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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 16 Dec 2014 08:02:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/16/t1418717103gr76jj6mjwchp79.htm/, Retrieved Thu, 31 Oct 2024 23:10:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269156, Retrieved Thu, 31 Oct 2024 23:10:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-16 08:02:07] [d33b7eb92cfcc384850e3711242e8bfe] [Current]
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Dataseries X:
12
45
37
37
108
10
68
72
143
9
55
17
37
27
37
58
66
21
19
78
35
48
27
43
30
25
69
72
23
13
61
43
51
67
36
44
45
34
36
72
39
43
25
56
80
40
73
34
72
42
61
23
74
16
66
9
41
57
48
51
53
29
29
55
54
43
51
20
79
39
61
55
30
55
22
37
2
38
27
56
25
39
33
43
57
43
23
44
54
28
36
39
16
23
40
24
78
57
37
27
61
27
69
34
44
34
39
51
34
31
13
12
51
24
19
30
81
42
22
85
27
25
22
19
14
45
45
28
51
41
31
74
19
51
73
24
61
23
14
54
51
62
36
59
24
26
54
39
16
36
31
31
42
39
25
31
38
31
17
22
55
62
51
30
49
Dataseries Y:
51
56
67
69
57
56
55
63
67
65
47
76
64
68
64
65
71
63
60
68
72
70
61
61
62
71
71
51
56
70
73
76
68
48
52
60
59
57
79
60
60
59
62
59
61
71
57
66
63
69
58
59
48
66
73
67
61
68
75
62
69
58
60
74
55
62
63
69
58
58
68
72
62
62
65
69
66
72
62
75
58
66
55
47
72
62
64
64
19
50
68
70
79
69
71
48
73
74
66
71
74
78
75
53
60
70
69
65
78
78
59
72
70
63
63
71
74
67
66
62
80
73
67
61
73
74
32
69
69
84
64
58
59
78
57
60
68
68
73
69
67
60
65
66
74
81
72
55
49
74
53
64
65
57
51
80
67
70
74
75
70
69
65
55
71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269156&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269156&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean41.709090909090964.7878787878788
Biased Variance413.9517355371979.1004591368228
Biased Standard Deviation20.34580388033838.89384388983879
Covariance-12.5925720620843
Correlation-0.0691687604016632
Determination0.00478431741550269
T-Test-0.885207712858303
p-value (2 sided)0.377348586261963
p-value (1 sided)0.188674293130982
Degrees of Freedom163
Number of Observations165

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 41.7090909090909 & 64.7878787878788 \tabularnewline
Biased Variance & 413.95173553719 & 79.1004591368228 \tabularnewline
Biased Standard Deviation & 20.3458038803383 & 8.89384388983879 \tabularnewline
Covariance & -12.5925720620843 \tabularnewline
Correlation & -0.0691687604016632 \tabularnewline
Determination & 0.00478431741550269 \tabularnewline
T-Test & -0.885207712858303 \tabularnewline
p-value (2 sided) & 0.377348586261963 \tabularnewline
p-value (1 sided) & 0.188674293130982 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269156&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]41.7090909090909[/C][C]64.7878787878788[/C][/ROW]
[ROW][C]Biased Variance[/C][C]413.95173553719[/C][C]79.1004591368228[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]20.3458038803383[/C][C]8.89384388983879[/C][/ROW]
[ROW][C]Covariance[/C][C]-12.5925720620843[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0691687604016632[/C][/ROW]
[ROW][C]Determination[/C][C]0.00478431741550269[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.885207712858303[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.377348586261963[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.188674293130982[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]163[/C][/ROW]
[ROW][C]Number of Observations[/C][C]165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269156&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
Mean41.709090909090964.7878787878788
Biased Variance413.9517355371979.1004591368228
Biased Standard Deviation20.34580388033838.89384388983879
Covariance-12.5925720620843
Correlation-0.0691687604016632
Determination0.00478431741550269
T-Test-0.885207712858303
p-value (2 sided)0.377348586261963
p-value (1 sided)0.188674293130982
Degrees of Freedom163
Number of Observations165







Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 89.2924, p-value < 2.2e-16
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4017, p-value = 0.00122
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 89.2924, p-value < 2.2e-16
alternative hypothesis: greater
\tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater
\tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4017, p-value = 0.00122
\tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=269156&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 89.2924, p-value < 2.2e-16
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4017, p-value = 0.00122
[/C][/ROW] [ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=269156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269156&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 = 89.2924, p-value < 2.2e-16
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 139.8607, p-value < 2.2e-16
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4017, p-value = 0.00122
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1343, p-value = 0.005585



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()