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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 computationWed, 28 Oct 2009 10:45:00 -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/2009/Oct/28/t1256748356nf82hdpc8cno0gv.htm/, Retrieved Mon, 06 May 2024 06:54:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51540, Retrieved Mon, 06 May 2024 06:54:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD    [Pearson Correlation] [WS4 Pearson X²] [2009-10-28 16:45:00] [557d56ec4b06cd0135c259898de8ce95] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98101950.13
187968318.5
188999043.8
210743289
230609073.9
130468610.9
190983186.8
162537001
262991089
175244644
153536881
218451087.3
116973495.2
218177896.1
139972561
142356218
112613295.5
253547719.2
123096251.3
262749137.1
102010000
147614906.3
135590955.4
85561526.32
80654369.49
104950319.4
155190863.4
177088669.1
117497470.1
139892713.1
119376190.6
113962030.1
86439787.29
108851881.9
150342218.5
119054770.4
87131416.39
135840396.2
122766400
96828411.45
55486359.51
69933078.76
71667060.61
67583576.24
108844643.7
72887198.76
72854150.57
63959435
39707815.79
57692632.99
51846967.98
37853044.1
36775240.36
52851578.19
43275872.83
59417285.63
40974770.56
49590376.35
68830403.8
92416177.78
Dataseries Y:
Download CSV
Histogram 
10284.5
12792
12823.61538
13845.66667
15335.63636
11188.5
13633.25
12298.46667
15353.63636
12696.15385
12213.93333
13683.72727
11214.14286
13950.23077
11179.13333
11801.875
11188.82353
16456.27273
11110.0625
16530.69231
10038.41176
11681.25
11148.88235
8631
9386.444444
9764.736842
12043.75
12948.06667
10987.125
11648.3125
10633.35294
10219.3
9037.6
10296.31579
11705.41176
10681.94444
9362.947368
11306.35294
10984.45
10062.61905
8118.583333
8867.48
8346.72
8529.307692
10697.18182
8591.84
8695.607143
8125.571429
7009.758621
7883.466667
7527.645161
6763.758621
6682.333333
7855.681818
6738.88
7895.434783
6361.884615
6935.956522
8344.454545
9107.944444

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51540&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51540&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean119686895.22810520.46805535
Biased Variance35074848761402866017024.77834778
Biased Standard Deviation59224022.79599292452.96244943696
Covariance145611030936.825
Correlation0.985612571913441
Determination0.971432141913828
T-Test44.4100632141349
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 119686895.228 & 10520.46805535 \tabularnewline
Biased Variance & 3507484876140286 & 6017024.77834778 \tabularnewline
Biased Standard Deviation & 59224022.7959929 & 2452.96244943696 \tabularnewline
Covariance & 145611030936.825 \tabularnewline
Correlation & 0.985612571913441 \tabularnewline
Determination & 0.971432141913828 \tabularnewline
T-Test & 44.4100632141349 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51540&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]119686895.228[/C][C]10520.46805535[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3507484876140286[/C][C]6017024.77834778[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]59224022.7959929[/C][C]2452.96244943696[/C][/ROW]
[ROW][C]Covariance[/C][C]145611030936.825[/C][/ROW]
[ROW][C]Correlation[/C][C]0.985612571913441[/C][/ROW]
[ROW][C]Determination[/C][C]0.971432141913828[/C][/ROW]
[ROW][C]T-Test[/C][C]44.4100632141349[/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]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51540&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
Mean119686895.22810520.46805535
Biased Variance35074848761402866017024.77834778
Biased Standard Deviation59224022.79599292452.96244943696
Covariance145611030936.825
Correlation0.985612571913441
Determination0.971432141913828
T-Test44.4100632141349
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60


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')