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Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSat, 02 May 2015 04:44:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/02/t1430538420ushd4xaaah4h70k.htm/, Retrieved Fri, 29 Mar 2024 13:10:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278997, Retrieved Fri, 29 Mar 2024 13:10:01 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
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Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [2014-waspage-firs...] [2015-05-02 03:44:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3,55
3,52
3,53
3,55
3,43
3,46
3,47
3,48
3,48
3,49
3,5
3,5
3,51
3,54
3,55
3,55
3,56
3,56
3,57
3,57
3,59
3,63
3,37
3,39
3,43
3,45
3,45
3,45
3,48
3,48
3,48
3,48
3,49
3,49
3,5
3,5
3,51
3,51
3,51
3,52
3,52
3,52
3,52
3,52
3,52
3,52
3,53
3,53
3,54
3,54
3,54
3,55
3,55
3,56
3,56
3,56
3,57
3,57
3,57
3,57
3,58
3,58
3,58
3,59
3,6
3,6
3,42
3,43
3,45
3,45
3,47
3,48
3,48
3,48
3,48
3,48
3,49
3,49
3,49
3,49
3,49
3,49
3,49
3,49
3,5
3,5
3,5
3,5
3,5
3,5
3,5
3,51
3,51
3,51
3,51
3,52
3,52
3,53
3,53
3,53
3,53
3,54
3,54
3,56
3,56
3,56
3,56
3,57
3,57
3,57
3,58
3,58
3,58
3,6
3,69
3,33
3,34
3,39
3,4
3,44
3,45
3,47
3,47
3,47
3,48
3,48
3,48
3,48
3,49
3,49
3,49
3,49
3,49
3,49
3,5
3,5
3,5
3,5
3,5
3,5
3,51
3,51
3,51
3,51
3,51
3,51
3,52
3,52
3,52
3,53
3,54
3,54
3,54
3,55
3,55
3,55
3,55
3,56
3,58
3,58
3,58
3,59
3,62
3,29
3,4
3,41
3,43
3,44
3,44
3,44
3,45
3,45
3,46
3,46
3,46
3,47
3,48
3,48
3,48
3,49
3,5
3,5
3,51
3,51
3,52
3,52
3,53
3,54
3,56
3,56
3,57
3,58
3,32
3,4
3,41
3,42
3,42
3,42
3,43
3,43
3,48
3,5
3,5
3,51
3,51
3,53
3,53
3,53
3,53
3,54
3,54
3,54
3,39
3,45
3,45
3,47
3,47
3,47
3,48
3,48
3,48
3,48
3,49
3,49
3,51
3,52
3,53
3,53
3,54
3,54
3,56
3,43
3,45
3,47
3,47
3,54
3,43
3,5
3,55
3,37
3,48
3,5
3,5
3,51
3,46
3,49
3,5
Dataseries Y:
1
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
11
11
11
12
12
12
12
13
14
17
23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278997&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278997&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'George Udny Yule' @ yule.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.503117408906886.08097165991903
Biased Variance0.002986638037010936.31733022996607
Biased Standard Deviation0.05465014214996092.51342997315741
Covariance-0.0350095454395839
Correlation-0.253843788076435
Determination0.0644366687449941
T-Test-4.107834957736
p-value (2 sided)5.44794492276262e-05
p-value (1 sided)2.72397246138131e-05
Degrees of Freedom245
Number of Observations247

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.50311740890688 & 6.08097165991903 \tabularnewline
Biased Variance & 0.00298663803701093 & 6.31733022996607 \tabularnewline
Biased Standard Deviation & 0.0546501421499609 & 2.51342997315741 \tabularnewline
Covariance & -0.0350095454395839 \tabularnewline
Correlation & -0.253843788076435 \tabularnewline
Determination & 0.0644366687449941 \tabularnewline
T-Test & -4.107834957736 \tabularnewline
p-value (2 sided) & 5.44794492276262e-05 \tabularnewline
p-value (1 sided) & 2.72397246138131e-05 \tabularnewline
Degrees of Freedom & 245 \tabularnewline
Number of Observations & 247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278997&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]3.50311740890688[/C][C]6.08097165991903[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.00298663803701093[/C][C]6.31733022996607[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.0546501421499609[/C][C]2.51342997315741[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.0350095454395839[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.253843788076435[/C][/ROW]
[ROW][C]Determination[/C][C]0.0644366687449941[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.107834957736[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.44794492276262e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.72397246138131e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]245[/C][/ROW]
[ROW][C]Number of Observations[/C][C]247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278997&T=1

As an alternative you can also use a QR Code:  

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

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.503117408906886.08097165991903
Biased Variance0.002986638037010936.31733022996607
Biased Standard Deviation0.05465014214996092.51342997315741
Covariance-0.0350095454395839
Correlation-0.253843788076435
Determination0.0644366687449941
T-Test-4.107834957736
p-value (2 sided)5.44794492276262e-05
p-value (1 sided)2.72397246138131e-05
Degrees of Freedom245
Number of Observations247







Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 34.4365, p-value = 3.328e-08
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 951.3736, p-value < 2.2e-16
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6783, p-value = 0.0002575
> ad.y
	Anderson-Darling normality test
data:  y
A = 6.4269, p-value = 8.201e-16

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 34.4365, p-value = 3.328e-08
alternative hypothesis: greater
\tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 951.3736, p-value < 2.2e-16
alternative hypothesis: greater
\tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6783, p-value = 0.0002575
\tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 6.4269, p-value = 8.201e-16
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=278997&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 34.4365, p-value = 3.328e-08
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 951.3736, p-value < 2.2e-16
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6783, p-value = 0.0002575
[/C][/ROW] [ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 6.4269, p-value = 8.201e-16
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=278997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278997&T=2

As an alternative you can also use a QR Code:  

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

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 34.4365, p-value = 3.328e-08
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 951.3736, p-value < 2.2e-16
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6783, p-value = 0.0002575
> ad.y
	Anderson-Darling normality test
data:  y
A = 6.4269, p-value = 8.201e-16



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab, sub=main)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson', na.rm = T)
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()