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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

Wed, 14 Dec 2011 08:22:53 -0500

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/2011/Dec/14/t1323868986laqeyzk07p2rtg1.htm/, Retrieved Wed, 01 May 2024 19:08:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154936, Retrieved Wed, 01 May 2024 19:08:15 +0000

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Estimated Impact

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

-       [Pearson Correlation] [] [2011-12-14 13:22:53] [abd09a04ddc145afbf81a913bd861ab8] [Current]

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Dataseries X:

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Dataseries Y:

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Histogram

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	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154936&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154936&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	'AstonUniversity' @ aston.wessa.net

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	1416.73702422145	138088.051903114
Biased Variance	540109.453335089	6756318290.58208
Biased Standard Deviation	734.921392623109	82196.8265237903
Covariance	54120146.8643911
Correlation	0.892807174666543
Determination	0.797104651136055
T-Test	33.5785991668759
p-value (2 sided)	0
p-value (1 sided)	0
Degrees of Freedom	287
Number of Observations	289

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1416.73702422145 & 138088.051903114 \tabularnewline
Biased Variance & 540109.453335089 & 6756318290.58208 \tabularnewline
Biased Standard Deviation & 734.921392623109 & 82196.8265237903 \tabularnewline
Covariance & 54120146.8643911 \tabularnewline
Correlation & 0.892807174666543 \tabularnewline
Determination & 0.797104651136055 \tabularnewline
T-Test & 33.5785991668759 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 287 \tabularnewline
Number of Observations & 289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154936&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]1416.73702422145[/C][C]138088.051903114[/C][/ROW]
[ROW][C]Biased Variance[/C][C]540109.453335089[/C][C]6756318290.58208[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]734.921392623109[/C][C]82196.8265237903[/C][/ROW]
[ROW][C]Covariance[/C][C]54120146.8643911[/C][/ROW]
[ROW][C]Correlation[/C][C]0.892807174666543[/C][/ROW]
[ROW][C]Determination[/C][C]0.797104651136055[/C][/ROW]
[ROW][C]T-Test[/C][C]33.5785991668759[/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]287[/C][/ROW]
[ROW][C]Number of Observations[/C][C]289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154936&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	1416.73702422145	138088.051903114
Biased Variance	540109.453335089	6756318290.58208
Biased Standard Deviation	734.921392623109	82196.8265237903
Covariance	54120146.8643911
Correlation	0.892807174666543
Determination	0.797104651136055
T-Test	33.5785991668759
p-value (2 sided)	0
p-value (1 sided)	0
Degrees of Freedom	287
Number of Observations	289

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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code