Free Statistics

of Irreproducible Research!

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 Sat, 28 Jan 2023 10:04:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=54648, Retrieved Sat, 28 Jan 2023 10:04:28 +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 Impact227
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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Dataseries X:
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:
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

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 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:

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

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135

 Pearson Product Moment Correlation - Ungrouped Data Statistic Variable X Variable Y Mean 4.22007079646018 4.09221238938053 Biased Variance 1.07778795958963 1.43834891064296 Biased Standard Deviation 1.03816567058906 1.19931184878786 Covariance 1.10740551685182 Correlation 0.887847856896121 Determination 0.788273816995035 T-Test 45.7831282962707 p-value (2 sided) 0 p-value (1 sided) 0 Degrees of Freedom 563 Number of Observations 565

\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:

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

 Pearson Product Moment Correlation - Ungrouped Data Statistic Variable X Variable Y Mean 4.22007079646018 4.09221238938053 Biased Variance 1.07778795958963 1.43834891064296 Biased Standard Deviation 1.03816567058906 1.19931184878786 Covariance 1.10740551685182 Correlation 0.887847856896121 Determination 0.788273816995035 T-Test 45.7831282962707 p-value (2 sided) 0 p-value (1 sided) 0 Degrees of Freedom 563 Number of Observations 565

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)/lxvarx = var(x)*makebiasedvary = var(y)*makebiasedcorxy <- 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')