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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 computationThu, 24 Nov 2011 17:50:02 -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/24/t1322175046gy48hm0bxe7icd8.htm/, Retrieved Fri, 19 Apr 2024 18:31:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147229, Retrieved Fri, 19 Apr 2024 18:31:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [DJ/Nikkei] [2011-11-24 22:50:02] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10539.51
10723.78
10682.06
10283.19
10377.18
10486.64
10545.38
10554.27
10532.54
10324.31
10695.25
10827.81
10872.48
10971.19
11145.65
11234.68
11333.88
10997.97
11036.89
11257.35
11533.59
11963.12
12185.15
12377.62
12512.89
12631.48
12268.53
12754.8
13407.75
13480.21
13673.28
13239.71
13557.69
13901.28
13200.58
13406.97
12538.12
12419.57
12193.88
12656.63
12812.48
12056.67
11322.38
11530.75
11114.08
9181.73
8614.55
8595.56
8396.2
7690.5
7235.47
7992.12
8398.37
8593
8679.75
9374.63
9634.97
9857.34
10238.83
10433.44
10471.24
Dataseries Y:
Download CSV
Histogram 
11394,84
11545,71
11809,38
11395,64
11082,38
11402,75
11716,87
12204,98
12986,62
13392,79
14368,05
15650,83
16102,64
16187,64
16311,54
17232,97
16397,83
14990,31
15147,55
15786,78
15934,09
16519,44
16101,07
16775,08
17286,32
17741,23
17128,37
17460,53
17611,14
18001,37
17974,77
16460,95
16235,39
16903,36
15543,76
15532,18
13731,31
13547,84
12602,93
13357,7
13995,33
14084,6
13168,91
12989,35
12123,53
9117,03
8531,45
8460,94
8331,49
7694,78
7764,58
8767,96
9304,43
9810,31
9691,12
10430,35
10302,87
10066,24
9633,83
10169,02
10661,62

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147229&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147229&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean11041.785573770513355.0273770492
Biased Variance2636081.30745099449607.97698328
Biased Standard Deviation1623.60133883013074.02146657815
Covariance4345874.7377482
Correlation0.856470330762995
Determination0.733541427477274
T-Test12.7445199182099
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 11041.7855737705 & 13355.0273770492 \tabularnewline
Biased Variance & 2636081.3074509 & 9449607.97698328 \tabularnewline
Biased Standard Deviation & 1623.6013388301 & 3074.02146657815 \tabularnewline
Covariance & 4345874.7377482 \tabularnewline
Correlation & 0.856470330762995 \tabularnewline
Determination & 0.733541427477274 \tabularnewline
T-Test & 12.7445199182099 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147229&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]11041.7855737705[/C][C]13355.0273770492[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2636081.3074509[/C][C]9449607.97698328[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1623.6013388301[/C][C]3074.02146657815[/C][/ROW]
[ROW][C]Covariance[/C][C]4345874.7377482[/C][/ROW]
[ROW][C]Correlation[/C][C]0.856470330762995[/C][/ROW]
[ROW][C]Determination[/C][C]0.733541427477274[/C][/ROW]
[ROW][C]T-Test[/C][C]12.7445199182099[/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]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147229&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
Mean11041.785573770513355.0273770492
Biased Variance2636081.30745099449607.97698328
Biased Standard Deviation1623.60133883013074.02146657815
Covariance4345874.7377482
Correlation0.856470330762995
Determination0.733541427477274
T-Test12.7445199182099
p-value (2 sided)0
p-value (1 sided)0
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')