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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_linear_regression.wasp
Title produced by softwareLinear Regression Graphical Model Validation
Date of computationMon, 20 Dec 2010 18:07:09 +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/20/t1292868383rtyh8x09drqws4r.htm/, Retrieved Fri, 03 May 2024 22:47:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113042, Retrieved Fri, 03 May 2024 22:47:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Linear Regression Graphical Model Validation] [] [2010-12-15 17:33:32] [7f2363d2c77d3bf71367965cc53be730]
-    D    [Linear Regression Graphical Model Validation] [] [2010-12-20 18:07:09] [4dba6678eac10ee5c3460d144a14bd5c] [Current]
-    D      [Linear Regression Graphical Model Validation] [] [2010-12-20 18:10:24] [7f2363d2c77d3bf71367965cc53be730]
-    D      [Linear Regression Graphical Model Validation] [] [2010-12-20 18:15:58] [7f2363d2c77d3bf71367965cc53be730]
-    D        [Linear Regression Graphical Model Validation] [] [2010-12-20 18:28:05] [7f2363d2c77d3bf71367965cc53be730]
-    D          [Linear Regression Graphical Model Validation] [] [2010-12-20 18:38:13] [7f2363d2c77d3bf71367965cc53be730]
- RMPD          [Multiple Regression] [] [2010-12-20 18:49:41] [7f2363d2c77d3bf71367965cc53be730]
-   P             [Multiple Regression] [] [2010-12-22 13:52:50] [7f2363d2c77d3bf71367965cc53be730]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17.98
17.83
19.45
21.04
20.03
20.01
19.64
18.52
19.59
20.09
19.82
21.09
22.64
22.11
20.42
18.58
18.24
16.87
18.64
27.17
33.69
35.92
32.30
27.34
24.96
20.52
19.86
20.82
21.24
20.20
21.42
21.69
21.86
23.23
22.47
19.52
18.82
19.00
18.92
20.24
20.94
22.38
21.76
21.35
21.90
21.69
20.34
19.41
19.08
20.05
20.35
20.27
19.94
19.07
17.87
18.01
17.51
18.15
16.70
14.51
15.00
14.78
14.66
16.38
17.88
19.07
19.65
18.38
17.46
17.71
18.10
17.16
17.99
18.53
18.55
19.87
19.74
18.42
17.30
18.03
18.23
17.44
17.99
19.04
18.88
19.07
21.36
23.57
21.25
20.45
21.32
21.96
23.99
24.90
23.71
25.39
25.17
22.21
20.99
19.72
20.83
19.17
19.63
19.93
19.79
21.26
20.17
18.32
16.71
16.06
15.02
15.44
14.86
13.66
14.08
13.36
14.95
14.39
12.85
11.28
12.47
12.01
14.66
17.34
17.75
17.89
20.07
21.26
23.88
22.64
24.97
26.08
27.18
29.35
29.89
25.74
28.78
31.83
29.77
31.22
33.88
33.08
34.40
28.46
29.58
29.61
27.24
27.41
28.64
27.60
26.45
27.47
25.88
22.21
19.67
19.33
19.67
20.74
24.42
26.27
27.02
25.52
26.94
28.38
29.67
28.85
26.27
29.42
32.94
35.87
33.55
28.25
28.14
30.72
30.76
31.59
28.29
30.33
31.09
32.15
34.27
34.74
36.76
36.69
40.28
38.02
40.69
44.94
45.95
53.13
48.46
43.33
46.84
47.97
54.31
53.04
49.83
56.26
58.70
64.97
65.57
62.37
58.30
59.43
65.51
61.63
62.90
69.69
70.94
70.96
74.41
73.05
63.87
58.88
59.37
62.03
54.57
59.26
60.56
63.97
63.46
67.48
74.18
72.39
79.93
86.20
94.62
91.73
92.95
95.35
105.56
112.57
125.39
133.93
133.44
116.61
103.90
76.65
57.44
41.02
41.74
39.16
47.98
49.79
59.16
69.68
64.09
71.06
69.46
75.82
78.08
74.30
Dataseries Y:
Download CSV
Histogram 
586,9642
582,1727
586,19396
590,49531
589,70506
590,07518
595,2568
604,1796
605,00987
610,71165
618,31404
614,74292
609,16284
611,73756
620,77222
618,00755
612,3328
604,04309
605,08732
569,6086
595,0899
598,49214
606,67306
608,78857
606,9776
603,86769
606,42144
592,42386
590,6524
592,57978
602,51677
595,5471
605,94461
605,4981
607,95824
612,04311
612,7243
604,3511
597,85685
601,4573
590,17392
592,59948
597,24933
597,11685
599,7328
607,71194
604,82143
608,02913
606,1822
609,73516
602,5858
595,55291
597,41659
594,57492
600,63662
598,85984
598,97301
603,61033
604,24871
608,12389
610,69475
608,90087
607,98959
603,37721
607,81136
610,96411
606,97026
605,89335
611,97502
616,95077
618,69499
621,90975
617,85264
623,04912
615,57
623,58574
623,63317
615,04568
624,57004
625,8824
629,83163
626,42181
628,40528
632,30782
631,60361
635,57585
634,08687
632,61106
632,6136
635,80934
636,67236
633,388
638,09523
641,6666
646,15675
651,88736
651,22665
654,79548
654,65449
659,91121
653,37456
645,67016
650,11779
658,91968
662,42603
667,60539
666,14582
664,27573
676,48872
680,1659
678,99055
677,61221
672,24744
669,48689
668,19145
658,29031
659,15736
660,34479
668,77636
667,01524
669,37186
672,58801
669,36903
654,958
653,03433
642,61224
657,74554
656,64312
657,08444
662,14989
661,94064
653,83966
664,17629
670,41666
670,73615
677,35214
682,47259
680,40158
686,65088
694,91907
695,01497
699,45908
705,01325
692,39885
691,58396
686,89767
693,52192
684,19211
677,3194
661,73269
681,12618
682,86649
678,14703
677,16558
680,69632
676,53337
668,03667
668,97155
666,98498
661,76808
667,50585
666,06849
670,68352
667,93756
673,30419
687,39311
688,37189
671,79872
677,22114
693,12414
698,4465
687,64631
687,61812
679,51819
685,70631
690,25711
696,94325
705,98803
708,31175
720,88209
717,75784
717,55138
716,99835
716,65894
713,41968
729,40358
733,9712
723,67358
729,87932
736,03188
732,64932
728,98133
731,63834
734,6898
737,88677
740,78089
741,90176
738,40627
736,92209
737,36337
732,89592
733,55081
738,51387
741,46149
736,41252
735,99137
734,26023
734,85552
730,46576
729,38976
739,7233
736,24305
733,40158
736,50854
733,27274
731,06448
727,84077
730,40812
729,59849
731,9837
727,2243
723,33322
728,46526
721,99641
729,75831
736,52441
733,60152
737,86398
738,99614
740,62804
742,35983
736,59008
739,67615
739,77171
746,85967
734,762
725,37503
735,5332
733,90288
725,90513
715,5104
720,74408
718,75698
719,95689
716,1199
718,00358
727,08914
722,45696
726,53179
731,11631
731,65889
728,91337

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113042&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]4 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=113042&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113042&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term610.3498881636183.78541803077257161.2371165355950
slope1.603205165549710.09003070176616817.80731610549510

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 610.349888163618 & 3.78541803077257 & 161.237116535595 & 0 \tabularnewline
slope & 1.60320516554971 & 0.090030701766168 & 17.8073161054951 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113042&T=1

[TABLE]
[ROW][C]Simple Linear Regression[/C][/ROW]
[ROW][C]Statistics[/C][C]Estimate[/C][C]S.D.[/C][C]T-STAT (H0: coeff=0)[/C][C]P-value (two-sided)[/C][/ROW]
[ROW][C]constant term[/C][C]610.349888163618[/C][C]3.78541803077257[/C][C]161.237116535595[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]1.60320516554971[/C][C]0.090030701766168[/C][C]17.8073161054951[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113042&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113042&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:

Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term610.3498881636183.78541803077257161.2371165355950
slope1.603205165549710.09003070176616817.80731610549510


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 3
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Input Parameters & R Code

Parameters (Session):
par1 = 0 ;
Parameters (R input):
par1 = 0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
library(lattice)
z <- as.data.frame(cbind(x,y))
m <- lm(y~x)
summary(m)
bitmap(file='test1.png')
plot(z,main='Scatterplot, lowess, and regression line')
lines(lowess(z),col='red')
abline(m)
grid()
dev.off()
bitmap(file='test2.png')
m2 <- lm(m$fitted.values ~ x)
summary(m2)
z2 <- as.data.frame(cbind(x,m$fitted.values))
names(z2) <- list('x','Fitted')
plot(z2,main='Scatterplot, lowess, and regression line')
lines(lowess(z2),col='red')
abline(m2)
grid()
dev.off()
bitmap(file='test3.png')
m3 <- lm(m$residuals ~ x)
summary(m3)
z3 <- as.data.frame(cbind(x,m$residuals))
names(z3) <- list('x','Residuals')
plot(z3,main='Scatterplot, lowess, and regression line')
lines(lowess(z3),col='red')
abline(m3)
grid()
dev.off()
bitmap(file='test4.png')
m4 <- lm(m$fitted.values ~ m$residuals)
summary(m4)
z4 <- as.data.frame(cbind(m$residuals,m$fitted.values))
names(z4) <- list('Residuals','Fitted')
plot(z4,main='Scatterplot, lowess, and regression line')
lines(lowess(z4),col='red')
abline(m4)
grid()
dev.off()
bitmap(file='test5.png')
myr <- as.ts(m$residuals)
z5 <- as.data.frame(cbind(lag(myr,1),myr))
names(z5) <- list('Lagged Residuals','Residuals')
plot(z5,main='Lag plot')
m5 <- lm(z5)
summary(m5)
abline(m5)
grid()
dev.off()
bitmap(file='test6.png')
hist(m$residuals,main='Residual Histogram',xlab='Residuals')
dev.off()
bitmap(file='test7.png')
if (par1 > 0)
{
densityplot(~m$residuals,col='black',main=paste('Density Plot   bw = ',par1),bw=par1)
} else {
densityplot(~m$residuals,col='black',main='Density Plot')
}
dev.off()
bitmap(file='test8.png')
acf(m$residuals,main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test9.png')
qqnorm(x)
qqline(x)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Simple Linear Regression',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistics',1,TRUE)
a<-table.element(a,'Estimate',1,TRUE)
a<-table.element(a,'S.D.',1,TRUE)
a<-table.element(a,'T-STAT (H0: coeff=0)',1,TRUE)
a<-table.element(a,'P-value (two-sided)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'constant term',header=TRUE)
a<-table.element(a,m$coefficients[[1]])
sd <- sqrt(vcov(m)[1,1])
a<-table.element(a,sd)
tstat <- m$coefficients[[1]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'slope',header=TRUE)
a<-table.element(a,m$coefficients[[2]])
sd <- sqrt(vcov(m)[2,2])
a<-table.element(a,sd)
tstat <- m$coefficients[[2]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')