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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, 31 Aug 2014 15:06:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/31/t1409494058v4iukr9b83dd1dn.htm/, Retrieved Wed, 15 May 2024 13:01:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235781, Retrieved Wed, 15 May 2024 13:01:48 +0000
QR Codes:

Original text written by user:Real (2009) Revenue vs Men's unemployment the following year.
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Revenue vs unempl...] [2014-08-31 14:06:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
347.01
324.85
316.36
385.13
479.12
489.38
495.3
461.73
504.76
523.15
505.44
495.27
570.51
573.02
556.76
588.55
612.57
624.04
679.84
751.48
740.88
862.65
845.44
780.89
829.11
875.4
916.08
888.96
899.97
1010.87
1061.45
1136.95
1164
1233.78
1197.54
1119.99
1200.24
1281.01
1315.76
1425.02
1465.38
1537.54
1543.8
1527.45
1544.66
1596.04
1703.88
1792.69
1892.42
2022.15
2180.96
2282.28
2473.05
2376.94
2178.78
2054.45
2109.36
2341.12
2538.4
2638.3
2543.42
2104.99
2136.84
2232.08
2333.43
2603.53
Dataseries Y:
Download CSV
Histogram 
6.2
4.4
2.4
2.7
2.2
5.1
3.4
3.4
3.4
7.0
4.3
4.7
6.0
4.6
4.3
3.7
3.1
2.5
2.3
2.1
2.1
3.7
4.3
4.0
3.1
3.6
7.0
6.0
5.1
4.1
4.1
6.8
5.9
8.9
8.8
6.5
6.2
6.3
5.4
4.6
4.4
4.9
6.5
7.2
6.5
5.5
4.8
4.6
4.0
3.9
3.6
3.3
4.1
5.3
5.9
5.0
4.2
4.1
4.2
5.4
9.8
9.6
8.8
7.7
7.0
5.7

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=235781&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=235781&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235781&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
Mean1285.215151515155.00454545454545
Biased Variance508028.7160158863.29770661157025
Biased Standard Deviation712.7613317344641.8159588683586
Covariance492.991191608392
Correlation0.375109827789816
Determination0.140707382904505
T-Test3.23726229885779
p-value (2 sided)0.00191345163918388
p-value (1 sided)0.000956725819591941
Degrees of Freedom64
Number of Observations66

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1285.21515151515 & 5.00454545454545 \tabularnewline
Biased Variance & 508028.716015886 & 3.29770661157025 \tabularnewline
Biased Standard Deviation & 712.761331734464 & 1.8159588683586 \tabularnewline
Covariance & 492.991191608392 \tabularnewline
Correlation & 0.375109827789816 \tabularnewline
Determination & 0.140707382904505 \tabularnewline
T-Test & 3.23726229885779 \tabularnewline
p-value (2 sided) & 0.00191345163918388 \tabularnewline
p-value (1 sided) & 0.000956725819591941 \tabularnewline
Degrees of Freedom & 64 \tabularnewline
Number of Observations & 66 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235781&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]1285.21515151515[/C][C]5.00454545454545[/C][/ROW]
[ROW][C]Biased Variance[/C][C]508028.716015886[/C][C]3.29770661157025[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]712.761331734464[/C][C]1.8159588683586[/C][/ROW]
[ROW][C]Covariance[/C][C]492.991191608392[/C][/ROW]
[ROW][C]Correlation[/C][C]0.375109827789816[/C][/ROW]
[ROW][C]Determination[/C][C]0.140707382904505[/C][/ROW]
[ROW][C]T-Test[/C][C]3.23726229885779[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00191345163918388[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000956725819591941[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]64[/C][/ROW]
[ROW][C]Number of Observations[/C][C]66[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235781&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235781&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
Mean1285.215151515155.00454545454545
Biased Variance508028.7160158863.29770661157025
Biased Standard Deviation712.7613317344641.8159588683586
Covariance492.991191608392
Correlation0.375109827789816
Determination0.140707382904505
T-Test3.23726229885779
p-value (2 sided)0.00191345163918388
p-value (1 sided)0.000956725819591941
Degrees of Freedom64
Number of Observations66






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7256, p-value = 0.05711
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.1059, p-value = 0.07785
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8085, p-value = 0.0001126

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7877, p-value = 0.03898


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7256, p-value = 0.05711
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.1059, p-value = 0.07785
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8085, p-value = 0.0001126

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7877, p-value = 0.03898

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235781&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7256, p-value = 0.05711
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.1059, p-value = 0.07785
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8085, p-value = 0.0001126

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7877, p-value = 0.03898

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235781&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235781&T=2

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


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

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.7256, p-value = 0.05711
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 5.1059, p-value = 0.07785
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.8085, p-value = 0.0001126

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.7877, p-value = 0.03898


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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, sub=main)
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', na.rm = T)
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')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()