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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 computationMon, 20 Oct 2008 12:10:48 -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/2008/Oct/20/t1224526280b5bfqunkmx7r5lt.htm/, Retrieved Sun, 19 May 2024 15:20:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17827, Retrieved Sun, 19 May 2024 15:20:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Correlatie Vlaand...] [2008-10-20 18:10:48] [bda7fba231d49184c6a1b627868bbb81] [Current]
Feedback Forum
2008-10-23 09:24:45 [Ellen Smolders] [reply] 
De student gaf het juiste antwoord. De correlatie bedraagt inderdaad 71.23%. Dit is nog steeds een gemiddeld positief lineair verband. Men kan inderdaad de werkloosheid in Vlaanderen en in Brussel deels relateren.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
189917
184128
175335
179566
181140
177876
175041
169292
166070
166972
206348
215706
202108
195411
193111
195198
198770
194163
190420
189733
186029
191531
232571
243477
227247
217859
208679
213188
216234
213587
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
Dataseries Y:
Download CSV
Histogram 
72157
72928
75340
74812
74593
76003
75112
75452
75634
75653
78645
73100
79699
82848
81834
81736
82267
84120
83819
82734
81842
81735
83227
81934
89521
88827
85874
85211
87130
88620
89563
89056
88542
89504
89428
86040
96240
94423
93028
92285
91685
94260
93858
92437
92980
92099
92803
88551
98334
98329
96455
97109
97687
98512
98673
96028
98014
95580
97838
97760
99913

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17827&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17827&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean213089.26229508287367.5573770492
Biased Variance591345696.45579166360480.1155603
Biased Standard Deviation24317.60054889868146.19421052312
Covariance143456285.801366
Correlation0.712304220767885
Determination0.507377302923744
T-Test7.79532658705887
p-value (2 sided)1.21483711978954e-10
p-value (1 sided)6.07418559894768e-11
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 213089.262295082 & 87367.5573770492 \tabularnewline
Biased Variance & 591345696.455791 & 66360480.1155603 \tabularnewline
Biased Standard Deviation & 24317.6005488986 & 8146.19421052312 \tabularnewline
Covariance & 143456285.801366 \tabularnewline
Correlation & 0.712304220767885 \tabularnewline
Determination & 0.507377302923744 \tabularnewline
T-Test & 7.79532658705887 \tabularnewline
p-value (2 sided) & 1.21483711978954e-10 \tabularnewline
p-value (1 sided) & 6.07418559894768e-11 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17827&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]213089.262295082[/C][C]87367.5573770492[/C][/ROW]
[ROW][C]Biased Variance[/C][C]591345696.455791[/C][C]66360480.1155603[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]24317.6005488986[/C][C]8146.19421052312[/C][/ROW]
[ROW][C]Covariance[/C][C]143456285.801366[/C][/ROW]
[ROW][C]Correlation[/C][C]0.712304220767885[/C][/ROW]
[ROW][C]Determination[/C][C]0.507377302923744[/C][/ROW]
[ROW][C]T-Test[/C][C]7.79532658705887[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.21483711978954e-10[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.07418559894768e-11[/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=17827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17827&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
Mean213089.26229508287367.5573770492
Biased Variance591345696.45579166360480.1155603
Biased Standard Deviation24317.60054889868146.19421052312
Covariance143456285.801366
Correlation0.712304220767885
Determination0.507377302923744
T-Test7.79532658705887
p-value (2 sided)1.21483711978954e-10
p-value (1 sided)6.07418559894768e-11
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')