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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 computationFri, 21 Dec 2012 12:30:01 -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/2012/Dec/21/t13561121677lw3hdwgr2dk61e.htm/, Retrieved Thu, 28 Mar 2024 16:51:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204028, Retrieved Thu, 28 Mar 2024 16:51:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
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   [Multiple Regression] [Unemployment] [2010-11-30 13:40:15] [b98453cac15ba1066b407e146608df68]
- R       [Multiple Regression] [] [2012-12-09 15:44:55] [804e94d57d6cf1d4fdbaf6716baf8784]
- RMPD        [Standard Deviation-Mean Plot] [SDMP] [2012-12-21 17:30:01] [70625068b3924f89f7a6efd1a4acaa7e] [Current]
- RMP           [ARIMA Backward Selection] [arima backwards] [2012-12-21 18:37:05] [4e21aa900c332d40e9c065e2c79814a0]
- RMPD          [ARIMA Forecasting] [arima forecast] [2012-12-21 18:54:05] [4e21aa900c332d40e9c065e2c79814a0]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




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' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204028&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204028&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204028&T=0

As an alternative you can also use a 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' @ fisher.wessa.net







Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
140.16666666666675.905826604192521
25614.875238729940758
398.166666666666730.700409631064494
4112.66666666666724.432963327637981
5146.08333333333347.2333825195954146
6208.58333333333356.7377673373234151
7273.7547.8997532732306141
8312.58333333333341.6554227253096152
9351.33333333333383.0567531415974246

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 40.1666666666667 & 5.9058266041925 & 21 \tabularnewline
2 & 56 & 14.8752387299407 & 58 \tabularnewline
3 & 98.1666666666667 & 30.7004096310644 & 94 \tabularnewline
4 & 112.666666666667 & 24.4329633276379 & 81 \tabularnewline
5 & 146.083333333333 & 47.2333825195954 & 146 \tabularnewline
6 & 208.583333333333 & 56.7377673373234 & 151 \tabularnewline
7 & 273.75 & 47.8997532732306 & 141 \tabularnewline
8 & 312.583333333333 & 41.6554227253096 & 152 \tabularnewline
9 & 351.333333333333 & 83.0567531415974 & 246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204028&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]40.1666666666667[/C][C]5.9058266041925[/C][C]21[/C][/ROW]
[ROW][C]2[/C][C]56[/C][C]14.8752387299407[/C][C]58[/C][/ROW]
[ROW][C]3[/C][C]98.1666666666667[/C][C]30.7004096310644[/C][C]94[/C][/ROW]
[ROW][C]4[/C][C]112.666666666667[/C][C]24.4329633276379[/C][C]81[/C][/ROW]
[ROW][C]5[/C][C]146.083333333333[/C][C]47.2333825195954[/C][C]146[/C][/ROW]
[ROW][C]6[/C][C]208.583333333333[/C][C]56.7377673373234[/C][C]151[/C][/ROW]
[ROW][C]7[/C][C]273.75[/C][C]47.8997532732306[/C][C]141[/C][/ROW]
[ROW][C]8[/C][C]312.583333333333[/C][C]41.6554227253096[/C][C]152[/C][/ROW]
[ROW][C]9[/C][C]351.333333333333[/C][C]83.0567531415974[/C][C]246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204028&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204028&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
140.16666666666675.905826604192521
25614.875238729940758
398.166666666666730.700409631064494
4112.66666666666724.432963327637981
5146.08333333333347.2333825195954146
6208.58333333333356.7377673373234151
7273.7547.8997532732306141
8312.58333333333341.6554227253096152
9351.33333333333383.0567531415974246







Regression: S.E.(k) = alpha + beta * Mean(k)
alpha7.93166528614156
beta0.175768567974959
S.D.0.0399693629823875
T-STAT4.39758241962503
p-value0.00316612509551108

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.93166528614156 \tabularnewline
beta & 0.175768567974959 \tabularnewline
S.D. & 0.0399693629823875 \tabularnewline
T-STAT & 4.39758241962503 \tabularnewline
p-value & 0.00316612509551108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204028&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.93166528614156[/C][/ROW]
[ROW][C]beta[/C][C]0.175768567974959[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0399693629823875[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.39758241962503[/C][/ROW]
[ROW][C]p-value[/C][C]0.00316612509551108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204028&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204028&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha7.93166528614156
beta0.175768567974959
S.D.0.0399693629823875
T-STAT4.39758241962503
p-value0.00316612509551108







Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.31542559934179
beta0.961264670540118
S.D.0.158003733780894
T-STAT6.08380984131122
p-value0.000498987067881504
Lambda0.0387353294598818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.31542559934179 \tabularnewline
beta & 0.961264670540118 \tabularnewline
S.D. & 0.158003733780894 \tabularnewline
T-STAT & 6.08380984131122 \tabularnewline
p-value & 0.000498987067881504 \tabularnewline
Lambda & 0.0387353294598818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204028&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.31542559934179[/C][/ROW]
[ROW][C]beta[/C][C]0.961264670540118[/C][/ROW]
[ROW][C]S.D.[/C][C]0.158003733780894[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.08380984131122[/C][/ROW]
[ROW][C]p-value[/C][C]0.000498987067881504[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0387353294598818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204028&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204028&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.31542559934179
beta0.961264670540118
S.D.0.158003733780894
T-STAT6.08380984131122
p-value0.000498987067881504
Lambda0.0387353294598818



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')