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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, 01 Sep 2014 17:54:32 +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/Sep/01/t1409590597wfe5t26ou1dgmld.htm/, Retrieved Sat, 11 May 2024 04:26:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235782, Retrieved Sat, 11 May 2024 04:26:36 +0000
QR Codes:

Original text written by user:X = Overall Federal Taxation as percent of GDP 1913-2013 Y = Indexed consumer prices 1913-2013
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Taxation v Cost o...] [2014-09-01 16:54:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.43
2.53
2.14
1.77
2.03
5.28
7.2
8.27
8.32
5.75
4.96
4.9
4.43
4.31
4.63
4.4
4.1
5.24
5.14
4.43
5.7
5.82
6.1
6.1
6.67
8.27
7.61
6.8
7.29
9.68
13.43
22.88
23.31
20.37
17.86
17.2
16.19
14.5
16.33
19.53
19.05
19.39
16.87
18.06
18.33
17.84
16.36
18.37
17.99
16.47
16.69
16.42
15.71
16.05
17.27
16.23
18.32
17.92
16.02
16.17
16.16
17
16.52
15.87
17.05
16.95
17.6
18.07
18.66
18.47
16.51
16.49
16.89
16.76
17.54
17.31
17.52
17.26
17.09
16.69
16.78
17.22
17.64
17.94
18.35
18.94
18.91
19.68
18.74
16.88
15.48
15.31
16.45
17.37
17.73
17.15
14.6
14.46
14.83
15.08
16.52
Dataseries Y:
Download CSV
Histogram 
29.7
30.1
30.4
32.7
38.4
45.1
51.8
60.0
53.6
50.2
51.1
51.2
52.5
53.0
52.0
51.3
51.3
50.0
45.6
40.9
38.8
40.1
41.1
41.5
43.0
42.2
41.6
42.0
44.1
48.8
51.8
52.7
53.9
58.5
66.9
72.1
71.4
72.1
77.8
79.5
80.1
80.5
80.2
81.4
84.3
86.6
87.3
88.7
89.6
90.6
91.7
92.9
94.5
97.2
100.0
104.2
109.8
116.3
121.3
125.3
133.1
147.7
161.2
170.5
181.5
195.3
217.7
247.0
272.3
288.6
297.4
307.6
318.5
323.4
335.0
348.4
365.2
384.4
399.9
411.5
423.1
433.8
446.1
459.1
469.3
475.6
486.2
503.1
516.8
523.9
535.6
549.5
568.9
587.2
603.982
628.661
624.423
637.342
660.005
673.868
683.087

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235782&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235782&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'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13.7415841584158206.921465346535
Biased Variance32.40068659935340147.9689427636
Biased Standard Deviation5.692160099589200.369580881839
Covariance526.721702055446
Correlation0.457247081696597
Determination0.209074893720055
T-Test5.11565041692956
p-value (2 sided)1.53314715678476e-06
p-value (1 sided)7.66573578392382e-07
Degrees of Freedom99
Number of Observations101

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13.7415841584158 & 206.921465346535 \tabularnewline
Biased Variance & 32.400686599353 & 40147.9689427636 \tabularnewline
Biased Standard Deviation & 5.692160099589 & 200.369580881839 \tabularnewline
Covariance & 526.721702055446 \tabularnewline
Correlation & 0.457247081696597 \tabularnewline
Determination & 0.209074893720055 \tabularnewline
T-Test & 5.11565041692956 \tabularnewline
p-value (2 sided) & 1.53314715678476e-06 \tabularnewline
p-value (1 sided) & 7.66573578392382e-07 \tabularnewline
Degrees of Freedom & 99 \tabularnewline
Number of Observations & 101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235782&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]13.7415841584158[/C][C]206.921465346535[/C][/ROW]
[ROW][C]Biased Variance[/C][C]32.400686599353[/C][C]40147.9689427636[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.692160099589[/C][C]200.369580881839[/C][/ROW]
[ROW][C]Covariance[/C][C]526.721702055446[/C][/ROW]
[ROW][C]Correlation[/C][C]0.457247081696597[/C][/ROW]
[ROW][C]Determination[/C][C]0.209074893720055[/C][/ROW]
[ROW][C]T-Test[/C][C]5.11565041692956[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.53314715678476e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]7.66573578392382e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]99[/C][/ROW]
[ROW][C]Number of Observations[/C][C]101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235782&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
Mean13.7415841584158206.921465346535
Biased Variance32.40068659935340147.9689427636
Biased Standard Deviation5.692160099589200.369580881839
Covariance526.721702055446
Correlation0.457247081696597
Determination0.209074893720055
T-Test5.11565041692956
p-value (2 sided)1.53314715678476e-06
p-value (1 sided)7.66573578392382e-07
Degrees of Freedom99
Number of Observations101






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 13.8028, p-value = 0.001006
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 17.9083, p-value = 0.0001292
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.5487, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.7776, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 13.8028, p-value = 0.001006
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 17.9083, p-value = 0.0001292
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.5487, p-value < 2.2e-16

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.7776, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235782&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 13.8028, p-value = 0.001006
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 17.9083, p-value = 0.0001292
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 8.5487, p-value < 2.2e-16

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 8.7776, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235782&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235782&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 = 13.8028, p-value = 0.001006
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 17.9083, p-value = 0.0001292
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 8.5487, p-value < 2.2e-16

> ad.y
	Anderson-Darling normality test
data:  y
A = 8.7776, p-value < 2.2e-16


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()