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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 computationTue, 02 Dec 2008 14:55:08 -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/02/t12282549857bbrx3rxjx1vkzm.htm/, Retrieved Tue, 14 May 2024 18:08:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28497, Retrieved Tue, 14 May 2024 18:08:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact229

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RM D  [Cross Correlation Function] [Opdracht 1 - Blok...] [2008-11-26 22:16:36] [8094ad203a218aaca2d1cea2c78c2d6e]
- RM D      [Standard Deviation-Mean Plot] [Opdracht 1 - Blok...] [2008-12-02 21:55:08] [1351baa662f198be3bff32f9007a9a6d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,1
101,1
111,1
93,3
100
108
70,4
75,4
105,5
112,3
102,5
93,5
86,7
95,2
103,8
97
95,5
101
67,5
64
106,7
100,6
101,2
93,1
84,2
85,8
91,8
92,4
80,3
79,7
62,5
57,1
100,8
100,7
86,2
83,2
71,7
77,5
89,8
80,3
78,7
93,8
57,6
60,6
91
85,3
77,4
77,3
68,3
69,9
81,7
75,1
69,9
84
54,3
60
89,9
77
85,3
77,6
69,2

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=28497&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=28497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28497&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
197.613.070299433170141.9
292.691666666666713.652269763558442.7
383.72513.206136658938043.7
478.416666666666711.178618660260136.2
574.416666666666710.492753632287335.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.6 & 13.0702994331701 & 41.9 \tabularnewline
2 & 92.6916666666667 & 13.6522697635584 & 42.7 \tabularnewline
3 & 83.725 & 13.2061366589380 & 43.7 \tabularnewline
4 & 78.4166666666667 & 11.1786186602601 & 36.2 \tabularnewline
5 & 74.4166666666667 & 10.4927536322873 & 35.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28497&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]97.6[/C][C]13.0702994331701[/C][C]41.9[/C][/ROW]
[ROW][C]2[/C][C]92.6916666666667[/C][C]13.6522697635584[/C][C]42.7[/C][/ROW]
[ROW][C]3[/C][C]83.725[/C][C]13.2061366589380[/C][C]43.7[/C][/ROW]
[ROW][C]4[/C][C]78.4166666666667[/C][C]11.1786186602601[/C][C]36.2[/C][/ROW]
[ROW][C]5[/C][C]74.4166666666667[/C][C]10.4927536322873[/C][C]35.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28497&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
197.613.070299433170141.9
292.691666666666713.652269763558442.7
383.72513.206136658938043.7
478.416666666666711.178618660260136.2
574.416666666666710.492753632287335.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.95732003276606
beta0.121385681116044
S.D.0.0447776720690947
T-STAT2.71085287615530
p-value0.0731117639392628

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.95732003276606 \tabularnewline
beta & 0.121385681116044 \tabularnewline
S.D. & 0.0447776720690947 \tabularnewline
T-STAT & 2.71085287615530 \tabularnewline
p-value & 0.0731117639392628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28497&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.95732003276606[/C][/ROW]
[ROW][C]beta[/C][C]0.121385681116044[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0447776720690947[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.71085287615530[/C][/ROW]
[ROW][C]p-value[/C][C]0.0731117639392628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28497&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28497&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)
alpha1.95732003276606
beta0.121385681116044
S.D.0.0447776720690947
T-STAT2.71085287615530
p-value0.0731117639392628






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.42790186498590
beta0.88562131428056
S.D.0.301730202779800
T-STAT2.93514307192800
p-value0.0607477961440794
Lambda0.114378685719440

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.42790186498590 \tabularnewline
beta & 0.88562131428056 \tabularnewline
S.D. & 0.301730202779800 \tabularnewline
T-STAT & 2.93514307192800 \tabularnewline
p-value & 0.0607477961440794 \tabularnewline
Lambda & 0.114378685719440 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28497&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.42790186498590[/C][/ROW]
[ROW][C]beta[/C][C]0.88562131428056[/C][/ROW]
[ROW][C]S.D.[/C][C]0.301730202779800[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.93514307192800[/C][/ROW]
[ROW][C]p-value[/C][C]0.0607477961440794[/C][/ROW]
[ROW][C]Lambda[/C][C]0.114378685719440[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28497&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28497&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-1.42790186498590
beta0.88562131428056
S.D.0.301730202779800
T-STAT2.93514307192800
p-value0.0607477961440794
Lambda0.114378685719440


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Airline ; par2 = Box-Jenkins ; par3 = Airline Passengers ;
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')