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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 computationSat, 13 Dec 2008 10:43:27 -0700
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/Dec/13/t12291902490jbq0zsbr5ye1tq.htm/, Retrieved Sat, 25 May 2024 02:11:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33194, Retrieved Sat, 25 May 2024 02:11:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

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] [Import uit Amerika] [2008-10-13 18:55:55] [b943bd7078334192ff8343563ee31113]
- RMPD  [Histogram] [Paper Analyse (1)] [2008-12-13 13:37:46] [b943bd7078334192ff8343563ee31113]
- RMP     [Tukey lambda PPCC Plot] [Paper Analyse (2)] [2008-12-13 14:19:33] [b943bd7078334192ff8343563ee31113]
- RM        [Central Tendency] [Paper Analyse (3)] [2008-12-13 14:48:04] [b943bd7078334192ff8343563ee31113]
- RMP         [Mean Plot] [Paper Analyse (4)] [2008-12-13 16:59:19] [b943bd7078334192ff8343563ee31113]
- RMPD          [Pearson Correlation] [Paper Analyse (5)] [2008-12-13 17:21:52] [b943bd7078334192ff8343563ee31113]
-    D              [Pearson Correlation] [Paper Analyse (6)] [2008-12-13 17:43:27] [620b6ad5c4696049e39cb73ce029682c] [Current]
- RM D                [Partial Correlation] [Paper Analyse (7)] [2008-12-13 19:17:34] [b943bd7078334192ff8343563ee31113]
- RMPD                  [Standard Deviation-Mean Plot] [Paper Analyse (8)] [2008-12-13 20:10:46] [b943bd7078334192ff8343563ee31113]
- RM                      [Variance Reduction Matrix] [Paper Analyse (9)] [2008-12-13 20:12:45] [b943bd7078334192ff8343563ee31113]
- RMP                       [(Partial) Autocorrelation Function] [Paper Analyse (10)] [2008-12-14 09:58:13] [b943bd7078334192ff8343563ee31113]
-   P                         [(Partial) Autocorrelation Function] [Paper Analyse (11)] [2008-12-14 09:59:43] [b943bd7078334192ff8343563ee31113]
-   P                           [(Partial) Autocorrelation Function] [Paper Analyse (12)] [2008-12-14 10:02:10] [b943bd7078334192ff8343563ee31113]
- RMP                             [ARIMA Backward Selection] [Paper Analyse (13)] [2008-12-14 10:33:42] [b943bd7078334192ff8343563ee31113]
- RMP                           [Spectral Analysis] [Paper Analyse (14)] [2008-12-17 14:20:55] [b943bd7078334192ff8343563ee31113]
- RM                            [Spectral Analysis] [Paper Analyse (15)] [2008-12-17 14:41:03] [b943bd7078334192ff8343563ee31113]
- RMP                           [ARIMA Backward Selection] [ARIMA Backward Mo...] [2008-12-17 15:08:32] [b943bd7078334192ff8343563ee31113]
-   P                         [(Partial) Autocorrelation Function] [Paper Analyse (16)] [2008-12-21 11:54:36] [b943bd7078334192ff8343563ee31113]
-   P                           [(Partial) Autocorrelation Function] [Paper Analyse (17)] [2008-12-21 11:57:49] [b943bd7078334192ff8343563ee31113]
- RMP                             [Spectral Analysis] [Paper Analyse (18)] [2008-12-21 12:02:44] [b943bd7078334192ff8343563ee31113]
-   P                               [Spectral Analysis] [Paper Analyse (19)] [2008-12-21 12:06:49] [b943bd7078334192ff8343563ee31113]
- RMP                                 [ARIMA Backward Selection] [Paper Analyse (20)] [2008-12-21 12:13:35] [b943bd7078334192ff8343563ee31113]
- RMP                                   [ARIMA Forecasting] [Paper Analyse (21)] [2008-12-21 13:12:31] [b943bd7078334192ff8343563ee31113]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1593
1477.9
1733.7
1569.7
1843.7
1950.3
1657.5
1772.1
1568.3
1809.8
1646.7
1808.5
1763.9
1625.5
1538.8
1342.4
1645.1
1619.9
1338.1
1505.5
1529.1
1511.9
1656.7
1694.4
1662.3
1588.7
1483.3
1585.6
1658.9
1584.4
1470.6
1618.7
1407.6
1473.9
1515.3
1485.4
1496.1
1493.5
1298.4
1375.3
1507.9
1455.3
1363.3
1392.8
1348.8
1880.3
1669.2
1543.6
1701.2
1516.5
1466.8
1484.1
1577.2
1684.5
1414.7
1674.5
1598.7
1739.1
1674.6
1671.8
1802
1526.8
1580.9
1634.8
1610.3
1712
1678.8
1708.1
1680.6
2056
1624
2021.4
1861.1
1750.8
1767.5
1710.3
2151.5
2047.9
1915.4
1984.7
1896.5
2170.8
2139.9
2330.5
2121.8
2226.8
1857.9
2155.9
2341.7
2290.2
2006.5
2111.9
1731.3
1762.2
1863.2
1943.5
1975.2
Dataseries Y:
Download CSV
Histogram 
4,5
4,7
4,75
4,75
4,75
4,75
4,75
4,75
4,58
4,5
4,5
4,49
4,03
3,75
3,39
3,25
3,25
3,25
3,25
3,25
3,25
3,25
3,25
3,25
3,25
3,25
3,25
2,85
2,75
2,75
2,55
2,5
2,5
2,1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2,21
2,25
2,25
2,45
2,5
2,5
2,64
2,75
2,93
3
3,17
3,25
3,39
3,5
3,5
3,65
3,75
3,75
3,9
4
4
4
4
4
4
4
4
4
4
4
4
4,18
4,25
4,25

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'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33194&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33194&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1706.351546391753.09237113402062
Biased Variance57561.16167286640.901611903496652
Biased Standard Deviation239.9190731744070.949532465741247
Covariance117.553876503436
Correlation0.510695299386902
Determination0.260809688815877
T-Test5.7895596151155
p-value (2 sided)9.0741543168349e-08
p-value (1 sided)4.53707715841745e-08
Degrees of Freedom95
Number of Observations97

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1706.35154639175 & 3.09237113402062 \tabularnewline
Biased Variance & 57561.1616728664 & 0.901611903496652 \tabularnewline
Biased Standard Deviation & 239.919073174407 & 0.949532465741247 \tabularnewline
Covariance & 117.553876503436 \tabularnewline
Correlation & 0.510695299386902 \tabularnewline
Determination & 0.260809688815877 \tabularnewline
T-Test & 5.7895596151155 \tabularnewline
p-value (2 sided) & 9.0741543168349e-08 \tabularnewline
p-value (1 sided) & 4.53707715841745e-08 \tabularnewline
Degrees of Freedom & 95 \tabularnewline
Number of Observations & 97 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33194&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]1706.35154639175[/C][C]3.09237113402062[/C][/ROW]
[ROW][C]Biased Variance[/C][C]57561.1616728664[/C][C]0.901611903496652[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]239.919073174407[/C][C]0.949532465741247[/C][/ROW]
[ROW][C]Covariance[/C][C]117.553876503436[/C][/ROW]
[ROW][C]Correlation[/C][C]0.510695299386902[/C][/ROW]
[ROW][C]Determination[/C][C]0.260809688815877[/C][/ROW]
[ROW][C]T-Test[/C][C]5.7895596151155[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.0741543168349e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.53707715841745e-08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]95[/C][/ROW]
[ROW][C]Number of Observations[/C][C]97[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33194&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
Mean1706.351546391753.09237113402062
Biased Variance57561.16167286640.901611903496652
Biased Standard Deviation239.9190731744070.949532465741247
Covariance117.553876503436
Correlation0.510695299386902
Determination0.260809688815877
T-Test5.7895596151155
p-value (2 sided)9.0741543168349e-08
p-value (1 sided)4.53707715841745e-08
Degrees of Freedom95
Number of Observations97


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')