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Description of Statistical Computation

Author's title

standard deviation-mean plot prijsindexcijfer ruwe aardolie_Jan De Cleermae...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 12 May 2008 12:40:46 -0600
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/May/12/t12106176837pbg6xkssfu8aco.htm/, Retrieved Tue, 14 May 2024 22:19:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12408, Retrieved Tue, 14 May 2024 22:19:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [standard deviatio...] [2008-05-12 18:40:46] [3e68c9212ad297cb41373898449ccda3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68.4
70.6
83.9
90.1
90.6
87.1
90.8
94.1
99.8
96.8
87
96.3
107.1
115.2
106.1
89.5
91.3
97.6
100.7
104.6
94.7
101.8
102.5
105.3
110.3
109.8
117.3
118.8
131.3
125.9
133.1
147
145.8
164.4
149.8
137.7
151.7
156.8
180
180.4
170.4
191.6
199.5
218.2
217.5
205
194
199.3
219.3
211.1
215.2
240.2
242.2
240.7
255.4
253
218.2
203.7
205.6
215.6
188.5
202.9
214
230.3
230
241
259.6
247.8
270.3
289.7
322.7
315
320.2

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'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12408&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12408&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
178.2510.454504611250921.7
290.652.859487133502567
394.9755.5367710204895912.8
4104.47510.78281812267425.7
598.555.6181254287647713.3
6101.0754.5110050616981910.6
7114.054.663689526544419
8134.3258.9867958694965321.1
9149.42511.180451690338826.7
10167.22515.127100405122828.7
11194.92519.792149116926847.8
12203.9510.088442231914023.5
13221.4512.940504884534729.1
14247.8257.4513421609801414.7000000000000
15210.7757.1936893640653314.5
16208.92517.664724736038241.8
17244.612.401075222200229.6
18299.42523.994079130763352.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 78.25 & 10.4545046112509 & 21.7 \tabularnewline
2 & 90.65 & 2.85948713350256 & 7 \tabularnewline
3 & 94.975 & 5.53677102048959 & 12.8 \tabularnewline
4 & 104.475 & 10.782818122674 & 25.7 \tabularnewline
5 & 98.55 & 5.61812542876477 & 13.3 \tabularnewline
6 & 101.075 & 4.51100506169819 & 10.6 \tabularnewline
7 & 114.05 & 4.66368952654441 & 9 \tabularnewline
8 & 134.325 & 8.98679586949653 & 21.1 \tabularnewline
9 & 149.425 & 11.1804516903388 & 26.7 \tabularnewline
10 & 167.225 & 15.1271004051228 & 28.7 \tabularnewline
11 & 194.925 & 19.7921491169268 & 47.8 \tabularnewline
12 & 203.95 & 10.0884422319140 & 23.5 \tabularnewline
13 & 221.45 & 12.9405048845347 & 29.1 \tabularnewline
14 & 247.825 & 7.45134216098014 & 14.7000000000000 \tabularnewline
15 & 210.775 & 7.19368936406533 & 14.5 \tabularnewline
16 & 208.925 & 17.6647247360382 & 41.8 \tabularnewline
17 & 244.6 & 12.4010752222002 & 29.6 \tabularnewline
18 & 299.425 & 23.9940791307633 & 52.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12408&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]78.25[/C][C]10.4545046112509[/C][C]21.7[/C][/ROW]
[ROW][C]2[/C][C]90.65[/C][C]2.85948713350256[/C][C]7[/C][/ROW]
[ROW][C]3[/C][C]94.975[/C][C]5.53677102048959[/C][C]12.8[/C][/ROW]
[ROW][C]4[/C][C]104.475[/C][C]10.782818122674[/C][C]25.7[/C][/ROW]
[ROW][C]5[/C][C]98.55[/C][C]5.61812542876477[/C][C]13.3[/C][/ROW]
[ROW][C]6[/C][C]101.075[/C][C]4.51100506169819[/C][C]10.6[/C][/ROW]
[ROW][C]7[/C][C]114.05[/C][C]4.66368952654441[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]134.325[/C][C]8.98679586949653[/C][C]21.1[/C][/ROW]
[ROW][C]9[/C][C]149.425[/C][C]11.1804516903388[/C][C]26.7[/C][/ROW]
[ROW][C]10[/C][C]167.225[/C][C]15.1271004051228[/C][C]28.7[/C][/ROW]
[ROW][C]11[/C][C]194.925[/C][C]19.7921491169268[/C][C]47.8[/C][/ROW]
[ROW][C]12[/C][C]203.95[/C][C]10.0884422319140[/C][C]23.5[/C][/ROW]
[ROW][C]13[/C][C]221.45[/C][C]12.9405048845347[/C][C]29.1[/C][/ROW]
[ROW][C]14[/C][C]247.825[/C][C]7.45134216098014[/C][C]14.7000000000000[/C][/ROW]
[ROW][C]15[/C][C]210.775[/C][C]7.19368936406533[/C][C]14.5[/C][/ROW]
[ROW][C]16[/C][C]208.925[/C][C]17.6647247360382[/C][C]41.8[/C][/ROW]
[ROW][C]17[/C][C]244.6[/C][C]12.4010752222002[/C][C]29.6[/C][/ROW]
[ROW][C]18[/C][C]299.425[/C][C]23.9940791307633[/C][C]52.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12408&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
178.2510.454504611250921.7
290.652.859487133502567
394.9755.5367710204895912.8
4104.47510.78281812267425.7
598.555.6181254287647713.3
6101.0754.5110050616981910.6
7114.054.663689526544419
8134.3258.9867958694965321.1
9149.42511.180451690338826.7
10167.22515.127100405122828.7
11194.92519.792149116926847.8
12203.9510.088442231914023.5
13221.4512.940504884534729.1
14247.8257.4513421609801414.7000000000000
15210.7757.1936893640653314.5
16208.92517.664724736038241.8
17244.612.401075222200229.6
18299.42523.994079130763352.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.31002996200828
beta0.0565508550617332
S.D.0.0161278176472339
T-STAT3.50641706762057
p-value0.00292365228056082

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.31002996200828 \tabularnewline
beta & 0.0565508550617332 \tabularnewline
S.D. & 0.0161278176472339 \tabularnewline
T-STAT & 3.50641706762057 \tabularnewline
p-value & 0.00292365228056082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12408&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.31002996200828[/C][/ROW]
[ROW][C]beta[/C][C]0.0565508550617332[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0161278176472339[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.50641706762057[/C][/ROW]
[ROW][C]p-value[/C][C]0.00292365228056082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12408&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)
alpha1.31002996200828
beta0.0565508550617332
S.D.0.0161278176472339
T-STAT3.50641706762057
p-value0.00292365228056082






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.21235485216986
beta0.88254046821622
S.D.0.256631322769540
T-STAT3.43894291114558
p-value0.00337135868384417
Lambda0.117459531783779

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.21235485216986 \tabularnewline
beta & 0.88254046821622 \tabularnewline
S.D. & 0.256631322769540 \tabularnewline
T-STAT & 3.43894291114558 \tabularnewline
p-value & 0.00337135868384417 \tabularnewline
Lambda & 0.117459531783779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12408&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.21235485216986[/C][/ROW]
[ROW][C]beta[/C][C]0.88254046821622[/C][/ROW]
[ROW][C]S.D.[/C][C]0.256631322769540[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.43894291114558[/C][/ROW]
[ROW][C]p-value[/C][C]0.00337135868384417[/C][/ROW]
[ROW][C]Lambda[/C][C]0.117459531783779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12408&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12408&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-2.21235485216986
beta0.88254046821622
S.D.0.256631322769540
T-STAT3.43894291114558
p-value0.00337135868384417
Lambda0.117459531783779


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')