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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, 20 Dec 2011 17:16:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/20/t1324419410lv7a11b66xa7dsl.htm/, Retrieved Fri, 17 May 2024 10:42:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158313, Retrieved Fri, 17 May 2024 10:42:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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]
- R PD    [Standard Deviation-Mean Plot] [WS9 3.2 SMP] [2010-12-07 14:36:57] [afe9379cca749d06b3d6872e02cc47ed]
- R  D      [Standard Deviation-Mean Plot] [] [2011-12-04 11:12:53] [ec2187f7727da5d5d939740b21b8b68a]
-   PD          [Standard Deviation-Mean Plot] [] [2011-12-20 22:16:20] [542c32830549043c4555f1bd78aefedb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90604
97527
111940
100280
100009
95558
98533
92694
97920
110933
110855
111716
96348
105425
114874
104199
101166
99010
101607
97492
106088
113536
112475
115491
97733
102591
114783
100397
97772
96128
91261
90686
97792
108848
109989
109453
93945
98750
119043
104776
103262
106735
101600
99358
105240
114079
121637
111747
99496
104992
124255
108258
106940
104939
105896
107287
110783
122139
125823
120480
103296
117121
129924
118589
118062
113597
117161
112893
119657
136562
140446
138744
120324
118113
130257
125510
117986
118316
122075
117573
122566
135934
138394
137999
118780
117907
142932
132200
125666
127958
127718
124368
135241
144734
142320
141481
120471
123422
145829
134572
132156
140265
137771
134035
144016
151905
155791
148440
129862
134264
151952
143191
137242
136993
134431
132523
133486
140120
137521
112193
94256
99047
109761
102160
104792
104341
112430
113034
114197
127876
135199
123663
112578
117104
139703
114961
134222
128390
134197
135963
135936
146803
143231
131510

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158313&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158313&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1101547.4166666677760.7538581615721336
2105642.5833333336919.4466470603819143
3101452.757749.4883130201824097
41066818414.5062513819227692
51117748899.6190010379926327
612217111592.896061420937150
7125420.5833333338126.8755313167620821
8131775.4166666679507.9645413567326827
9139056.08333333310827.38697141635320
10135314.8333333339296.5940667765139759
11111729.66666666712160.122833809440943
12131216.511040.833676526834225

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101547.416666667 & 7760.75385816157 & 21336 \tabularnewline
2 & 105642.583333333 & 6919.44664706038 & 19143 \tabularnewline
3 & 101452.75 & 7749.48831302018 & 24097 \tabularnewline
4 & 106681 & 8414.50625138192 & 27692 \tabularnewline
5 & 111774 & 8899.61900103799 & 26327 \tabularnewline
6 & 122171 & 11592.8960614209 & 37150 \tabularnewline
7 & 125420.583333333 & 8126.87553131676 & 20821 \tabularnewline
8 & 131775.416666667 & 9507.96454135673 & 26827 \tabularnewline
9 & 139056.083333333 & 10827.386971416 & 35320 \tabularnewline
10 & 135314.833333333 & 9296.59406677651 & 39759 \tabularnewline
11 & 111729.666666667 & 12160.1228338094 & 40943 \tabularnewline
12 & 131216.5 & 11040.8336765268 & 34225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158313&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]101547.416666667[/C][C]7760.75385816157[/C][C]21336[/C][/ROW]
[ROW][C]2[/C][C]105642.583333333[/C][C]6919.44664706038[/C][C]19143[/C][/ROW]
[ROW][C]3[/C][C]101452.75[/C][C]7749.48831302018[/C][C]24097[/C][/ROW]
[ROW][C]4[/C][C]106681[/C][C]8414.50625138192[/C][C]27692[/C][/ROW]
[ROW][C]5[/C][C]111774[/C][C]8899.61900103799[/C][C]26327[/C][/ROW]
[ROW][C]6[/C][C]122171[/C][C]11592.8960614209[/C][C]37150[/C][/ROW]
[ROW][C]7[/C][C]125420.583333333[/C][C]8126.87553131676[/C][C]20821[/C][/ROW]
[ROW][C]8[/C][C]131775.416666667[/C][C]9507.96454135673[/C][C]26827[/C][/ROW]
[ROW][C]9[/C][C]139056.083333333[/C][C]10827.386971416[/C][C]35320[/C][/ROW]
[ROW][C]10[/C][C]135314.833333333[/C][C]9296.59406677651[/C][C]39759[/C][/ROW]
[ROW][C]11[/C][C]111729.666666667[/C][C]12160.1228338094[/C][C]40943[/C][/ROW]
[ROW][C]12[/C][C]131216.5[/C][C]11040.8336765268[/C][C]34225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158313&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
1101547.4166666677760.7538581615721336
2105642.5833333336919.4466470603819143
3101452.757749.4883130201824097
41066818414.5062513819227692
51117748899.6190010379926327
612217111592.896061420937150
7125420.5833333338126.8755313167620821
8131775.4166666679507.9645413567326827
9139056.08333333310827.38697141635320
10135314.8333333339296.5940667765139759
11111729.66666666712160.122833809440943
12131216.511040.833676526834225






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1744.97518932769
beta0.0641648764877621
S.D.0.0332713939415766
T-STAT1.9285298536164
p-value0.0826351502536997

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1744.97518932769 \tabularnewline
beta & 0.0641648764877621 \tabularnewline
S.D. & 0.0332713939415766 \tabularnewline
T-STAT & 1.9285298536164 \tabularnewline
p-value & 0.0826351502536997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158313&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1744.97518932769[/C][/ROW]
[ROW][C]beta[/C][C]0.0641648764877621[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0332713939415766[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.9285298536164[/C][/ROW]
[ROW][C]p-value[/C][C]0.0826351502536997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158313&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)
alpha1744.97518932769
beta0.0641648764877621
S.D.0.0332713939415766
T-STAT1.9285298536164
p-value0.0826351502536997






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.15915505614448
beta0.881012813161826
S.D.0.404207831201798
T-STAT2.17960352361899
p-value0.0542818572670516
Lambda0.118987186838174

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.15915505614448 \tabularnewline
beta & 0.881012813161826 \tabularnewline
S.D. & 0.404207831201798 \tabularnewline
T-STAT & 2.17960352361899 \tabularnewline
p-value & 0.0542818572670516 \tabularnewline
Lambda & 0.118987186838174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158313&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.15915505614448[/C][/ROW]
[ROW][C]beta[/C][C]0.881012813161826[/C][/ROW]
[ROW][C]S.D.[/C][C]0.404207831201798[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.17960352361899[/C][/ROW]
[ROW][C]p-value[/C][C]0.0542818572670516[/C][/ROW]
[ROW][C]Lambda[/C][C]0.118987186838174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158313&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-1.15915505614448
beta0.881012813161826
S.D.0.404207831201798
T-STAT2.17960352361899
p-value0.0542818572670516
Lambda0.118987186838174


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
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')