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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 computationFri, 30 Nov 2012 09:29:02 -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/Nov/30/t1354285876zilvke1rnj0sj40.htm/, Retrieved Fri, 03 May 2024 18:46:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195067, Retrieved Fri, 03 May 2024 18:46:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:09:37] [b98453cac15ba1066b407e146608df68]
- RMPD    [Spectral Analysis] [Aantal werklozen ...] [2012-11-30 13:59:58] [3e2c7966ca4198d187b4c59e4eb5d004]
- R P       [Spectral Analysis] [Aantal werklozen ...] [2012-11-30 14:10:07] [3e2c7966ca4198d187b4c59e4eb5d004]
-   P         [Spectral Analysis] [Aantal werklozen ...] [2012-11-30 14:14:07] [3e2c7966ca4198d187b4c59e4eb5d004]
- RMP             [Standard Deviation-Mean Plot] [Aantal werklozen ...] [2012-11-30 14:29:02] [7ac586d7aaad1f98cbd1d1bd98b37cf0] [Current]
- RMP               [ARIMA Backward Selection] [Aantal werklozen ...] [2012-11-30 14:59:36] [3e2c7966ca4198d187b4c59e4eb5d004]
- RMP               [ARIMA Backward Selection] [Aantal werklozen ...] [2012-11-30 14:59:36] [3e2c7966ca4198d187b4c59e4eb5d004]
- RMP               [ARIMA Forecasting] [Aantal werklozen ...] [2012-11-30 16:34:15] [3e2c7966ca4198d187b4c59e4eb5d004]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
116
111
104
100
93
91
119
139
134
124
113
109
109
106
101
98
93
91
122
139
140
132
117
114
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
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
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195067&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195067&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1112.7514.882112508890448
2113.51749
3121.518.768929838238750
4132.66666666666718.391368199305551
513716.53096268439148
6133.33333333333316.188286075449945
7126.514.317821063276439
8110.58333333333311.704376285920837
9103.2511.670670308707436
10116.7512.842578330764438
11116.7511.794644393267536
12108.2511.505927326224735

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 112.75 & 14.8821125088904 & 48 \tabularnewline
2 & 113.5 & 17 & 49 \tabularnewline
3 & 121.5 & 18.7689298382387 & 50 \tabularnewline
4 & 132.666666666667 & 18.3913681993055 & 51 \tabularnewline
5 & 137 & 16.530962684391 & 48 \tabularnewline
6 & 133.333333333333 & 16.1882860754499 & 45 \tabularnewline
7 & 126.5 & 14.3178210632764 & 39 \tabularnewline
8 & 110.583333333333 & 11.7043762859208 & 37 \tabularnewline
9 & 103.25 & 11.6706703087074 & 36 \tabularnewline
10 & 116.75 & 12.8425783307644 & 38 \tabularnewline
11 & 116.75 & 11.7946443932675 & 36 \tabularnewline
12 & 108.25 & 11.5059273262247 & 35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195067&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]112.75[/C][C]14.8821125088904[/C][C]48[/C][/ROW]
[ROW][C]2[/C][C]113.5[/C][C]17[/C][C]49[/C][/ROW]
[ROW][C]3[/C][C]121.5[/C][C]18.7689298382387[/C][C]50[/C][/ROW]
[ROW][C]4[/C][C]132.666666666667[/C][C]18.3913681993055[/C][C]51[/C][/ROW]
[ROW][C]5[/C][C]137[/C][C]16.530962684391[/C][C]48[/C][/ROW]
[ROW][C]6[/C][C]133.333333333333[/C][C]16.1882860754499[/C][C]45[/C][/ROW]
[ROW][C]7[/C][C]126.5[/C][C]14.3178210632764[/C][C]39[/C][/ROW]
[ROW][C]8[/C][C]110.583333333333[/C][C]11.7043762859208[/C][C]37[/C][/ROW]
[ROW][C]9[/C][C]103.25[/C][C]11.6706703087074[/C][C]36[/C][/ROW]
[ROW][C]10[/C][C]116.75[/C][C]12.8425783307644[/C][C]38[/C][/ROW]
[ROW][C]11[/C][C]116.75[/C][C]11.7946443932675[/C][C]36[/C][/ROW]
[ROW][C]12[/C][C]108.25[/C][C]11.5059273262247[/C][C]35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195067&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
1112.7514.882112508890448
2113.51749
3121.518.768929838238750
4132.66666666666718.391368199305551
513716.53096268439148
6133.33333333333316.188286075449945
7126.514.317821063276439
8110.58333333333311.704376285920837
9103.2511.670670308707436
10116.7512.842578330764438
11116.7511.794644393267536
12108.2511.505927326224735






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.400878918501
beta0.167785197652517
S.D.0.0590955751071241
T-STAT2.83921761228939
p-value0.0175719534478382

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.400878918501 \tabularnewline
beta & 0.167785197652517 \tabularnewline
S.D. & 0.0590955751071241 \tabularnewline
T-STAT & 2.83921761228939 \tabularnewline
p-value & 0.0175719534478382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195067&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.400878918501[/C][/ROW]
[ROW][C]beta[/C][C]0.167785197652517[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0590955751071241[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.83921761228939[/C][/ROW]
[ROW][C]p-value[/C][C]0.0175719534478382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195067&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-5.400878918501
beta0.167785197652517
S.D.0.0590955751071241
T-STAT2.83921761228939
p-value0.0175719534478382






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.14936597324215
beta1.42646872637872
S.D.0.474261689193608
T-STAT3.00776714392461
p-value0.0131677448673329
Lambda-0.426468726378719

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.14936597324215 \tabularnewline
beta & 1.42646872637872 \tabularnewline
S.D. & 0.474261689193608 \tabularnewline
T-STAT & 3.00776714392461 \tabularnewline
p-value & 0.0131677448673329 \tabularnewline
Lambda & -0.426468726378719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195067&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.14936597324215[/C][/ROW]
[ROW][C]beta[/C][C]1.42646872637872[/C][/ROW]
[ROW][C]S.D.[/C][C]0.474261689193608[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.00776714392461[/C][/ROW]
[ROW][C]p-value[/C][C]0.0131677448673329[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.426468726378719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195067&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195067&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-4.14936597324215
beta1.42646872637872
S.D.0.474261689193608
T-STAT3.00776714392461
p-value0.0131677448673329
Lambda-0.426468726378719


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')