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Description of Statistical Computation

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, 04 Dec 2018 16:39:26 +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/2018/Dec/04/t15439380809xsrzvhc2scwkm1.htm/, Retrieved Thu, 09 May 2024 02:05:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315756, Retrieved Thu, 09 May 2024 02:05:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCountries GDP - Footprint
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson correlati...] [2018-12-04 15:39:26] [1fa0b6d83deab05e8f8a52e2846ed0da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.79
2.21
2.12
0.93
5.38
3.14
2.23
11.88
9.31
6.06
2.31
6.84
7.49
0.72
4.48
5.09
7.44
1.41
5.77
4.84
2.96
3.12
3.83
3.11
2.86
4.06
3.32
1.21
0.8
2.52
1.21
1.17
8.17
5.65
1.24
1.46
4.36
3.38
1.87
1.03
1.29
0.82
2.84
1.27
3.92
1.95
4.21
5.19
5.51
2.19
2.57
1.53
2.17
2.15
2.07
3.97
0.42
6.86
1.02
2.9
5.87
5.14
2.34
4.73
2.02
1.03
1.58
5.3
1.97
4.38
2.98
3.23
1.89
1.41
1.53
3.07
0.61
1.68
2.92
1.16
1.58
2.79
1.88
5.57
6.22
4.61
1.89
5.02
2.1
5.55
1.03
1.17
5.69
8.13
1.91
1.22
6.29
3.84
1.66
1.21
3.69
5.83
15.82
3.26
0.99
0.81
3.71
1.53
2.08
2.54
3.46
2.89
1.78
6.08
3.78
7.78
1.68
0.87
1.43
2.48
2.94
0.98
5.28
3.58
5.6
1.39
1.56
1.16
4.98
7.52
0.79
2.79
1.91
4.16
2.28
1.1
4.44
3.88
10.8
3.65
2.71
5.69
0.87
4.94
2.45
3.11
2.77
1.49
5.61
1.21
2.7
1.24
7.97
4.06
5.81
1.29
1.24
3.31
3.67
1.32
4.25
2.01
7.25
5.79
1.51
0.91
1.32
2.66
0.48
1.13
2.7
7.92
2.34
3.33
5.47
1.24
2.84
4.94
7.93
8.22
2.91
2.32
3.57
1.65
2.07
1.03
0.99
1.37
Dataseries Y:
Download CSV
Histogram 
614.66
4534.37
5430.57
4665.91
13205.1
13540
3426.39
NA
66604.2
51274.1
7106.04
22647.3
24299
857.5
15722.8
6300.45
48053.3
746.83
70626.3
2395
2253.09
4708.85
7743.5
13237.6
NA
47097.4
7615.28
671.07
276.69
3801.45
877.64
1271.21
52145.4
NA
495.04
1161.22
14525.8
5560.94
7305.22
860.24
1943.69
338.63
8979.96
1016.83
14522.8
5175.94
31454.7
21676.3
61413.6
1433.17
7088.01
6085.89
5192.88
2930.33
3696.33
24064
439.73
17304.4
379.38
4201.37
50960.2
45430.3
NA
NA
11989
505.76
3710.7
46822.4
1627.9
25987.4
7410.48
NA
3233.8
459.09
681.25
3269.46
749.13
2269.51
13964.2
1513.85
3688.53
7511.1
5848.54
52853.6
33718.9
38412
5226.3
46201.6
4615.17
11278
1062.11
NA
24155.8
41830.5
1116.37
1236.24
13732
9143.86
1338.42
397.38
5859.43
14373.7
114665
5174.89
456.33
493.84
10252.6
741.22
NA
1524.39
8811.15
10123.9
1971.03
3736.07
7251.6
NA
3149.43
538.82
1117.58
5880.8
NA
700.07
53589.9
NA
37488.3
1626.85
410.91
2612.12
100172
22622.8
1218.6
8410.77
1871.21
3557.31
5684.73
2379.44
13769.5
23217.3
99431.5
NA
9213.94
13320.2
628.08
12952.5
7737.2
6171.48
4067.15
1384.53
23593.8
1079.27
6426.18
499.89
53122.4
18103.1
25040.5
1647.86
NA
8089.87
32008.7
2880.03
8190.7
4657.48
59381.9
88506.2
NA
836.17
765.33
5479.29
5167.86
580.86
4330.9
18310.8
4305.07
10437.7
5290.14
601.35
3589.63
40980.5
40817.4
49725
14238.1
1560.85
10237.8
1532.31
NA
1302.3
1740.64
865.91

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time8 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315756&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]8 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315756&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.2774566473988414238.3249132948
Biased Variance5.39575538106853435418282.389939
Biased Standard Deviation2.3228765316022620866.6787580089
Covariance38973.3526794294
Correlation0.799411984795148
Determination0.639059521434119
T-Test17.4000667853786
p-value (2 sided)1.0999494643326e-39
p-value (1 sided)5.49974732166301e-40
95% CI of Correlation[0.738266617053899, 0.847525746670319]
Degrees of Freedom171
Number of Observations173

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.27745664739884 & 14238.3249132948 \tabularnewline
Biased Variance & 5.39575538106853 & 435418282.389939 \tabularnewline
Biased Standard Deviation & 2.32287653160226 & 20866.6787580089 \tabularnewline
Covariance & 38973.3526794294 \tabularnewline
Correlation & 0.799411984795148 \tabularnewline
Determination & 0.639059521434119 \tabularnewline
T-Test & 17.4000667853786 \tabularnewline
p-value (2 sided) & 1.0999494643326e-39 \tabularnewline
p-value (1 sided) & 5.49974732166301e-40 \tabularnewline
95% CI of Correlation & [0.738266617053899, 0.847525746670319] \tabularnewline
Degrees of Freedom & 171 \tabularnewline
Number of Observations & 173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315756&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]3.27745664739884[/C][C]14238.3249132948[/C][/ROW]
[ROW][C]Biased Variance[/C][C]5.39575538106853[/C][C]435418282.389939[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.32287653160226[/C][C]20866.6787580089[/C][/ROW]
[ROW][C]Covariance[/C][C]38973.3526794294[/C][/ROW]
[ROW][C]Correlation[/C][C]0.799411984795148[/C][/ROW]
[ROW][C]Determination[/C][C]0.639059521434119[/C][/ROW]
[ROW][C]T-Test[/C][C]17.4000667853786[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.0999494643326e-39[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.49974732166301e-40[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.738266617053899, 0.847525746670319][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]171[/C][/ROW]
[ROW][C]Number of Observations[/C][C]173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315756&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:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3.2774566473988414238.3249132948
Biased Variance5.39575538106853435418282.389939
Biased Standard Deviation2.3228765316022620866.6787580089
Covariance38973.3526794294
Correlation0.799411984795148
Determination0.639059521434119
T-Test17.4000667853786
p-value (2 sided)1.0999494643326e-39
p-value (1 sided)5.49974732166301e-40
95% CI of Correlation[0.738266617053899, 0.847525746670319]
Degrees of Freedom171
Number of Observations173






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 196.26, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 406.22, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 5.2249, p-value = 5.923e-13

> ad.y
	Anderson-Darling normality test
data:  y
A = 19.946, p-value < 2.2e-16


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 196.26, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 406.22, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 5.2249, p-value = 5.923e-13

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 19.946, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315756&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 196.26, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 406.22, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 5.2249, p-value = 5.923e-13

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 19.946, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315756&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:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 196.26, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 406.22, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 5.2249, p-value = 5.923e-13

> ad.y
	Anderson-Darling normality test
data:  y
A = 19.946, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()