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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 computationMon, 20 Oct 2008 13:50:07 -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/20/t1224532291ydnz0g5vuoqma0l.htm/, Retrieved Wed, 29 May 2024 06:41:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18008, Retrieved Wed, 29 May 2024 06:41:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [Pearson Correlati...] [2008-10-20 19:50:07] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
Feedback Forum
2008-10-23 20:33:48 [Kenny Simons] [reply] 
Onze correlatie ligt hier bijna tegen 1, wat wil zeggen dat er een positief verband is tussen deze 2 reeksen. Als we naar de scatter plot kijken, merken we op dat we een oplopende rechte kunnen tekenen, doorheen de observaties. Er is dus een positief verband tussen de invoer van België en in de invoer van het Vlaams Gewest. Als de invoer van België dus toeneemt, dan komt dit omdat het Vlaamse Geweest meer ingevoert heeft gedurende een bepaalde periode.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14433,5
13691,5
14194,1
13519,2
11857,9
14616
15643,4
14077,3
14887,5
14159,9
14643
17192,4
15386,1
14287,1
17526,6
14497
14398,3
16629,6
16670,7
16614,8
16869,2
15663,9
16359,9
18447,7
16889
16505
18320,9
15052,1
15699,8
18135,3
16768,7
18883
19021
18101,9
17776,1
21489,9
17065,3
18690
18953,1
16398,9
16895,6
18553
19270
19422,1
17579,4
18637,3
18076,7
20438,6
18075,2
19563
19899,2
19227,5
17789,6
19220,8
22058,6
21230,8
19504,4
23913,1
23165,7
23574,3
Dataseries Y:
Download CSV
Histogram 
11447,5
10849,2
11337,3
10713,6
9505,1
11704,2
12459,3
11180,7
11710,8
11200,1
11485,9
13675,8
12386,4
11420,2
14157,6
11729,6
11661,7
13465,5
13518,6
13300,1
13258,7
12949,8
13545
15344,9
14069,1
13796,5
15273,2
12581
13082,5
15142,5
13803,7
15624,5
15683,9
14983
14737,6
17785,3
14183,6
15574,7
15647,8
13674,7
14021,7
15367,7
15993,9
16174,2
14520,6
15429,3
14982,7
16939,8
15046,2
16441
16569,5
15961,8
14902
15802,1
18391,3
17709,7
16058
19816,8
19341,3
19676

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18008&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]4 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=18008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18008&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17435.191666666714313.28
Biased Variance6585248.487763895279445.68626667
Biased Standard Deviation2566.173900530492297.70443840514
Covariance5975022.08576271
Correlation0.996460365956866
Determination0.992933260922892
T-Test90.2743765965842
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17435.1916666667 & 14313.28 \tabularnewline
Biased Variance & 6585248.48776389 & 5279445.68626667 \tabularnewline
Biased Standard Deviation & 2566.17390053049 & 2297.70443840514 \tabularnewline
Covariance & 5975022.08576271 \tabularnewline
Correlation & 0.996460365956866 \tabularnewline
Determination & 0.992933260922892 \tabularnewline
T-Test & 90.2743765965842 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18008&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]17435.1916666667[/C][C]14313.28[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6585248.48776389[/C][C]5279445.68626667[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2566.17390053049[/C][C]2297.70443840514[/C][/ROW]
[ROW][C]Covariance[/C][C]5975022.08576271[/C][/ROW]
[ROW][C]Correlation[/C][C]0.996460365956866[/C][/ROW]
[ROW][C]Determination[/C][C]0.992933260922892[/C][/ROW]
[ROW][C]T-Test[/C][C]90.2743765965842[/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]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18008&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
Mean17435.191666666714313.28
Biased Variance6585248.487763895279445.68626667
Biased Standard Deviation2566.173900530492297.70443840514
Covariance5975022.08576271
Correlation0.996460365956866
Determination0.992933260922892
T-Test90.2743765965842
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60


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')