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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 computationSun, 26 Dec 2010 20:12:20 +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/Dec/26/t1293394243layuzw9sncmc3ue.htm/, Retrieved Tue, 07 May 2024 01:03:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115792, Retrieved Tue, 07 May 2024 01:03:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-12-06 12:09:10] [f4dc4aa51d65be851b8508203d9f6001]
-   PD      [Standard Deviation-Mean Plot] [SMP BRU Passengers] [2010-12-19 17:02:21] [f4dc4aa51d65be851b8508203d9f6001]
-    D          [Standard Deviation-Mean Plot] [Review SMP] [2010-12-26 20:12:20] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121

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=115792&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=115792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115792&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
1133.33333333333316.188286075449945
2126.514.317821063276439
3110.58333333333311.704376285920837
4103.2511.670670308707436
5116.7512.842578330764438

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 133.333333333333 & 16.1882860754499 & 45 \tabularnewline
2 & 126.5 & 14.3178210632764 & 39 \tabularnewline
3 & 110.583333333333 & 11.7043762859208 & 37 \tabularnewline
4 & 103.25 & 11.6706703087074 & 36 \tabularnewline
5 & 116.75 & 12.8425783307644 & 38 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115792&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]133.333333333333[/C][C]16.1882860754499[/C][C]45[/C][/ROW]
[ROW][C]2[/C][C]126.5[/C][C]14.3178210632764[/C][C]39[/C][/ROW]
[ROW][C]3[/C][C]110.583333333333[/C][C]11.7043762859208[/C][C]37[/C][/ROW]
[ROW][C]4[/C][C]103.25[/C][C]11.6706703087074[/C][C]36[/C][/ROW]
[ROW][C]5[/C][C]116.75[/C][C]12.8425783307644[/C][C]38[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115792&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
1133.33333333333316.188286075449945
2126.514.317821063276439
3110.58333333333311.704376285920837
4103.2511.670670308707436
5116.7512.842578330764438






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.80229424979789
beta0.153679949154171
S.D.0.0244817535688572
T-STAT6.27732603883672
p-value0.00816257808420497

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.80229424979789 \tabularnewline
beta & 0.153679949154171 \tabularnewline
S.D. & 0.0244817535688572 \tabularnewline
T-STAT & 6.27732603883672 \tabularnewline
p-value & 0.00816257808420497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115792&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.80229424979789[/C][/ROW]
[ROW][C]beta[/C][C]0.153679949154171[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0244817535688572[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.27732603883672[/C][/ROW]
[ROW][C]p-value[/C][C]0.00816257808420497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115792&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-4.80229424979789
beta0.153679949154171
S.D.0.0244817535688572
T-STAT6.27732603883672
p-value0.00816257808420497






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.70055513591466
beta1.31810319270044
S.D.0.21600033620009
T-STAT6.1023200976846
p-value0.00884130821888857
Lambda-0.318103192700439

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70055513591466 \tabularnewline
beta & 1.31810319270044 \tabularnewline
S.D. & 0.21600033620009 \tabularnewline
T-STAT & 6.1023200976846 \tabularnewline
p-value & 0.00884130821888857 \tabularnewline
Lambda & -0.318103192700439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115792&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70055513591466[/C][/ROW]
[ROW][C]beta[/C][C]1.31810319270044[/C][/ROW]
[ROW][C]S.D.[/C][C]0.21600033620009[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.1023200976846[/C][/ROW]
[ROW][C]p-value[/C][C]0.00884130821888857[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.318103192700439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115792&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-3.70055513591466
beta1.31810319270044
S.D.0.21600033620009
T-STAT6.1023200976846
p-value0.00884130821888857
Lambda-0.318103192700439


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')