b7d76e6ab90ac]
-             [Variance Reduction Matrix] [variance reduction] [2008-12-09 00:17:49] [4ddbf81f78ea7c738951638c7e93f6ee]
-             [Variance Reduction Matrix] [] [2008-12-09 00:23:30] [29747f79f5beb5b2516e1271770ecb47]
- RMP       [(Partial) Autocorrelation Function] [ACF d=o en D=0] [2008-12-06 12:48:15] [ed2ba3b6182103c15c0ab511ae4e6284]
-   P         [(Partial) Autocorrelation Function] [ACF d=0 en D=0 la...] [2008-12-07 15:39:10] [ed2ba3b6182103c15c0ab511ae4e6284]
-   P           [(Partial) Autocorrelation Function] [acf ] [2008-12-08 11:41:37] [ed2ba3b6182103c15c0ab511ae4e6284]
F   P             [(Partial) Autocorrelation Function] [acf] [2008-12-08 19:38:35] [4ad596f10399a71ad29b7d76e6ab90ac]
F                 [(Partial) Autocorrelation Function] [] [2008-12-08 21:14:50] [28075c6928548bea087cb2be962cfe7e]
-                 [(Partial) Autocorrelation Function] [ACF] [2008-12-09 00:20:22] [4ddbf81f78ea7c738951638c7e93f6ee]
-                 [(Partial) Autocorrelation Function] [] [2008-12-09 00:24:15] [29747f79f5beb5b2516e1271770ecb47]
- RMP       [(Partial) Autocorrelation Function] [ACF d=1 en D=0] [2008-12-06 12:51:22] [ed2ba3b6182103c15c0ab511ae4e6284]
-   P         [(Partial) Autocorrelation Function] [acf d=1] [2008-12-08 11:43:53] [74be16979710d4c4e7c6647856088456]
-   P         [(Partial) Autocorrelation Function] [acf d=1] [2008-12-08 11:43:53] [ed2ba3b6182103c15c0ab511ae4e6284]
-               [(Partial) Autocorrelation Function] [acf d=1] [2008-12-08 19:45:09] [4ad596f10399a71ad29b7d76e6ab90ac]
-               [(Partial) Autocorrelation Function] [] [2008-12-08 21:16:19] [28075c6928548bea087cb2be962cfe7e]
-               [(Partial) Autocorrelation Function] [ACF d=1] [2008-12-09 00:23:10] [4ddbf81f78ea7c738951638c7e93f6ee]
-               [(Partial) Autocorrelation Function] [] [2008-12-09 00:25:46] [29747f79f5beb5b2516e1271770ecb47]
- RMP       [(Partial) Autocorrelation Function] [ACF d=1 en D=1] [2008-12-06 12:54:17] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMP       [Spectral Analysis] [spectrum ] [2008-12-06 13:17:20] [ed2ba3b6182103c15c0ab511ae4e6284]
F   P         [Spectral Analysis] [spectrale analyse] [2008-12-08 11:48:47] [ed2ba3b6182103c15c0ab511ae4e6284]
-               [Spectral Analysis] [Spectrum] [2008-12-08 19:51:12] [4ad596f10399a71ad29b7d76e6ab90ac]
-               [Spectral Analysis] [] [2008-12-08 21:24:23] [28075c6928548bea087cb2be962cfe7e]
-               [Spectral Analysis] [spectrale analyse] [2008-12-09 00:26:01] [4ddbf81f78ea7c738951638c7e93f6ee]
-               [Spectral Analysis] [spectrale analyse] [2008-12-09 00:28:17] [4ddbf81f78ea7c738951638c7e93f6ee]
-               [Spectral Analysis] [] [2008-12-09 00:31:58] [29747f79f5beb5b2516e1271770ecb47]
-               [Spectral Analysis] [] [2008-12-09 00:33:16] [29747f79f5beb5b2516e1271770ecb47]
-   PD        [Spectral Analysis] [Q9 laatste taak p...] [2008-12-08 18:39:46] [077ffec662d24c06be4c491541a44245]
F RMP       [(Partial) Autocorrelation Function] [ACF d=1 en D=1 la...] [2008-12-06 13:30:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RM          [ARIMA Backward Selection] [ARIMA model met q...] [2008-12-06 17:04:18] [4242609301e759e844b9196c1994e4ef]
-   P           [ARIMA Backward Selection] [ARima backward se...] [2008-12-08 11:53:47] [ed2ba3b6182103c15c0ab511ae4e6284]
-   P             [ARIMA Backward Selection] [MA controle] [2008-12-08 11:58:59] [ed2ba3b6182103c15c0ab511ae4e6284]
F                   [ARIMA Backward Selection] [ARIMA] [2008-12-08 20:02:58] [4ad596f10399a71ad29b7d76e6ab90ac]
- RMP                 [ARIMA Forecasting] [ARIMA forecast HI...] [2008-12-13 14:12:52] [ed2ba3b6182103c15c0ab511ae4e6284]
-                   [ARIMA Backward Selection] [] [2008-12-08 21:34:29] [28075c6928548bea087cb2be962cfe7e]
-   P               [ARIMA Backward Selection] [] [2008-12-09 00:38:49] [29747f79f5beb5b2516e1271770ecb47]
-                 [ARIMA Backward Selection] [ARIMA] [2008-12-08 20:00:39] [4ad596f10399a71ad29b7d76e6ab90ac]
F                 [ARIMA Backward Selection] [] [2008-12-08 21:33:18] [28075c6928548bea087cb2be962cfe7e]
-                 [ARIMA Backward Selection] [Arima backward se...] [2008-12-09 00:33:34] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P             [ARIMA Backward Selection] [] [2008-12-09 00:36:36] [29747f79f5beb5b2516e1271770ecb47]
-                 [ARIMA Backward Selection] [Arima backward se...] [2008-12-09 00:33:34] [4ddbf81f78ea7c738951638c7e93f6ee]
F RMP             [ARIMA Forecasting] [ARIMA forecasting] [2008-12-09 20:21:38] [ed2ba3b6182103c15c0ab511ae4e6284]
F                   [ARIMA Forecasting] [Arima forecasting...] [2008-12-15 09:55:01] [4ad596f10399a71ad29b7d76e6ab90ac]
F                   [ARIMA Forecasting] [ARIMA forecasting] [2008-12-15 09:56:32] [7506b5e9e41ec66c6657f4234f97306e]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92.66
94.2
94.37
94.45
94.62
94.37
93.43
94.79
94.88
94.79
94.62
94.71
93.77
95.73
95.99
95.82
95.47
95.82
94.71
96.33
96.5
96.16
96.33
96.33
95.05
96.84
96.92
97.44
97.78
97.69
96.67
98.29
98.2
98.71
98.54
98.2
96.92
99.06
99.65
99.82
99.99
100.33
99.31
101.1
101.1
100.93
100.85
100.93
99.6
101.88
101.81
102.38
102.74
102.82
101.72
103.47
102.98
102.68
102.9
103.03
101.29

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29521&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29521&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29521&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
194.11166666666670.7240833285380011.96000000000001
294.53666666666670.5491690692916561.44999999999999
395.43333333333330.8324582071591742.22
496.060.670044774623311.79000000000001
596.95333333333331.00990428589382.73000000000000
698.10166666666670.7302990255139782.03999999999999
799.2951.23707315870973.41000000000000
8100.7033333333330.6899758449878261.78999999999999
9101.8716666666671.189628793643913.22
10102.7966666666670.5873556560267951.75

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 94.1116666666667 & 0.724083328538001 & 1.96000000000001 \tabularnewline
2 & 94.5366666666667 & 0.549169069291656 & 1.44999999999999 \tabularnewline
3 & 95.4333333333333 & 0.832458207159174 & 2.22 \tabularnewline
4 & 96.06 & 0.67004477462331 & 1.79000000000001 \tabularnewline
5 & 96.9533333333333 & 1.0099042858938 & 2.73000000000000 \tabularnewline
6 & 98.1016666666667 & 0.730299025513978 & 2.03999999999999 \tabularnewline
7 & 99.295 & 1.2370731587097 & 3.41000000000000 \tabularnewline
8 & 100.703333333333 & 0.689975844987826 & 1.78999999999999 \tabularnewline
9 & 101.871666666667 & 1.18962879364391 & 3.22 \tabularnewline
10 & 102.796666666667 & 0.587355656026795 & 1.75 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29521&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]94.1116666666667[/C][C]0.724083328538001[/C][C]1.96000000000001[/C][/ROW]
[ROW][C]2[/C][C]94.5366666666667[/C][C]0.549169069291656[/C][C]1.44999999999999[/C][/ROW]
[ROW][C]3[/C][C]95.4333333333333[/C][C]0.832458207159174[/C][C]2.22[/C][/ROW]
[ROW][C]4[/C][C]96.06[/C][C]0.67004477462331[/C][C]1.79000000000001[/C][/ROW]
[ROW][C]5[/C][C]96.9533333333333[/C][C]1.0099042858938[/C][C]2.73000000000000[/C][/ROW]
[ROW][C]6[/C][C]98.1016666666667[/C][C]0.730299025513978[/C][C]2.03999999999999[/C][/ROW]
[ROW][C]7[/C][C]99.295[/C][C]1.2370731587097[/C][C]3.41000000000000[/C][/ROW]
[ROW][C]8[/C][C]100.703333333333[/C][C]0.689975844987826[/C][C]1.78999999999999[/C][/ROW]
[ROW][C]9[/C][C]101.871666666667[/C][C]1.18962879364391[/C][C]3.22[/C][/ROW]
[ROW][C]10[/C][C]102.796666666667[/C][C]0.587355656026795[/C][C]1.75[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29521&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29521&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
194.11166666666670.7240833285380011.96000000000001
294.53666666666670.5491690692916561.44999999999999
395.43333333333330.8324582071591742.22
496.060.670044774623311.79000000000001
596.95333333333331.00990428589382.73000000000000
698.10166666666670.7302990255139782.03999999999999
799.2951.23707315870973.41000000000000
8100.7033333333330.6899758449878261.78999999999999
9101.8716666666671.189628793643913.22
10102.7966666666670.5873556560267951.75






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.31524493180277
beta0.0218116554986401
S.D.0.0267615353679952
T-STAT0.815037523023632
p-value0.438639238022962

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.31524493180277 \tabularnewline
beta & 0.0218116554986401 \tabularnewline
S.D. & 0.0267615353679952 \tabularnewline
T-STAT & 0.815037523023632 \tabularnewline
p-value & 0.438639238022962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29521&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.31524493180277[/C][/ROW]
[ROW][C]beta[/C][C]0.0218116554986401[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0267615353679952[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.815037523023632[/C][/ROW]
[ROW][C]p-value[/C][C]0.438639238022962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29521&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29521&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-1.31524493180277
beta0.0218116554986401
S.D.0.0267615353679952
T-STAT0.815037523023632
p-value0.438639238022962






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.4469713383402
beta2.22805158499039
S.D.3.06972834934445
T-STAT0.725813925999738
p-value0.488639630012912
Lambda-1.22805158499039

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.4469713383402 \tabularnewline
beta & 2.22805158499039 \tabularnewline
S.D. & 3.06972834934445 \tabularnewline
T-STAT & 0.725813925999738 \tabularnewline
p-value & 0.488639630012912 \tabularnewline
Lambda & -1.22805158499039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29521&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.4469713383402[/C][/ROW]
[ROW][C]beta[/C][C]2.22805158499039[/C][/ROW]
[ROW][C]S.D.[/C][C]3.06972834934445[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.725813925999738[/C][/ROW]
[ROW][C]p-value[/C][C]0.488639630012912[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.22805158499039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29521&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29521&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-10.4469713383402
beta2.22805158499039
S.D.3.06972834934445
T-STAT0.725813925999738
p-value0.488639630012912
Lambda-1.22805158499039


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 6 ;
Parameters (R input):
par1 = 6 ;
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')