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Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwarePearson Correlation
Date of computationSun, 13 Nov 2011 12:25:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/13/t13212051545h8x71a7zxqeymd.htm/, Retrieved Thu, 28 Mar 2024 23:50:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=141815, Retrieved Thu, 28 Mar 2024 23:50:28 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [] [2010-11-16 18:44:21] [f3d662049ef6875ba0c96bb458434b66]
- RM      [Pearson Correlation] [] [2011-11-13 17:25:44] [583fc5a74bfa894f261a865501f20e1c] [Current]
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Dataseries X:
1280
1024
1120
1024
1280
1280
1280
1024
1280
1280
1280
1280
1280
1688
1440
1600
1280
1280
1280
1176
1280
1503
1440
1366
1280
1024
1280
2560
1280
1024
1280
1280
1440
1280
1440
1024
1440
1143
1280
1440
1280
1366
1024
1408
1366
1176
1920
1257
1280
1280
1440
1680
1440
1024
1140
1280
1280
1280
1280
1280
1440
1280
1152
1280
1280
1440
1280
1280
1440
1280
1280
1440
1280
1280
1600
1024
1366
1280
1280
1440
1366
1280
1024
1280
1440
1280
1280
1408
1280
1600
1600
1680
1440
1440
917
1280
1760
1280
1280
1280
1024
1366
1440
1280
1280
1920
1024
1024
1600
1117
1440
983
1024
1024
1280
1440
1280
1280
1280
1440
1280
1024
1024
1152
1280
1024
1366
1680
1680
1280
1366
1024
1440
1024
1280
1280
1280
1024
1280
Dataseries Y:
1024
768
700
768
800
1024
800
768
800
1024
800
800
1024
949
900
1200
800
800
768
735
800
845
900
768
768
768
800
1440
768
768
1024
800
900
800
900
768
900
857
800
900
800
768
768
880
768
735
1200
785
800
800
900
1050
900
768
641
1024
800
800
800
800
900
800
864
1024
800
900
800
1024
900
800
800
900
800
1024
900
768
768
800
800
900
768
800
768
800
900
800
800
880
800
900
900
1050
900
900
550
800
990
800
800
800
768
768
900
800
1024
1080
768
768
900
698
900
737
768
640
800
900
800
800
800
900
800
768
768
864
768
768
768
1050
1050
800
768
768
900
768
800
800
800
768
800




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141815&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=141815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141815&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1309.15107913669844.503597122302
Biased Variance45390.718182288712936.8686920967
Biased Standard Deviation213.050975548784113.740356479557
Covariance18734.6480033365
Correlation0.767558899807277
Determination0.589146664673358
T-Test14.0161451635828
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom137
Number of Observations139

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1309.15107913669 & 844.503597122302 \tabularnewline
Biased Variance & 45390.7181822887 & 12936.8686920967 \tabularnewline
Biased Standard Deviation & 213.050975548784 & 113.740356479557 \tabularnewline
Covariance & 18734.6480033365 \tabularnewline
Correlation & 0.767558899807277 \tabularnewline
Determination & 0.589146664673358 \tabularnewline
T-Test & 14.0161451635828 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 137 \tabularnewline
Number of Observations & 139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141815&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]1309.15107913669[/C][C]844.503597122302[/C][/ROW]
[ROW][C]Biased Variance[/C][C]45390.7181822887[/C][C]12936.8686920967[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]213.050975548784[/C][C]113.740356479557[/C][/ROW]
[ROW][C]Covariance[/C][C]18734.6480033365[/C][/ROW]
[ROW][C]Correlation[/C][C]0.767558899807277[/C][/ROW]
[ROW][C]Determination[/C][C]0.589146664673358[/C][/ROW]
[ROW][C]T-Test[/C][C]14.0161451635828[/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]137[/C][/ROW]
[ROW][C]Number of Observations[/C][C]139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=141815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141815&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
StatisticVariable XVariable Y
Mean1309.15107913669844.503597122302
Biased Variance45390.718182288712936.8686920967
Biased Standard Deviation213.050975548784113.740356479557
Covariance18734.6480033365
Correlation0.767558899807277
Determination0.589146664673358
T-Test14.0161451635828
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom137
Number of Observations139



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')