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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSun, 19 Oct 2008 12:12:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t1224439981atj1crr2mdga033.htm/, Retrieved Wed, 29 May 2024 04:52:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17020, Retrieved Wed, 29 May 2024 04:52:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Correlatie inflat...] [2008-10-19 18:12:13] [7f3f68cb5622d7511b280fd3e248ef1b] [Current]
Feedback Forum
2008-10-23 10:30:12 [Ellen Smolders] [reply] 
De student heeft het juiste antwoord gegeven. De correlatie bedraagt -0.401, dit is een negatieve correlatie die sterk aanleunt bij 0, dit betekent dat er eerder geen lineair verband is. Op de correlatiegrafiek bevinden de waarden zich overal op het veld zodat we ook visueel kunnen vaststellen dat er geen verband is tussen de twee datasets.
2008-10-24 14:16:48 [Stijn Van de Velde] [reply] 
Hier bekomt men een negatieve correlatie van 40%. Dit is wederom bijna de helft, waardoor de inflatie en werkloosheid toch voor een deel met elkaar worden geassocieerd.

In de praktijk wil dit zeggen dat wanner de inflatie stijgt, de werkloosheid gedeeltelijk daalt.
2008-10-26 13:52:32 [Natascha Meeus] [reply] 
Het antwoord is correct. Men bekomt hier een negatieve correlatie van -0.40. Hier kan men spreke over een matig verband tussen de inflatie en de werkloosheid.
2008-10-27 16:19:14 [Bonifer Spillemaeckers] [reply] 
De bekomen correlatie is hier negatief. We kunnen dus spreken van een matig verband tussen de 2 reeksen.
2008-10-27 19:31:59 [Jan Helsen] [reply] 
Het is hier inderdaag niet correct om te zeggen dat er geen verband is. Hoewel de correlatie negatief is ( en deze dichter bij 0 aanleunt) is er toch een klein 'omgekeerd' verband tussen beide datareeksen.

Op de grafiek kun je dit zien door de dalende rechten die je kan trekken.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,80
1,60
1,90
1,70
1,60
1,30
1,10
1,90
2,60
2,30
2,40
2,20
2,00
2,90
2,60
2,30
2,30
2,60
3,10
2,80
2,50
2,90
3,10
3,10
3,20
2,50
2,60
2,90
2,60
2,40
1,70
2,00
2,20
1,90
1,60
1,60
1,20
1,20
1,50
1,60
1,70
1,80
1,80
1,80
1,30
1,30
1,40
1,10
1,50
2,20
2,90
3,10
3,50
3,60
4,40
4,20
5,20
5,80
5,90
5,40
5,50
Dataseries Y:
Download CSV
Histogram 
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17020&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17020&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.50327868852459562.393442622951
Biased Variance1.365890889545821572.27143241064
Biased Standard Deviation1.1687133478940939.6518780439293
Covariance-18.9063114754098
Correlation-0.401288263363169
Determination0.161032270313028
T-Test-3.36519190543198
p-value (2 sided)0.00134971622764770
p-value (1 sided)0.000674858113823849
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.50327868852459 & 562.393442622951 \tabularnewline
Biased Variance & 1.36589088954582 & 1572.27143241064 \tabularnewline
Biased Standard Deviation & 1.16871334789409 & 39.6518780439293 \tabularnewline
Covariance & -18.9063114754098 \tabularnewline
Correlation & -0.401288263363169 \tabularnewline
Determination & 0.161032270313028 \tabularnewline
T-Test & -3.36519190543198 \tabularnewline
p-value (2 sided) & 0.00134971622764770 \tabularnewline
p-value (1 sided) & 0.000674858113823849 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17020&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]2.50327868852459[/C][C]562.393442622951[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.36589088954582[/C][C]1572.27143241064[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.16871334789409[/C][C]39.6518780439293[/C][/ROW]
[ROW][C]Covariance[/C][C]-18.9063114754098[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.401288263363169[/C][/ROW]
[ROW][C]Determination[/C][C]0.161032270313028[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.36519190543198[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00134971622764770[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000674858113823849[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17020&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.50327868852459562.393442622951
Biased Variance1.365890889545821572.27143241064
Biased Standard Deviation1.1687133478940939.6518780439293
Covariance-18.9063114754098
Correlation-0.401288263363169
Determination0.161032270313028
T-Test-3.36519190543198
p-value (2 sided)0.00134971622764770
p-value (1 sided)0.000674858113823849
Degrees of Freedom59
Number of Observations61


Figures (Output of Computation)

Input Parameters & R Code

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')