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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 computationSun, 19 Dec 2010 17:18:44 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292779402ez5phf7e18lywgj.htm/, Retrieved Sun, 05 May 2024 06:14:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112650, Retrieved Sun, 05 May 2024 06:14:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD          [Pearson Correlation] [Petrol price - Pe...] [2010-12-19 17:18:44] [2e49bff66bb3e1f5d7fa8957e12fbb12] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
47.25
50.89
51.52
43.95
51.03
55.52
52.78
55.13
60.13
58.85
60.6
47.39
48.63
51.05
46.9
48.1
51.63
50.54
46.49
48.38
46.92
38.86
35.03
34.71
35.9
37.44
44.31
47.67
48.15
45.9
48.27
50.19
53.01
51.59
46.47
52.27
57.67
61.63
56.9
47.78
48.85
52.31
53.59
55.62
50.38
54.38
54.58
56.14
58.85
58.7
63.1
63.18
70.52
66.61
71.09
78.86
78.05
87.84
79.15
73.27
80.38
83.52
95.46
94.91
89.61
101.01
105.65
115.97
115.55
109.05
103.04
105.85
116.88
111.92
114.2
127.44
128.6
127.99
135.9
134.59
116.16
108.62
108.96
114.34
100.08
107.93
113.58
122.01
122.01
127.8
138.08
131.44
144.14
153.98
171.07
167.61
170.21
175.7
190.88
204.39
230.1
246.51
248.43
214.73
186.1
136.25
101.28
77.84
82.3
78.27
88
94.23
108.9
129.57
121.18
134.25
128.17
138.85
145.37
140.35
Dataseries Y:
Download CSV
Histogram 
175.348
154.439
136.186
113.662
106.157
100.546
98.314
118.179
112.295
126.938
130.92
181.279
180.389
146.917
150.597
124.222
101.554
102.138
110.315
111.015
105.017
119.888
127.623
149.415
159.755
139.737
136.283
101.952
104.044
96.712
100.665
103.699
103.765
122.732
127.297
160.278
191.784
155.375
142.616
115.331
102.136
95.205
101.566
105.273
117.394
121.148
116.666
154.841
177.74
154.427
133.159
118.102
101.361
101.345
102.233
108.522
101.939
118.405
125.06
178
167.714
143.582
139.259
104.674
103.722
106.153
106.21
113.986
96.906
107.512
112.616
148.507
130.48
137.436
128.21
97.552
91.55
83.104
84.68
85.98
84.891
89.896
94.835
115.348
131.284
134.701
127.193
87.077
72.744
77.542
78.005
85.329
86.041
96.384
116.678
160.672
152.364
144.936
122.974
94.456
82.491
84.89
85.277
81.206
71.012
87.302
97.427
133.242
137.064
119.042
116.47
96.028
79.281
73.872
80.964
86.739
89.997
96.292
101.355
136.543

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 Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112650&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112650&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112650&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 Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean92.1640833333333116.329808333333
Biased Variance2291.19895249306729.441164088264
Biased Standard Deviation47.866470023316527.0081684697105
Covariance-543.546254420868
Correlation-0.416942040706666
Determination0.173840665308639
T-Test-4.98292997658462
p-value (2 sided)2.16764169750822e-06
p-value (1 sided)1.08382084875411e-06
Degrees of Freedom118
Number of Observations120

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 92.1640833333333 & 116.329808333333 \tabularnewline
Biased Variance & 2291.19895249306 & 729.441164088264 \tabularnewline
Biased Standard Deviation & 47.8664700233165 & 27.0081684697105 \tabularnewline
Covariance & -543.546254420868 \tabularnewline
Correlation & -0.416942040706666 \tabularnewline
Determination & 0.173840665308639 \tabularnewline
T-Test & -4.98292997658462 \tabularnewline
p-value (2 sided) & 2.16764169750822e-06 \tabularnewline
p-value (1 sided) & 1.08382084875411e-06 \tabularnewline
Degrees of Freedom & 118 \tabularnewline
Number of Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112650&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]92.1640833333333[/C][C]116.329808333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2291.19895249306[/C][C]729.441164088264[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]47.8664700233165[/C][C]27.0081684697105[/C][/ROW]
[ROW][C]Covariance[/C][C]-543.546254420868[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.416942040706666[/C][/ROW]
[ROW][C]Determination[/C][C]0.173840665308639[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.98292997658462[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.16764169750822e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.08382084875411e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]118[/C][/ROW]
[ROW][C]Number of Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112650&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112650&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
Mean92.1640833333333116.329808333333
Biased Variance2291.19895249306729.441164088264
Biased Standard Deviation47.866470023316527.0081684697105
Covariance-543.546254420868
Correlation-0.416942040706666
Determination0.173840665308639
T-Test-4.98292997658462
p-value (2 sided)2.16764169750822e-06
p-value (1 sided)1.08382084875411e-06
Degrees of Freedom118
Number of Observations120


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')