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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 17 Dec 2010 10:48:12 +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/17/t1292582771kai3p9o09s7hq9b.htm/, Retrieved Tue, 07 May 2024 04:25:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111379, Retrieved Tue, 07 May 2024 04:25:04 +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)
-       [Pearson Correlation] [correlatie huweli...] [2010-12-17 10:48:12] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3109
3414
4600
6462
10812
11065
9259
9635
14075
7347
4720
4930
3095
4483
4623
6220
11335
11530
8802
9834
12561
6514
4319
4758
3480
3385
4474
5860
9981
11688
7602
10402
10594
6155
4226
4244
3169
5098
4313
6014
11414
11525
7887
10742
10478
6643
4371
4417
3111
3995
5245
5588
10681
10516
7496
9935
10249
6271
3616
3724
2886
3318
4166
6401
9209
9820
7470
8207
9564
5309
3385
3706
2733
3045
3449
5542
10072
9418
7516
7840
10081
4956
3641
3970
2931
3170
3889
4850
8037
12370
6712
7297
10613
5184
3506
3810
2692
3073
3713
4555
7807
10869
9682
7704
9826
5456
3677
3431
2765
3483
3445
6081
8767
9407
6551
12480
9530
5960
3252
3717
2642
2989
3607
5366
8898
9435
7328
8594
11349
5797
3621
3851
Dataseries Y:
Download CSV
Histogram 
6743
6297
6873
8215
7720
8503
9690
12323
12800
9003
8742
6816
5989
9740
9486
8236
10589
9494
10840
14659
13933
11755
11448
6956
8094
8655
7633
8245
9960
8843
10483
13276
13078
11139
9234
9570
7615
6053
5172
6121
6561
5702
7886
10787
11055
8788
5438
6109
5140
4749
3635
4305
5805
4260
3869
7325
9280
6222
3272
7598
1345
1900
1480
1472
3823
4454
3357
5393
8329
4152
4042
7747
1451
911
406
1387
2150
1577
2642
4273
8064
3243
1112
2280
505
744
1369
531
1041
2076
577
5080
6584
3761
294
5020
1141
3805
2127
2531
3682
3263
2798
5936
10568
5296
1870
4390
3707
5201
3748
5282
5349
6249
5517
8640
15767
8850
5582
6496
3255
6189
6452
5099
6833
7046
7739
10142
16054
7721
6182
6490

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=111379&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=111379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111379&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
Mean6557.303030303036207.39393939394
Biased Variance8852892.6808999112421772.2235996
Biased Standard Deviation2975.381098430913524.45346452462
Covariance4853707.82627805
Correlation0.459342483343547
Determination0.210995517004217
T-Test5.89615042304743
p-value (2 sided)3.02424625342468e-08
p-value (1 sided)1.51212312671234e-08
Degrees of Freedom130
Number of Observations132

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6557.30303030303 & 6207.39393939394 \tabularnewline
Biased Variance & 8852892.68089991 & 12421772.2235996 \tabularnewline
Biased Standard Deviation & 2975.38109843091 & 3524.45346452462 \tabularnewline
Covariance & 4853707.82627805 \tabularnewline
Correlation & 0.459342483343547 \tabularnewline
Determination & 0.210995517004217 \tabularnewline
T-Test & 5.89615042304743 \tabularnewline
p-value (2 sided) & 3.02424625342468e-08 \tabularnewline
p-value (1 sided) & 1.51212312671234e-08 \tabularnewline
Degrees of Freedom & 130 \tabularnewline
Number of Observations & 132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111379&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]6557.30303030303[/C][C]6207.39393939394[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8852892.68089991[/C][C]12421772.2235996[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2975.38109843091[/C][C]3524.45346452462[/C][/ROW]
[ROW][C]Covariance[/C][C]4853707.82627805[/C][/ROW]
[ROW][C]Correlation[/C][C]0.459342483343547[/C][/ROW]
[ROW][C]Determination[/C][C]0.210995517004217[/C][/ROW]
[ROW][C]T-Test[/C][C]5.89615042304743[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.02424625342468e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.51212312671234e-08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]130[/C][/ROW]
[ROW][C]Number of Observations[/C][C]132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111379&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
Mean6557.303030303036207.39393939394
Biased Variance8852892.6808999112421772.2235996
Biased Standard Deviation2975.381098430913524.45346452462
Covariance4853707.82627805
Correlation0.459342483343547
Determination0.210995517004217
T-Test5.89615042304743
p-value (2 sided)3.02424625342468e-08
p-value (1 sided)1.51212312671234e-08
Degrees of Freedom130
Number of Observations132


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')