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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSun, 08 Nov 2009 23:46:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/09/t1257749407pof9q42hactxdxp.htm/, Retrieved Wed, 29 Nov 2023 21:28:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=54648, Retrieved Wed, 29 Nov 2023 21:28:40 +0000
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Original text written by user:This analysis computes the correlation between U.S. and Canadian bond yields from 1999 to 2009.
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact269

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Canadian / U.S. 5...] [2009-11-09 06:46:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.78
4.81
4.89
4.76
4.93
4.96
5.06
5.22
5.36
5.21
5.14
5.03
4.95
4.86
4.75
4.92
4.98
4.95
5.1
5.26
5.34
5.44
5.56
5.48
5.57
5.35
5.44
5.35
5.26
5.53
5.59
5.86
5.63
5.51
5.71
5.64
5.62
5.63
5.67
5.86
6
6.15
6.2
5.98
5.97
6.01
5.98
6.1
6
6.17
6.18
6.11
6.42
6.44
6.5
6.38
6.48
6.5
6.47
6.29
6.16
6.17
6.18
6.02
6.13
5.9
5.92
5.96
6.17
6.36
6.35
6.43
6.37
6.17
6.07
5.98
6.07
6.04
5.91
5.97
6.1
6
5.95
5.9
5.96
5.91
5.92
5.74
5.77
5.79
5.76
5.8
5.74
5.67
5.75
5.84
5.91
5.85
5.73
5.59
5.44
5.4
5.28
5.3
5.28
5.21
5.24
5.3
5.14
5.19
5.29
5.2
5.09
5.01
4.93
4.85
5.03
5.05
5.17
5.15
5.23
5.35
5.23
5.51
5.56
5.61
5.36
5.33
5.29
5.39
5.59
5.52
5.37
5.36
5.29
5.2
5.17
5.09
4.93
4.97
4.56
4.61
4.62
4.51
4.54
4.52
4.4
4.08
3.96
4.31
4.72
4.68
4.68
4.65
4.67
4.69
4.71
4.56
4.38
4.62
4.71
4.59
4.69
4.61
4.58
4.79
5.06
5.23
5.28
5.16
5.16
5.1
5.05
4.97
4.99
5.13
5
4.9
4.92
4.9
4.66
4.67
4.65
4.62
4.54
4.33
4.3
4.06
4.14
4.45
4.49
4.18
4.25
4.19
4.2
4.2
4.21
4.47
4.53
4.34
4.27
4.19
4.26
4.39
4.27
4.2
4.14
4.06
3.96
4.06
4.16
4.12
4.27
4.35
4.23
4.27
4.18
4.18
4.15
4.45
4.47
4.48
4.4
4.37
4.32
4.18
4.09
4.02
3.85
3.72
3.58
3.39
3.36
3.55
3.62
3.77
3.8
3.63
3.76
3.9
3.99
3.8
3.97
4.27
4.02
4.02
3.86
3.76
3.96
4.18
4.03
4.07
4.16
4.26
4.1
4.07
4.11
4.08
3.93
3.88
3.91
3.91
3.76
3.61
3.71
3.65
3.48
3.53
3.47
3.48
3.31
3.22
3.22
3.35
3.56
3.77
3.8
3.81
3.68
3.95
4.04
3.96
4.05
4.17
4.25
4.19
4.07
3.96
4
4.01
4.07
3.93
3.8
3.82
3.83
3.98
4.09
4.04
3.95
4
4.09
3.96
3.85
3.94
3.9
3.98
3.87
3.85
3.74
3.55
3.54
3.71
3.74
3.7
3.69
3.55
3.52
3.59
3.5
3.57
3.63
3.64
3.68
3.78
3.88
3.83
3.7
3.59
3.47
3.54
3.53
3.54
3.45
3.44
3.19
3.2
3.33
3.16
3.2
3.32
3.4
3.38
3.37
3.39
3.51
3.42
3.35
3.35
3.43
3.45
3.47
3.58
3.59
3.69
3.78
3.86
3.9
3.93
3.88
3.82
3.89
3.91
3.95
3.92
3.87
3.81
3.93
3.84
3.98
4.06
4.11
4.11
4.02
4.08
4.07
4.08
4.1
4.13
4.22
4.28
4.27
4.38
4.33
4.3
4.22
4.19
4.31
4.2
4.25
4.42
4.53
4.51
4.32
4.3
4.25
4.19
4.17
4.14
4.1
4.03
4.03
4.01
3.98
3.88
3.86
4.05
4.06
4.08
3.89
3.94
3.93
3.89
3.85
3.8
3.86
3.92
3.95
3.94
3.97
4.06
4.07
4.08
4.03
4.06
4.03
3.95
3.86
3.92
3.97
3.99
4.01
4.11
4.12
4.11
4.14
4.17
4.21
4.4
4.53
4.6
4.72
4.66
4.62
4.58
4.61
4.63
4.63
4.57
4.6
4.36
4.31
4.3
4.27
4.27
4.3
4.29
4.24
4.39
4.36
4.19
4.23
4.13
4.07
3.76
3.91
3.71
3.87
3.85
3.98
3.76
3.65
3.52
3.48
3.5
3.35
3.42
3.5
3.4
3.06
2.97
2.89
2.93
3.16
3.03
3.12
3.12
3.04
3.13
3.19
3.2
3.34
3.21
3.49
3.5
3.42
3.45
3.39
3.32
3.46
3.37
3.2
3.12
3.09
3.03
2.98
2.98
2.9
3.13
3.11
2.78
2.95
2.77
2.8
2.79
2.69
2.64
2.48
2.27
2.2
1.89
1.82
1.69
1.85
1.52
1.69
2.03
2.09
2.12
2.07
2.11
1.88
1.88
1.7
1.95
1.75
1.82
1.88
1.89
2.01
2.03
2.09
2.15
2.57
2.41
2.82
2.59
2.57
2.46
2.39
2.57
2.52
2.66
2.7
2.62
2.52
2.65
2.56
2.62
2.62
2.63
2.57
2.54
2.86
2.72
2.7
Dataseries Y:
Download CSV
Histogram 
4.59
4.63
4.61
4.6
4.56
4.76
4.84
4.96
5.11
5.29
5.13
5.05
5.11
5.12
5
5.05
5.1
5.15
5.32
5.39
5.53
5.51
5.75
5.81
5.8
5.88
5.76
5.75
5.61
5.61
5.75
5.86
5.97
5.81
5.71
5.86
5.82
5.8
5.77
5.81
5.95
6.03
6.09
6.09
5.95
5.88
5.95
6.03
6.13
6.03
6.14
6.3
6.33
6.46
6.56
6.65
6.63
6.66
6.76
6.74
6.59
6.58
6.6
6.5
6.44
6.42
6.2
6.18
6.24
6.42
6.66
6.74
6.74
6.65
6.49
6.35
6.27
6.29
6.25
6.13
6.18
6.24
6.16
6.09
6.04
6.11
6.04
6.02
5.95
5.95
5.95
5.9
5.9
5.79
5.7
5.73
5.82
5.82
5.69
5.63
5.52
5.33
5.25
5.02
4.98
4.8
4.81
4.85
4.94
4.87
4.9
4.95
4.93
4.74
4.75
4.64
4.51
4.65
4.6
4.71
4.86
4.83
4.91
4.78
4.96
5.01
5
4.88
4.8
4.7
4.82
4.91
4.83
4.72
4.69
4.65
4.66
4.57
4.53
4.47
4.53
4.12
3.96
3.94
3.88
3.99
3.94
3.94
3.73
3.58
3.97
4.25
4.25
4.23
4.41
4.45
4.49
4.47
4.31
4.19
4.37
4.4
4.3
4.33
4.27
4.3
4.55
4.77
4.84
4.88
4.79
4.66
4.62
4.56
4.52
4.5
4.58
4.48
4.4
4.34
4.23
4.09
4.08
4.05
3.92
3.85
3.56
3.53
3.29
3.25
3.32
3.29
3.03
3.08
2.93
2.79
2.72
2.71
3.15
3.22
2.9
2.95
2.93
3.13
3.26
3.24
3.06
3.02
2.89
2.91
3.12
3.11
2.96
3.01
3.02
2.94
2.87
2.76
2.61
2.62
2.97
2.93
2.84
2.92
2.98
2.97
2.88
2.7
2.52
2.35
2.32
2.27
2.13
2.27
2.36
2.49
2.6
2.82
3.08
3.31
3.24
3.35
3.39
3.49
3.51
3.23
3.1
3.07
2.94
3.13
3.32
3.24
3.22
3.37
3.36
3.16
3.27
3.4
3.27
3.2
3.22
3.28
3.24
3
3.02
3.16
3.16
3.06
3.04
3.01
2.98
2.72
2.7
2.71
2.91
3.21
3.38
3.49
3.6
3.74
3.96
3.88
3.83
3.91
3.98
3.97
3.89
3.81
3.65
3.64
3.67
3.78
3.61
3.47
3.41
3.45
3.39
3.42
3.35
3.29
3.35
3.46
3.31
3.29
3.3
3.39
3.53
3.52
3.6
3.7
3.56
3.54
3.58
3.65
3.71
3.72
3.7
3.71
3.72
3.66
3.77
3.89
4
4.11
4.18
4.27
4.24
4.13
4.02
3.9
3.91
3.88
3.91
3.83
3.81
3.69
3.75
3.88
3.77
3.76
3.87
3.95
4.02
4.07
4.17
4.21
4.11
4.07
3.94
3.93
3.98
4.03
4.13
4.24
4.31
4.32
4.42
4.51
4.52
4.46
4.36
4.41
4.43
4.4
4.38
4.33
4.3
4.34
4.29
4.38
4.49
4.54
4.59
4.61
4.66
4.76
4.67
4.67
4.78
4.84
4.91
4.91
4.95
5
5.03
5
4.95
4.99
4.95
5.02
5.16
5.18
5.14
5.06
5.03
4.98
4.89
4.87
4.85
4.77
4.73
4.73
4.73
4.66
4.56
4.56
4.74
4.75
4.74
4.6
4.62
4.61
4.58
4.48
4.44
4.53
4.56
4.65
4.65
4.7
4.76
4.82
4.85
4.76
4.74
4.69
4.51
4.48
4.46
4.48
4.51
4.58
4.66
4.6
4.56
4.55
4.56
4.66
4.77
4.86
4.98
5.13
5.04
4.97
5
5
4.93
4.74
4.6
4.6
4.42
4.34
4.28
4.16
4.12
4.25
4.26
4.25
4.38
4.23
4.04
4.04
3.89
3.77
3.48
3.39
3.35
3.49
3.52
3.63
3.29
3.13
2.97
2.74
2.84
2.72
2.73
2.89
2.8
2.51
2.47
2.34
2.58
2.64
2.66
2.79
3.05
3.1
3.07
3.12
3.12
3.36
3.26
3.57
3.64
3.5
3.32
3.18
3.26
3.44
3.31
3.24
3.18
3.07
3.06
2.93
2.92
2.69
3.02
2.77
2.63
2.9
2.64
2.77
2.56
2.41
2.12
2.06
1.63
1.62
1.36
1.5
1.55
1.62
1.42
1.58
1.74
1.88
1.83
1.79
1.97
1.87
1.93
1.75
1.76
1.73
1.88
1.79
1.89
1.98
2.09
2.01
2.13
2.38
2.58
2.88
2.76
2.66
2.5
2.31
2.43
2.48
2.63
2.73
2.65
2.47
2.48
2.33
2.34
2.43
2.41
2.28
2.24
2.36
2.38

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=54648&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=54648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54648&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.220070796460184.09221238938053
Biased Variance1.077787959589631.43834891064296
Biased Standard Deviation1.038165670589061.19931184878786
Covariance1.10740551685182
Correlation0.887847856896121
Determination0.788273816995035
T-Test45.7831282962707
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom563
Number of Observations565

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.22007079646018 & 4.09221238938053 \tabularnewline
Biased Variance & 1.07778795958963 & 1.43834891064296 \tabularnewline
Biased Standard Deviation & 1.03816567058906 & 1.19931184878786 \tabularnewline
Covariance & 1.10740551685182 \tabularnewline
Correlation & 0.887847856896121 \tabularnewline
Determination & 0.788273816995035 \tabularnewline
T-Test & 45.7831282962707 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 563 \tabularnewline
Number of Observations & 565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=54648&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]4.22007079646018[/C][C]4.09221238938053[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.07778795958963[/C][C]1.43834891064296[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.03816567058906[/C][C]1.19931184878786[/C][/ROW]
[ROW][C]Covariance[/C][C]1.10740551685182[/C][/ROW]
[ROW][C]Correlation[/C][C]0.887847856896121[/C][/ROW]
[ROW][C]Determination[/C][C]0.788273816995035[/C][/ROW]
[ROW][C]T-Test[/C][C]45.7831282962707[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]563[/C][/ROW]
[ROW][C]Number of Observations[/C][C]565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=54648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54648&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
Mean4.220070796460184.09221238938053
Biased Variance1.077787959589631.43834891064296
Biased Standard Deviation1.038165670589061.19931184878786
Covariance1.10740551685182
Correlation0.887847856896121
Determination0.788273816995035
T-Test45.7831282962707
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom563
Number of Observations565


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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)
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')
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')