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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, 06 Dec 2008 07:54:12 -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/06/t1228575281h5pbsi0zino9agr.htm/, Retrieved Sat, 18 May 2024 03:45:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29676, Retrieved Sat, 18 May 2024 03:45:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Back to Back Histogram] [] [2008-12-06 14:15:54] [4c8dfb519edec2da3492d7e6be9a5685]
-   PD  [Back to Back Histogram] [] [2008-12-06 14:41:51] [4c8dfb519edec2da3492d7e6be9a5685]
- RMP     [Pearson Correlation] [] [2008-12-06 14:47:15] [4c8dfb519edec2da3492d7e6be9a5685]
-    D        [Pearson Correlation] [] [2008-12-06 14:54:12] [6d40a467de0f28bd2350f82ac9522c51] [Current]
-    D          [Pearson Correlation] [] [2008-12-06 14:58:38] [4c8dfb519edec2da3492d7e6be9a5685]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2411
2361
1924
2487
2675
2296
2102
2322
2274
2501
2435
2273
2455
2329
1897
2608
2712
2322
2283
2241
2417
2829
2601
2321
2769
2457
2143
2764
2789
2680
2537
2683
2700
3098
3015
2878
3011
2612
2419
3097
3013
3397
3423
3299
3066
3918
3154
3335
3462
3019
2832
3301
3343
3464
3017
3201
3135
3550
3247
3442
3536
3385
2997
3403
3900
3776
3198
4022
3845
3818
Dataseries Y:
Download CSV
Histogram 
15107
15024
12083
15761
16943
15070
13660
14769
14725
15998
15371
14957
15470
15102
11704
16284
16727
14969
14861
14583
15306
17904
16379
15420
17871
15913
13867
17823
17872
17422
16705
15991
16584
19124
17839
17209
18587
16258
15142
19202
17747
19090
18040
17516
17752
21073
17170
19440
19795
17575
16165
19465
19932
19961
17343
18924
18574
21351
18595
19823
20844
19640
17735
19814
22239
20682
17819
21872
22117
21866

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29676&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29676&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2888.9428571428617393.5
Biased Variance270366.0538775515501545.76428571
Biased Standard Deviation519.9673584731562345.53741481259
Covariance1194905.08695652
Correlation0.965752885871823
Determination0.932678636569754
T-Test30.6933307571089
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom68
Number of Observations70

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2888.94285714286 & 17393.5 \tabularnewline
Biased Variance & 270366.053877551 & 5501545.76428571 \tabularnewline
Biased Standard Deviation & 519.967358473156 & 2345.53741481259 \tabularnewline
Covariance & 1194905.08695652 \tabularnewline
Correlation & 0.965752885871823 \tabularnewline
Determination & 0.932678636569754 \tabularnewline
T-Test & 30.6933307571089 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 68 \tabularnewline
Number of Observations & 70 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29676&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]2888.94285714286[/C][C]17393.5[/C][/ROW]
[ROW][C]Biased Variance[/C][C]270366.053877551[/C][C]5501545.76428571[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]519.967358473156[/C][C]2345.53741481259[/C][/ROW]
[ROW][C]Covariance[/C][C]1194905.08695652[/C][/ROW]
[ROW][C]Correlation[/C][C]0.965752885871823[/C][/ROW]
[ROW][C]Determination[/C][C]0.932678636569754[/C][/ROW]
[ROW][C]T-Test[/C][C]30.6933307571089[/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]68[/C][/ROW]
[ROW][C]Number of Observations[/C][C]70[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29676&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
Mean2888.9428571428617393.5
Biased Variance270366.0538775515501545.76428571
Biased Standard Deviation519.9673584731562345.53741481259
Covariance1194905.08695652
Correlation0.965752885871823
Determination0.932678636569754
T-Test30.6933307571089
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom68
Number of Observations70


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')