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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 2016 10:32:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482312762eqi2eeb8h7mhh8a.htm/, Retrieved Tue, 07 May 2024 00:59:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301944, Retrieved Tue, 07 May 2024 00:59:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-11 16:38:45] [48565d122ad1a5ad6c25b7f5730e03d6]
- RMP   [ARIMA Backward Selection] [Arima backward] [2016-12-18 16:46:17] [48565d122ad1a5ad6c25b7f5730e03d6]
- RM        [Standard Deviation-Mean Plot] [SDMP F1] [2016-12-21 09:32:02] [10299735033611e1e2dae6371997f8c9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3567.2
3968.25
4285.35
4130.95
4219.4
4626.2
3860.75
4174.15
4668.65
4630.05
4553.7
4603.85
4310.7
4831.3
5145.3
4886.65
4934.05
5304.7
4419.45
4804.85
5105
5132.6
4982.5
4906.7
4506.4
5010.85
5392.25
5049.7
5143.9
5449.9
4520.4
4936.95
5358.55
5289.5
5123.55
4985.65
4682.65
5175.55
5374.7
5289
5176.15
5604.25
4608.8
4898.15
5448.65
5373.05
5078.6
5233.4
4629.2
5387.8
5736.65
5357.9
5337.95
5795.5
4804.05
5120.5
5850.45
5734.75
5539
5582.85
4983.1
5672
6185.8
5835.6
5930.4
6444.65
5171.05
5739.1
6413.9
6230.2
6015.45
6174.25
5579.25
6133.45
6478.7
6184.4
6185.65
6556
5123.25
6028.9
6499.95
6190.05
6027.95
6034
5128.75
6087.7
6628.15
6075.3
6352.1
6824
5412.35
6171.25
6521.35
6457.6
5930.95
5842.7
5120.1
5719.95
5946.7
5921.1
6072
6489.4
5291.15
5986.45
6538.15
6442.8
6169.55
5793
5254.85
6050.75
6606.15
6221.15
6293.4
6908.4
5498.95
6145.35

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301944&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301944&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14274.04166666667355.6001750135921101.45
24896.98333333333289.221133810142994
35063.96666666667306.881022498455943.5
45161.9125301.741372645365995.45
55406.38333333333389.6575584776821221.25
65899.625456.7681560804021461.55
76085.12916666667401.3802003192651432.75
86119.35494.000512053471695.25
95957.52916666667441.5566063054311418.05

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4274.04166666667 & 355.600175013592 & 1101.45 \tabularnewline
2 & 4896.98333333333 & 289.221133810142 & 994 \tabularnewline
3 & 5063.96666666667 & 306.881022498455 & 943.5 \tabularnewline
4 & 5161.9125 & 301.741372645365 & 995.45 \tabularnewline
5 & 5406.38333333333 & 389.657558477682 & 1221.25 \tabularnewline
6 & 5899.625 & 456.768156080402 & 1461.55 \tabularnewline
7 & 6085.12916666667 & 401.380200319265 & 1432.75 \tabularnewline
8 & 6119.35 & 494.00051205347 & 1695.25 \tabularnewline
9 & 5957.52916666667 & 441.556606305431 & 1418.05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301944&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]4274.04166666667[/C][C]355.600175013592[/C][C]1101.45[/C][/ROW]
[ROW][C]2[/C][C]4896.98333333333[/C][C]289.221133810142[/C][C]994[/C][/ROW]
[ROW][C]3[/C][C]5063.96666666667[/C][C]306.881022498455[/C][C]943.5[/C][/ROW]
[ROW][C]4[/C][C]5161.9125[/C][C]301.741372645365[/C][C]995.45[/C][/ROW]
[ROW][C]5[/C][C]5406.38333333333[/C][C]389.657558477682[/C][C]1221.25[/C][/ROW]
[ROW][C]6[/C][C]5899.625[/C][C]456.768156080402[/C][C]1461.55[/C][/ROW]
[ROW][C]7[/C][C]6085.12916666667[/C][C]401.380200319265[/C][C]1432.75[/C][/ROW]
[ROW][C]8[/C][C]6119.35[/C][C]494.00051205347[/C][C]1695.25[/C][/ROW]
[ROW][C]9[/C][C]5957.52916666667[/C][C]441.556606305431[/C][C]1418.05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301944&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
14274.04166666667355.6001750135921101.45
24896.98333333333289.221133810142994
35063.96666666667306.881022498455943.5
45161.9125301.741372645365995.45
55406.38333333333389.6575584776821221.25
65899.625456.7681560804021461.55
76085.12916666667401.3802003192651432.75
86119.35494.000512053471695.25
95957.52916666667441.5566063054311418.05






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-97.5986588301379
beta0.088308639266871
S.D.0.0284619365116718
T-STAT3.102692581394
p-value0.0172570228385417

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -97.5986588301379 \tabularnewline
beta & 0.088308639266871 \tabularnewline
S.D. & 0.0284619365116718 \tabularnewline
T-STAT & 3.102692581394 \tabularnewline
p-value & 0.0172570228385417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301944&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-97.5986588301379[/C][/ROW]
[ROW][C]beta[/C][C]0.088308639266871[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0284619365116718[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.102692581394[/C][/ROW]
[ROW][C]p-value[/C][C]0.0172570228385417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301944&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-97.5986588301379
beta0.088308639266871
S.D.0.0284619365116718
T-STAT3.102692581394
p-value0.0172570228385417






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.04106102997118
beta1.16013826754937
S.D.0.421977928521589
T-STAT2.74928660751037
p-value0.0285333159357744
Lambda-0.160138267549371

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.04106102997118 \tabularnewline
beta & 1.16013826754937 \tabularnewline
S.D. & 0.421977928521589 \tabularnewline
T-STAT & 2.74928660751037 \tabularnewline
p-value & 0.0285333159357744 \tabularnewline
Lambda & -0.160138267549371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301944&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.04106102997118[/C][/ROW]
[ROW][C]beta[/C][C]1.16013826754937[/C][/ROW]
[ROW][C]S.D.[/C][C]0.421977928521589[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.74928660751037[/C][/ROW]
[ROW][C]p-value[/C][C]0.0285333159357744[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.160138267549371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301944&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301944&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-4.04106102997118
beta1.16013826754937
S.D.0.421977928521589
T-STAT2.74928660751037
p-value0.0285333159357744
Lambda-0.160138267549371


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')