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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 computationSat, 20 Oct 2007 07:40:02 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/20/h5gjxdlo6jro7fq1192891080.htm/, Retrieved Thu, 02 May 2024 23:16:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1130, Retrieved Thu, 02 May 2024 23:16:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ5 juist
Estimated Impact420

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] [Q5 Relationship b...] [2007-10-20 14:40:02] [1a83104d28786df2e24859e2e02dc234] [Current]
F    D    [Pearson Correlation] [Q5 - relationship...] [2008-10-15 17:52:38] [a57f5cc542637534b8bb5bcb4d37eab1]
-    D    [Pearson Correlation] [Q5: Is there a re...] [2008-10-17 12:31:10] [1e1d8320a8a1170c475bf6e4ce119de6]
F    D    [Pearson Correlation] [Overeenkomst prod...] [2008-10-17 15:10:32] [cf45c678b7899ee33d7b061948f80651]
F    D    [Pearson Correlation] [Correlatie 3] [2008-10-17 21:30:07] [8b0d202c3a0c4ea223fd8b8e731dacd8]
-    D    [Pearson Correlation] [Correlatie kledin...] [2008-10-18 14:20:37] [d32f94eec6fe2d8c421bd223368a5ced]
F    D    [Pearson Correlation] [Correlation] [2008-10-19 09:04:04] [4396f984ebeab43316cd6baa88a4fd40]
F    D    [Pearson Correlation] [Investigating Ass...] [2008-10-19 09:32:23] [6743688719638b0cb1c0a6e0bf433315]
F    D    [Pearson Correlation] [Task 1 - Q5 - Rel...] [2008-10-19 11:36:12] [33f4701c7363e8b81858dafbf0350eed]
F    D    [Pearson Correlation] [Relatie tussen kl...] [2008-10-19 12:13:45] [93834488277b53a4510bfd06084ae13b]
F    D    [Pearson Correlation] [Task 3 Q5] [2008-10-19 13:48:37] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D    [Pearson Correlation] [Investigating ass...] [2008-10-19 14:37:25] [cbd3d88cd5aad6543e769146e7e26b0c]
F RM D    [Percentiles] [Investigating ass...] [2008-10-19 14:58:29] [cbd3d88cd5aad6543e769146e7e26b0c]
-    D    [Pearson Correlation] [controle: bestaat...] [2008-10-19 16:20:13] [5e74953d94072114d25d7276793b561e]
F    D    [Pearson Correlation] [Pearson] [2008-10-19 17:38:52] [8d78428855b119373cac369316c08983]
F    D    [Pearson Correlation] [Q5 Correlation] [2008-10-19 17:59:42] [2bd2ad6af3eef3a703e9ec23e39bd695]
F    D    [Pearson Correlation] [Q5 Pearson Correl...] [2008-10-20 09:40:59] [38f43994ada0e6172896e12525dcc585]
F    D    [Pearson Correlation] [q5 clothing prod ...] [2008-10-20 12:14:33] [dd679c9a7f849ed0333823e9c020c5a6]
F    D    [Pearson Correlation] [Correlatie produc...] [2008-10-20 13:21:35] [1d988b04e8982749ec309eda662241b4]
F R  D    [Pearson Correlation] [Correlatie produc...] [2008-10-20 13:23:02] [a7f04e0e73ce3683561193958d653479]
F    D    [Pearson Correlation] [Q5 Relationship b...] [2008-10-20 13:52:59] [e562c84ebfc887cc5a7a99782625ca3b]
F    D    [Pearson Correlation] [Samenhang product...] [2008-10-20 13:52:28] [1376d48f59a7212e8dd85a587491a69b]
-    D    [Pearson Correlation] [Correlation Cloth...] [2008-10-20 14:26:08] [43d870b30ac8a7afeb5de9ee11dcfc1a]
F R PD    [Pearson Correlation] [Q5 relatie tussen...] [2008-10-20 14:49:28] [84dda5145c389bd11bcc662bd33fe4ba]
F    D    [Pearson Correlation] [Q5: relatie tusse...] [2008-10-20 15:31:39] [82d201ca7b4e7cd2c6f885d29b5b6937]
F R  D    [Pearson Correlation] [taak 1 vraag 5 Ko...] [2008-10-20 15:34:21] [f21e40d80585aedc38277df87deba3c6]
F           [Pearson Correlation] [Pearson correlati...] [2008-10-20 17:32:51] [e242ef2117cdd06cb7827a9ae01189a0]
F    D    [Pearson Correlation] [Q5: Is there a re...] [2008-10-20 16:52:20] [fe7291e888d31b8c4db0b24d6c0f75c6]
F    D    [Pearson Correlation] [Q5 reproduce ] [2008-10-20 16:53:32] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F    D    [Pearson Correlation] [Q5 Pearson correl...] [2008-10-20 16:57:10] [2d4aec5ed1856c4828162be37be304d9]
F    D    [Pearson Correlation] [Back to back hist...] [2008-10-20 16:59:34] [b635de6fc42b001d22cbe6e730fec936]
F    D    [Pearson Correlation] [Pearson correlati...] [2008-10-20 17:14:42] [b82ef11dce0545f3fd4676ec3ebed828]
F    D    [Pearson Correlation] [Q5] [2008-10-20 17:33:36] [6f54f97492451bf8edc5dd186465ee4a]
F    D    [Pearson Correlation] [Q5: Is there a re...] [2008-10-20 17:47:39] [491a70d26f8c977398d8a0c1c87d3dd4]
F    D    [Pearson Correlation] [Q5-Pearson correl...] [2008-10-20 18:04:26] [b187fac1a1b0cb3920f54366df47fea3]
F    D    [Pearson Correlation] [Q4 Oplossing Prij...] [2008-10-20 18:04:58] [f9b9e85820b2a54b20380c3265aca831]
F    D    [Pearson Correlation] [Relatie tussen pr...] [2008-10-20 18:07:13] [23bfa928dab4b48567707937094f7011]
F    D    [Pearson Correlation] [Q5 Oplossing Kled...] [2008-10-20 18:16:25] [f9b9e85820b2a54b20380c3265aca831]
F    D    [Pearson Correlation] [correlatie] [2008-10-20 18:32:33] [7173087adebe3e3a714c80ea2417b3eb]
F    D    [Pearson Correlation] [task 1 Q5] [2008-10-20 18:54:49] [1e82cb4c98d4057b5653dbe7a07f2cda]
F RMPD    [Harrell-Davis Quantiles] [Q7 Oplossing 95% ...] [2008-10-20 18:43:37] [f9b9e85820b2a54b20380c3265aca831]
- RMPD    [Harrell-Davis Quantiles] [Taak 2 opdracht 1] [2008-10-20 19:19:08] [f9b9e85820b2a54b20380c3265aca831]
- RMPD    [Back to Back Histogram] [BtB-Histo Q8.1] [2008-10-20 19:50:37] [f9b9e85820b2a54b20380c3265aca831]
F    D    [Pearson Correlation] [Productie kleding...] [2008-10-20 20:02:18] [dff692ae32125bdbbfc005d665e23b83]
- R PD    [Pearson Correlation] [Correlatie Inflat...] [2008-10-20 20:19:33] [f9b9e85820b2a54b20380c3265aca831]
- R PD    [Pearson Correlation] [Correlatie Ruwe A...] [2008-10-20 20:24:13] [f9b9e85820b2a54b20380c3265aca831]
- R PD    [Pearson Correlation] [Correlatie Werklo...] [2008-10-20 20:27:09] [f9b9e85820b2a54b20380c3265aca831]
- R PD    [Pearson Correlation] [Correlatie Inflat...] [2008-10-20 20:31:40] [f9b9e85820b2a54b20380c3265aca831]
-   PD      [Pearson Correlation] [Paper 1ste Hypothese] [2008-12-15 20:49:30] [f9b9e85820b2a54b20380c3265aca831]

[Truncated]
Feedback Forum
2008-10-22 13:21:46 [Ellen Smolders] [reply] 
Het antwoord op de correlatie is juist, de verdere argumentatie niet.
De correlatie bedraagt 0.04, dit is minimaal, hier kunnen we uit besluiten dat er bijna geen verband bestaat tussen de kledingproductie en investeringen.
In zijn redenering vermeldt de student dat de investeringen een licht dalende trend vertonen en de productie een stijgende trend, dit is niet correct. Aan de hand van deze Correlatiegrafiek kunnen we niet afleiden welke trend de datasets vertonen omdat deze niet chronologisch geordend zijn.
  2008-10-23 11:24:31 [Bas van Keken] [reply] 
Waar heeft u deze argumentatie gevonden? In het document onder Q4 kan ik dit niet vinden.
2008-10-23 11:26:45 [Bas van Keken] [reply] 
De grafieken vertonen op het oog ook een kleine mate van overeenkomst. U kunt dit gebruiken in uw observaties.
  2008-10-23 13:18:28 [Dana Molenberghs] [reply] 
Er is inderdaad een overeenkomst, MAAR de 2 outliers bovenaan beinvloeden de correlatie gewoon erg hard. Je kan deze best wegwerken, dan zal je zien dat de correlatie zal stijgen (en het verband dus ook)
2008-10-23 13:36:27 [Peter Smolders] [reply] 
In haar conclusie heeft de student geen rekening gehouden met de outliers die het resultaat zeer sterk beïnvloeden. Het had beter geweest wanneer zij een gemiddelde had berekend van de waarden, waardoor de outliers konden worden weggewerkt.
2008-10-26 13:28:58 [Natascha Meeus] [reply] 
Het verband wordt inderdaad sterk beïnvloed door de twee outliers die zichtbaar zijn op het plot. (bovenaan links) Moesten deze er niet zijn dan kon mijn spreken van positieve correlatie en van een verband tussen de twee.
2008-10-26 14:55:03 [Steven Hulsmans] [reply] 
Er is inderdaad sprake van een zeer kleine correlatie. Maar de conclusie is niet correct. Zoals we op de grafiek kunnen zien liggen er links bovenaan 2 outliners. Deze 2 hebben een zeer sterke invloed op de correlatie, en wel in negatieve zin. Ze zorgen ervoor dat de correlatie 'uit mekaar getrokken wordt', waardoor de rechte gaat afbuigen, waardoor er sprake is van een zeer kleine mate van correlatie.
2008-10-27 18:30:19 [Jeroen Aerts] [reply] 
Er zijn sterke outliers,deze beïnvloeden het resultaat enorm, zonder deze outliers zou het resultaat 'juister' zijn.
2008-10-27 18:53:44 [Michaël De Kuyer] [reply] 
Deze vraag is fout beantwoord. Als men de scatter plot bekijkt, stelt men vast dat twee waarden er voor zorgen dat de correlatie laag is. Als men deze waarden buiten beschouwing laat, zal men vaststellen dat de correlatie veel groter is.
2008-10-27 19:56:11 [Evelyn Ongena] [reply] 
Ik sluit me aan bij dana. Door de ouliers weg te werken zal je een beter resultaat bekomen!
2008-10-27 20:15:07 [Dries Van Gheluwe] [reply] 
De correlatie wordt zoals in de les besproken sterk beinvloed door de twee ouliers in de grafiek
2008-10-28 06:52:33 [An De Koninck] [reply] 
Vraag 5 werd correct beantwoord, maar er werd geen uitleg gegeven. Misschien kon de student erbij verwijzen naar de productiecapaciteit. Een bedrijf weet immers wat er maandelijks geproduceerd wordt en kan ook seizoensschommelingen inschatten. De infrastructuur (dus machines en dergelijke) is hierop afgestemd, dus zal een stijging van de productie niet onmiddellijk meer investeringen teweegbrengen. Dit zal enkel gebeuren in uitzonderlijke situaties waarbij de productie zo erg stijgt dat de productiecapaciteit uitgebreid moet worden (dat is dan de overige 4%)


2008-10-28 07:10:23 [Evelyne Slegers] [reply] 
Het is inderdaad zo dat er een zeer zwakke correlatie is en dat dit komt door enkele outliers. De student spreekt ook van een stijgende en dalende trend voor productie en investering. Je kan echter hier niet zien of de productie en investering daalt of stijgt want de chronologie van de tijdreeks wordt niet behouden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109.20
88.60
94.30
98.30
86.40
80.60
104.10
108.20
93.40
71.90
94.10
94.90
96.40
91.10
84.40
86.40
88.00
75.10
109.70
103.00
82.10
68.00
96.40
94.30
90.00
88.00
76.10
82.50
81.40
66.50
97.20
94.10
80.70
70.50
87.80
89.50
99.60
84.20
75.10
92.00
80.80
73.10
99.80
90.00
83.10
72.40
78.80
87.30
91.00
80.10
73.60
86.40
74.50
71.20
92.40
81.50
85.30
69.90
84.20
90.70
100.30
Dataseries Y:
Download CSV
Histogram 
72,50
59,40
85,70
88,20
62,80
87,00
79,20
112,00
79,20
132,10
40,10
69,00
59,40
73,80
57,40
81,10
46,60
41,40
71,20
67,90
72,00
145,50
39,70
51,90
73,70
70,90
60,80
61,00
54,50
39,10
66,60
58,50
59,80
80,90
37,30
44,60
48,70
54,00
49,50
61,60
35,00
35,70
51,30
49,00
41,50
72,50
42,10
44,10
45,10
50,30
40,90
47,20
36,90
40,90
38,30
46,30
28,40
78,40
36,80
50,70
42,80

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1130&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1130&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean86.893442622950859.8491803278689
Biased Variance109.891760279495494.798892770761
Biased Standard Deviation10.482927085480222.2440754532698
Covariance10.0804945355191
Correlation0.0425212799870432
Determination0.00180805925173652
T-Test0.326907817024733
p-value (2 sided)0.744894582950829
p-value (1 sided)0.372447291475414
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 86.8934426229508 & 59.8491803278689 \tabularnewline
Biased Variance & 109.891760279495 & 494.798892770761 \tabularnewline
Biased Standard Deviation & 10.4829270854802 & 22.2440754532698 \tabularnewline
Covariance & 10.0804945355191 \tabularnewline
Correlation & 0.0425212799870432 \tabularnewline
Determination & 0.00180805925173652 \tabularnewline
T-Test & 0.326907817024733 \tabularnewline
p-value (2 sided) & 0.744894582950829 \tabularnewline
p-value (1 sided) & 0.372447291475414 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1130&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]86.8934426229508[/C][C]59.8491803278689[/C][/ROW]
[ROW][C]Biased Variance[/C][C]109.891760279495[/C][C]494.798892770761[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.4829270854802[/C][C]22.2440754532698[/C][/ROW]
[ROW][C]Covariance[/C][C]10.0804945355191[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0425212799870432[/C][/ROW]
[ROW][C]Determination[/C][C]0.00180805925173652[/C][/ROW]
[ROW][C]T-Test[/C][C]0.326907817024733[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.744894582950829[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.372447291475414[/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=1130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1130&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
Mean86.893442622950859.8491803278689
Biased Variance109.891760279495494.798892770761
Biased Standard Deviation10.482927085480222.2440754532698
Covariance10.0804945355191
Correlation0.0425212799870432
Determination0.00180805925173652
T-Test0.326907817024733
p-value (2 sided)0.744894582950829
p-value (1 sided)0.372447291475414
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')