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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 computationFri, 23 Dec 2011 03:38:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324629524xz62h3p6eulz8t5.htm/, Retrieved Tue, 18 Feb 2025 21:57:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160195, Retrieved Tue, 18 Feb 2025 21:57:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Connected vs Sepa...] [2010-10-04 07:35:56] [b98453cac15ba1066b407e146608df68]
- R PD  [Pearson Correlation] [Paper: Scatterplot] [2011-12-21 15:12:04] [f722e8e78b9e5c5ebaa2263f273aa636]
-   PD    [Pearson Correlation] [Paper: Scatterplo...] [2011-12-22 21:49:19] [f722e8e78b9e5c5ebaa2263f273aa636]
-   PD      [Pearson Correlation] [Paper: Scatterplo...] [2011-12-23 08:36:11] [f722e8e78b9e5c5ebaa2263f273aa636]
-    D        [Pearson Correlation] [Paper: Scatterplo...] [2011-12-23 08:37:15] [f722e8e78b9e5c5ebaa2263f273aa636]
-    D            [Pearson Correlation] [Paper: Scatterplo...] [2011-12-23 08:38:29] [3e64eea457df40fcb7af8f28e1ee6256] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24.90
25.06
25.10
24.92
25.46
25.89
25.39
25.38
25.25
24.88
25.00
25.00
24.07
23.60
23.18
23.25
23.04
22.77
22.25
22.41
22.50
22.91
22.88
21.69
21.19
21.56
22.00
22.13
22.27
22.30
21.94
22.40
22.77
22.90
23.03
23.05
22.41
22.26
21.90
22.01
22.62
22.76
23.40
23.63
24.05
23.82
23.71
23.95
23.61
23.98
23.56
23.99
24.33
24.48
24.31
24.38
24.63
25.54
25.75
25.73
25.85
25.78
25.86
26.86
27.36
27.38
26.58
27.65
27.73
27.18
27.32
27.30
26.90
26.70
26.75
26.41
26.29
27.51
27.91
27.70
27.28
28.25
27.62
27.30
25.94
24.99
25.50
24.42
26.58
25.84
26.76
26.74
26.68
25.55
26.40
25.19
23.94
24.20
24.20
23.07
24.07
25.02
24.65
24.68
24.63
24.49
25.05
24.31
23.90
23.68
24.50
25.22
25.48
26.00
26.07
26.06
26.22
26.70
27.20
26.77
26.11
25.43
24.99
25.51
24.00
23.86
22.96
23.41
23.17
24.12
23.87
24.27
24.40
24.16
25.15
25.09
24.60
24.33
24.14
24.36
25.40
26.15
26.77
26.94
26.33
26.24
26.23
25.88
27.00
26.91
27.15
27.78
28.73
28.83
28.68
27.56
27.15
27.41
27.47
28.76
28.47
27.94
27.23
27.01
26.15
26.11
27.20
27.36
27.33
27.43
28.92
29.45
29.01
29.25
29.14
29.64
30.40
30.62
31.25
31.75
31.30
30.70
31.03
31.46
31.28
31.03
30.95
31.17
31.29
31.91
32.10
31.71
31.90
32.02
32.65
33.77
33.51
34.26
34.21
34.13
34.73
34.73
34.57
34.80
33.98
34.40
34.21
34.61
35.25
35.23
35.00
34.52
33.82
34.35
34.81
34.96
36.69
36.42
36.44
37.41
36.40
36.15
35.78
36.95
36.14
36.36
37.31
37.58
38.00
37.23
37.00
37.87
37.70
36.17
36.56
37.70
38.77
39.02
39.88
39.56
38.52
37.20
38.58
39.41
39.08
38.81
38.73
38.70
39.23
39.82
39.97
40.37
39.54
39.21
39.07
39.78
39.40
38.92
Dataseries Y:
Download CSV
Histogram 
1,439
1,444
1,435
1,430
1,427
1,453
1,448
1,456
1,449
1,437
1,437
1,428
1,413
1,406
1,414
1,415
1,409
1,407
1,400
1,397
1,391
1,394
1,398
1,385
1,369
1,368
1,376
1,374
1,372
1,357
1,361
1,365
1,373
1,357
1,352
1,363
1,358
1,355
1,349
1,357
1,353
1,355
1,364
1,367
1,358
1,366
1,356
1,361
1,366
1,377
1,371
1,372
1,376
1,366
1,355
1,347
1,352
1,334
1,336
1,335
1,347
1,348
1,348
1,347
1,340
1,334
1,330
1,338
1,359
1,358
1,362
1,354
1,354
1,343
1,349
1,337
1,334
1,331
1,332
1,329
1,325
1,326
1,332
1,324
1,309
1,292
1,273
1,275
1,297
1,270
1,267
1,259
1,249
1,235
1,243
1,227
1,233
1,250
1,236
1,222
1,231
1,226
1,238
1,231
1,216
1,222
1,227
1,206
1,196
1,194
1,201
1,205
1,213
1,225
1,226
1,228
1,236
1,237
1,239
1,226
1,227
1,226
1,229
1,234
1,220
1,227
1,233
1,255
1,253
1,258
1,257
1,266
1,264
1,257
1,257
1,270
1,283
1,300
1,296
1,284
1,282
1,285
1,290
1,293
1,303
1,299
1,307
1,303
1,307
1,322
1,321
1,318
1,318
1,325
1,313
1,302
1,279
1,280
1,282
1,286
1,288
1,284
1,271
1,270
1,261
1,261
1,269
1,271
1,270
1,268
1,280
1,282
1,283
1,287
1,274
1,270
1,272
1,273
1,280
1,285
1,299
1,308
1,306
1,307
1,312
1,336
1,332
1,341
1,348
1,346
1,361
1,365
1,373
1,371
1,378
1,386
1,397
1,387
1,394
1,383
1,396
1,410
1,409
1,390
1,386
1,386
1,402
1,393
1,403
1,391
1,380
1,386
1,386
1,393
1,402
1,401
1,424
1,408
1,392
1,395
1,377
1,370
1,371
1,363
1,361
1,348
1,365
1,367
1,365
1,350
1,334
1,332
1,323
1,315
1,300
1,312
1,316
1,325
1,328
1,336
1,320
1,321
1,324
1,327
1,344
1,336
1,324
1,326
1,315
1,316
1,311
1,306
1,310
1,314
1,320
1,314
1,328
1,336

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160195&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160195&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean28.58155038759691.32577131782946
Biased Variance28.23159837149210.0035940833633796
Biased Standard Deviation5.313341544780660.0599506744197228
Covariance0.0549196555364522
Correlation0.171743146519715
Determination0.0294957083764922
T-Test2.78933494626076
p-value (2 sided)0.00567854596075468
p-value (1 sided)0.00283927298037734
Degrees of Freedom256
Number of Observations258

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 28.5815503875969 & 1.32577131782946 \tabularnewline
Biased Variance & 28.2315983714921 & 0.0035940833633796 \tabularnewline
Biased Standard Deviation & 5.31334154478066 & 0.0599506744197228 \tabularnewline
Covariance & 0.0549196555364522 \tabularnewline
Correlation & 0.171743146519715 \tabularnewline
Determination & 0.0294957083764922 \tabularnewline
T-Test & 2.78933494626076 \tabularnewline
p-value (2 sided) & 0.00567854596075468 \tabularnewline
p-value (1 sided) & 0.00283927298037734 \tabularnewline
Degrees of Freedom & 256 \tabularnewline
Number of Observations & 258 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160195&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]28.5815503875969[/C][C]1.32577131782946[/C][/ROW]
[ROW][C]Biased Variance[/C][C]28.2315983714921[/C][C]0.0035940833633796[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.31334154478066[/C][C]0.0599506744197228[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0549196555364522[/C][/ROW]
[ROW][C]Correlation[/C][C]0.171743146519715[/C][/ROW]
[ROW][C]Determination[/C][C]0.0294957083764922[/C][/ROW]
[ROW][C]T-Test[/C][C]2.78933494626076[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00567854596075468[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00283927298037734[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]256[/C][/ROW]
[ROW][C]Number of Observations[/C][C]258[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160195&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
Mean28.58155038759691.32577131782946
Biased Variance28.23159837149210.0035940833633796
Biased Standard Deviation5.313341544780660.0599506744197228
Covariance0.0549196555364522
Correlation0.171743146519715
Determination0.0294957083764922
T-Test2.78933494626076
p-value (2 sided)0.00567854596075468
p-value (1 sided)0.00283927298037734
Degrees of Freedom256
Number of Observations258


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Valutakoersen Eur-Dollar ; par4 = 12 ;
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')