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Description of Statistical Computation

Author's title

Opgave 9: Extra oefening: hotelkamers: Standard Deviation Mean plot: Vincen...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 28 May 2008 02:42:39 -0600
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/May/28/t12119641912prqumzjkk2qosz.htm/, Retrieved Mon, 13 May 2024 22:49:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13407, Retrieved Mon, 13 May 2024 22:49:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Opgave 9: Extra o...] [2008-05-28 08:42:39] [3244ffc2cb3525df557e4a14321135d8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
65,05
65,84
66,6
67,55
68,07
69,06
69,06
69,11
69,29
69,38
69,28
69,75
69,9
70,21
70,48
71,55
72,18
72,64
72,77
72,74
73,13
73,44
73,34
73,34
73,81
74,26
74,72
75,11
75,26
75,89
75,91
76,43
76,56
76,76
76,76
76,56
76,82
77,09
77,51
77,76
77,86
77,89
77,94
77,99
78,17
78,91
78,87
78,88
79,08
79,41
79,51
79,73
80,38
80,56
80,46
80,45
80,58
80,68
80,52
81,49
81,66
81,95
82,3
82,4
83,14
83,17
83,11
83,21
83,33
83,88
83,8
83,73

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 10 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13407&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]10 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13407&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 time10 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
168.171.56488163943944.7
272.14333333333331.293503581421993.53999999999999
375.66916666666671.021402407862782.95
477.97416666666670.6697280090160532.09000000000000
580.23750.6736619735041112.41000000000000
682.97333333333330.7323974744672872.22

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.17 & 1.5648816394394 & 4.7 \tabularnewline
2 & 72.1433333333333 & 1.29350358142199 & 3.53999999999999 \tabularnewline
3 & 75.6691666666667 & 1.02140240786278 & 2.95 \tabularnewline
4 & 77.9741666666667 & 0.669728009016053 & 2.09000000000000 \tabularnewline
5 & 80.2375 & 0.673661973504111 & 2.41000000000000 \tabularnewline
6 & 82.9733333333333 & 0.732397474467287 & 2.22 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13407&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]68.17[/C][C]1.5648816394394[/C][C]4.7[/C][/ROW]
[ROW][C]2[/C][C]72.1433333333333[/C][C]1.29350358142199[/C][C]3.53999999999999[/C][/ROW]
[ROW][C]3[/C][C]75.6691666666667[/C][C]1.02140240786278[/C][C]2.95[/C][/ROW]
[ROW][C]4[/C][C]77.9741666666667[/C][C]0.669728009016053[/C][C]2.09000000000000[/C][/ROW]
[ROW][C]5[/C][C]80.2375[/C][C]0.673661973504111[/C][C]2.41000000000000[/C][/ROW]
[ROW][C]6[/C][C]82.9733333333333[/C][C]0.732397474467287[/C][C]2.22[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13407&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
168.171.56488163943944.7
272.14333333333331.293503581421993.53999999999999
375.66916666666671.021402407862782.95
477.97416666666670.6697280090160532.09000000000000
580.23750.6736619735041112.41000000000000
682.97333333333330.7323974744672872.22






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.90825287271764
beta-0.0645145207185424
S.D.0.0118712296614831
T-STAT-5.43452721901787
p-value0.00556315728668888

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.90825287271764 \tabularnewline
beta & -0.0645145207185424 \tabularnewline
S.D. & 0.0118712296614831 \tabularnewline
T-STAT & -5.43452721901787 \tabularnewline
p-value & 0.00556315728668888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13407&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.90825287271764[/C][/ROW]
[ROW][C]beta[/C][C]-0.0645145207185424[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0118712296614831[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.43452721901787[/C][/ROW]
[ROW][C]p-value[/C][C]0.00556315728668888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13407&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13407&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)
alpha5.90825287271764
beta-0.0645145207185424
S.D.0.0118712296614831
T-STAT-5.43452721901787
p-value0.00556315728668888






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha20.2152077207701
beta-4.68205760576193
S.D.0.932102853276335
T-STAT-5.02311262035572
p-value0.00736916459365989
Lambda5.68205760576193

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 20.2152077207701 \tabularnewline
beta & -4.68205760576193 \tabularnewline
S.D. & 0.932102853276335 \tabularnewline
T-STAT & -5.02311262035572 \tabularnewline
p-value & 0.00736916459365989 \tabularnewline
Lambda & 5.68205760576193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13407&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.2152077207701[/C][/ROW]
[ROW][C]beta[/C][C]-4.68205760576193[/C][/ROW]
[ROW][C]S.D.[/C][C]0.932102853276335[/C][/ROW]
[ROW][C]T-STAT[/C][C]-5.02311262035572[/C][/ROW]
[ROW][C]p-value[/C][C]0.00736916459365989[/C][/ROW]
[ROW][C]Lambda[/C][C]5.68205760576193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13407&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13407&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)
alpha20.2152077207701
beta-4.68205760576193
S.D.0.932102853276335
T-STAT-5.02311262035572
p-value0.00736916459365989
Lambda5.68205760576193


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')