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Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Sun, 19 Dec 2010 16:08:24 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t12927747724j53bmnka8cn1a7.htm/, Retrieved Sun, 05 May 2024 04:06:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112543, Retrieved Sun, 05 May 2024 04:06:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

120

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
-   PD  [Multiple Regression] [] [2010-12-01 13:36:35] [8d263c682820d5327cb5f02a8c3630cf]
- RMPD      [Pearson Correlation] [] [2010-12-19 16:08:24] [64cdeb58b12a5b72c79150d12c763b6f] [Current]

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Dataseries Y:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112543&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112543&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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	72313.505800464	49.8515081206497
Biased Variance	1028326984.4727	12756.163565011
Biased Standard Deviation	32067.5378610941	112.943187333327
Covariance	1292056.74504937
Correlation	0.355915676517354
Determination	0.126675968790806
T-Test	7.88838426050964
p-value (2 sided)	2.57571741713036e-14
p-value (1 sided)	1.28785870856518e-14
Degrees of Freedom	429
Number of Observations	431

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 72313.505800464 & 49.8515081206497 \tabularnewline
Biased Variance & 1028326984.4727 & 12756.163565011 \tabularnewline
Biased Standard Deviation & 32067.5378610941 & 112.943187333327 \tabularnewline
Covariance & 1292056.74504937 \tabularnewline
Correlation & 0.355915676517354 \tabularnewline
Determination & 0.126675968790806 \tabularnewline
T-Test & 7.88838426050964 \tabularnewline
p-value (2 sided) & 2.57571741713036e-14 \tabularnewline
p-value (1 sided) & 1.28785870856518e-14 \tabularnewline
Degrees of Freedom & 429 \tabularnewline
Number of Observations & 431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112543&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]72313.505800464[/C][C]49.8515081206497[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1028326984.4727[/C][C]12756.163565011[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]32067.5378610941[/C][C]112.943187333327[/C][/ROW]
[ROW][C]Covariance[/C][C]1292056.74504937[/C][/ROW]
[ROW][C]Correlation[/C][C]0.355915676517354[/C][/ROW]
[ROW][C]Determination[/C][C]0.126675968790806[/C][/ROW]
[ROW][C]T-Test[/C][C]7.88838426050964[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.57571741713036e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.28785870856518e-14[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]429[/C][/ROW]
[ROW][C]Number of Observations[/C][C]431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112543&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	72313.505800464	49.8515081206497
Biased Variance	1028326984.4727	12756.163565011
Biased Standard Deviation	32067.5378610941	112.943187333327
Covariance	1292056.74504937
Correlation	0.355915676517354
Determination	0.126675968790806
T-Test	7.88838426050964
p-value (2 sided)	2.57571741713036e-14
p-value (1 sided)	1.28785870856518e-14
Degrees of Freedom	429
Number of Observations	431

Figure 1

PNG link

Postscript link

PDF link

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')

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Tree of Dependent Computations

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Figures (Output of Computation)

Input Parameters & R Code