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*The author of this computation has been verified*

R Software Module: /rwasp_correlation.wasp (opens new window with default values)

Title produced by software: Pearson Correlation

Date of computation: Thu, 10 Dec 2009 10:04:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464985bfgx509jmq45dwj.htm/, Retrieved Thu, 10 Dec 2009 18:09:47 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464985bfgx509jmq45dwj.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

94.204 97.217 95.118 93.688 93.140 91.516 90.957 90.372 89.749 85.813 86.026 83.933 83.602 83.384 76.369 60.808 48.071 42.604 41.402 62.121 79.739 79.006 74.472 75.956 75.041 74.873 72.922 70.472 71.423 71.363 73.297 72.081 70.488 65.544 64.450 61.698 61.352 61.072 63.722 61.987 53.802 47.818 50.998 58.438 60.143 61.854 70.987 70.389 72.175 70.243 69.616 69.443 70.833 71.059 72.218 72.647 73.299 73.756 75.557 78.172 75.624 76.959 74.994 76.841 78.043 75.187 73.387 70.798 68.722 68.396 68.466 67.675 65.248 62.974 59.801 57.894 58.592 59.249 59.554 59.753 60.877 60.532 58.452 56.955 56.437 55.588 56.702 57.062 57.826 58.755 60.250 61.142 60.690 58.495 56.020 55.814 56.489 56.587 55.714 55.611 56.093 55.929 54.181 54.810 56.189 57.427 59.432 58.951

Dataseries Y:

» Textbox « » Textfile « » CSV «

99.026 101.851 99.958 97.875 97.927 95.149 94.551 93.999 93.297 89.901 89.742 87.096 86.863 86.718 80.020 63.483 51.289 44.071 43.654 66.115 84.518 83.395 78.307 80.049 78.346 78.317 75.918 73.739 74.530 74.179 76.974 75.408 73.336 69.210 67.286 64.606 64.159 64.423 66.411 64.270 56.521 50.599 54.751 62.227 63.932 65.391 75.744 74.590 76.035 74.427 73.354 73.081 75.309 75.463 75.910 76.151 76.882 78.632 80.137 82.490 79.896 81.303 79.344 81.355 82.328 79.669 77.249 75.101 72.520 72.438 72.653 71.429 69.189 66.451 63.354 61.379 61.880 62.274 62.429 63.905 63.917 64.295 61.930 60.440 59.353 58.695 60.569 60.386 60.938 61.795 63.304 64.270 63.492 61.333 59.341 58.412 58.725 59.277 58.562 57.858 58.790 58.243 57.044 57.339 59.429 60.575 61.950 61.712

Output produced by software:

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	'Gwilym Jenkins' @ 72.249.127.135

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	67.6080185185185	71.1084444444444
Biased Variance	141.123202647805	152.316529320988
Biased Standard Deviation	11.8795287216205	12.3416582889411
Covariance	147.847395786085
Correlation	0.999081625633777
Determination	0.99816409467903
T-Test	240.064954105674
p-value (2 sided)	0
p-value (1 sided)	0
Degrees of Freedom	106
Number of Observations	108

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464985bfgx509jmq45dwj/1wjd11260464695.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260464985bfgx509jmq45dwj/1wjd11260464695.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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