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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 20 Oct 2008 11:42:53 -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/t1224524632ct9fhjkpncg13jr.htm/, Retrieved Sun, 19 May 2024 16:36:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17774, Retrieved Sun, 19 May 2024 16:36:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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 tussen...] [2008-10-20 17:42:53] [db9a5fd0f9c3e1245d8075d8bb09236d] [Current]
Feedback Forum
2008-10-22 19:47:47 [Michaël De Kuyer] [reply] 
In het antwoord vind ik ook geen blijk van kritiek. Er zijn ook geen externe bronnen geraadpleegd om deze trend te bespreken. De correlatie die je hebt besproken is wel correct. Er is inderdaad een sterke correlatie tussen de invoer en de uitvoer van België. Ook hier is er geen besluit getrokken. Misschien kan je besluiten dat België een open of gesloten economie is?
2008-10-23 18:31:58 [Ciska Tanghe] [reply] 
De berekening van de correlatie klopt volledig. Helaas heeft de student zich beperkt tot het bespreken van de correlatie tussen slechts twee tijdreeksen. Er zijn meerdere berekeningen voor handen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
42142.2
43132
41787.8
46750.5
46743.5
45353.7
41891.5
43503.6
44355.8
45864
42867.9
45672.9
45492.1
45797.2
43089.1
46556.4
47793
49670.2
47602.5
51996.8
51698.3
53634.6
50601.8
54876.9
56339.7
56404.9
53204.9
57236.7
58848.9
59262.1
57189.2
60739.3
65855
66902.3
Dataseries Y:
Download CSV
Histogram 
40770.7
41163.5
40149.5
46065.6
45937.7
44393.1
39296.2
41327.3
41685.8
42613.8
39684
44408.5
44054.9
42319.1
39993.1
44608.1
45995.4
47199.8
45524.9
50154.7
50471.5
51714.9
48887.2
54672.7
57367.9
54708.4
51847.6
56271.5
57152.6
57537.4
56237.9
62793.8
70653.1
71014.5

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=17774&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=17774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17774&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
Mean50319.332352941249078.7264705882
Biased Variance47256922.437482768754455.4148875
Biased Standard Deviation6874.367057226638291.83064316244
Covariance58105392.8200267
Correlation0.989391838531633
Determination0.978896210153006
T-Test38.5268130899517
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom32
Number of Observations34

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 50319.3323529412 & 49078.7264705882 \tabularnewline
Biased Variance & 47256922.4374827 & 68754455.4148875 \tabularnewline
Biased Standard Deviation & 6874.36705722663 & 8291.83064316244 \tabularnewline
Covariance & 58105392.8200267 \tabularnewline
Correlation & 0.989391838531633 \tabularnewline
Determination & 0.978896210153006 \tabularnewline
T-Test & 38.5268130899517 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 32 \tabularnewline
Number of Observations & 34 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17774&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]50319.3323529412[/C][C]49078.7264705882[/C][/ROW]
[ROW][C]Biased Variance[/C][C]47256922.4374827[/C][C]68754455.4148875[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6874.36705722663[/C][C]8291.83064316244[/C][/ROW]
[ROW][C]Covariance[/C][C]58105392.8200267[/C][/ROW]
[ROW][C]Correlation[/C][C]0.989391838531633[/C][/ROW]
[ROW][C]Determination[/C][C]0.978896210153006[/C][/ROW]
[ROW][C]T-Test[/C][C]38.5268130899517[/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]32[/C][/ROW]
[ROW][C]Number of Observations[/C][C]34[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17774&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
Mean50319.332352941249078.7264705882
Biased Variance47256922.437482768754455.4148875
Biased Standard Deviation6874.367057226638291.83064316244
Covariance58105392.8200267
Correlation0.989391838531633
Determination0.978896210153006
T-Test38.5268130899517
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom32
Number of Observations34


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')