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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 17:02:55 -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/21/t1224543862l7idndqaas9r5ba.htm/, Retrieved Sun, 19 May 2024 21:00:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18291, Retrieved Sun, 19 May 2024 21:00:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Invoer België VS] [2008-10-13 18:50:00] [b8fbc01255310b0d45a84fea6711862e]
F RMPD    [Pearson Correlation] [Correlatie inflat...] [2008-10-20 23:02:55] [21d7d81e7693ad6dde5aadefb1046611] [Current]
Feedback Forum
2008-10-25 13:58:43 [Astrid Sniekers] [reply] 
Ik weet niet welke tijdreeksen de student heeft gekozen. Ik heb geen gegevens of grafieken van de tijdreeksen. Bijgevolg weet ik ook niet of de berekeningen die de student heeft gedaan juist zijn. De oplossing van de student is alles behalve duidelijk. Hij of zij gooit verschillende vragen door elkaar.
2008-10-26 22:45:20 [Elias Van Deun] [reply] 
Het is goed dat zij de correlatie onderling heeft nagegaan. Spijtig genoeg zijn er geen tijdreeksen gegevens bijgevoegd zodat de berekening niet na te rekenen valt.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8
2,8
2,8
2,2
2,6
2,8
2,5
2,4
2,3
1,9
1,7
2
2,1
1,7
1,8
1,8
1,8
1,3
1,3
1,3
1,2
1,4
2,2
2,9
3,1
3,5
3,6
4,4
4,1
5,1
5,8
5,9
5,4
5,5
Dataseries Y:
Download CSV
Histogram 
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,575
1,5557
1,5553

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18291&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18291&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.503278688524591.28960163934426
Biased Variance1.283267938726150.0119730126202634
Biased Standard Deviation1.132814167781350.109421262194618
Covariance0.0957406612021858
Correlation0.759726798170621
Determination0.577184807858584
T-Test8.97445656104774
p-value (2 sided)1.26010313294955e-12
p-value (1 sided)6.30051566474776e-13
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.50327868852459 & 1.28960163934426 \tabularnewline
Biased Variance & 1.28326793872615 & 0.0119730126202634 \tabularnewline
Biased Standard Deviation & 1.13281416778135 & 0.109421262194618 \tabularnewline
Covariance & 0.0957406612021858 \tabularnewline
Correlation & 0.759726798170621 \tabularnewline
Determination & 0.577184807858584 \tabularnewline
T-Test & 8.97445656104774 \tabularnewline
p-value (2 sided) & 1.26010313294955e-12 \tabularnewline
p-value (1 sided) & 6.30051566474776e-13 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18291&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]2.50327868852459[/C][C]1.28960163934426[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.28326793872615[/C][C]0.0119730126202634[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.13281416778135[/C][C]0.109421262194618[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0957406612021858[/C][/ROW]
[ROW][C]Correlation[/C][C]0.759726798170621[/C][/ROW]
[ROW][C]Determination[/C][C]0.577184807858584[/C][/ROW]
[ROW][C]T-Test[/C][C]8.97445656104774[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.26010313294955e-12[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.30051566474776e-13[/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=18291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18291&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
Mean2.503278688524591.28960163934426
Biased Variance1.283267938726150.0119730126202634
Biased Standard Deviation1.132814167781350.109421262194618
Covariance0.0957406612021858
Correlation0.759726798170621
Determination0.577184807858584
T-Test8.97445656104774
p-value (2 sided)1.26010313294955e-12
p-value (1 sided)6.30051566474776e-13
Degrees of Freedom59
Number of Observations61


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;
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')