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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 computationFri, 12 Nov 2010 11:48:01 +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/Nov/12/t1289562463nqz9i8mrhcb5dd2.htm/, Retrieved Fri, 09 May 2025 17:00:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94100, Retrieved Fri, 09 May 2025 17:00:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact251

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] [Colombia Coffee -...] [2008-02-26 10:22:06] [74be16979710d4c4e7c6647856088456]
-  M D  [Linear Regression Graphical Model Validation] [Scatterplot Tutorial] [2010-11-05 11:55:49] [aeb27d5c05332f2e597ad139ee63fbe4]
-    D      [Linear Regression Graphical Model Validation] [Simple Linear Reg...] [2010-11-12 11:48:01] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
-    D        [Linear Regression Graphical Model Validation] [Simple Linear Reg...] [2010-12-17 13:47:08] [aeb27d5c05332f2e597ad139ee63fbe4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
586111
604378
600991
544686
537034
551531
563250
574761
580112
575093
557560
564478
580523
596594
586570
536214
523597
536535
536322
532638
528222
516141
501866
506174
517945
533590
528379
477580
469357
490243
492622
507561
516922
514258
509846
527070
541657
564591
555362
498662
511038
525919
531673
548854
560576
557274
565742
587625
619916
625809
619567
572942
572775
574205
579799
590072
593408
597141
595404
612117
628232
628884
620735
569028
567456
573100
584428
589379
590865
595454
594167
611324
612613
610763
593530
542722
536662
543599
555332
560854
562325
554788
547344
565464
577992
579714
569323
506971
500857
509127
509933
517009
519164
512238
509239
518585
522975
525192
516847
455626
454724
461251
470439
474605
476049
471067
470984
502831
512927
509673
484015
431328
436087
442867
447988
460070
467037
460170
464196
485025
501492
520564
488180
439148
441977
456608
461935
480961
492865
Dataseries Y:
Download CSV
Histogram 
43880
43110
44496
44164
40399
36763
37903
35532
35533
32110
33374
35462
33508
36080
34560
38737
38144
37594
36424
36843
37246
38661
40454
44928
48441
48140
45998
47369
49554
47510
44873
45344
42413
36912
43452
42142
44382
43636
44167
44423
42868
43908
42013
38846
35087
33026
34646
37135
37985
43121
43722
43630
42234
39351
39327
35704
30466
28155
29257
29998
32529
34787
33855
34556
31348
30805
28353
24514
21106
21346
23335
24379
26290
30084
29429
30632
27349
27264
27474
24482
21453
18788
19282
19713
21917
23812
23785
24696
24562
23580
24939
23899
21454
19761
19815
20780
23462
25005
24725
26198
27543
26471
26558
25317
22896
22248
23406
25073
27691
30599
31948
32946
34012
32936
32974
30951
29812
29010
31068
32447
34844
35676
35387
36488
35652
33488
32914
29781
27951

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'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 & 4 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94100&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94100&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94100&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term30863.06894289117553.989581578674.085664748354237.7341559866273e-05
slope0.004306533348850680.01404834235432460.3065509965682870.759687171990939

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 30863.0689428911 & 7553.98958157867 & 4.08566474835423 & 7.7341559866273e-05 \tabularnewline
slope & 0.00430653334885068 & 0.0140483423543246 & 0.306550996568287 & 0.759687171990939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94100&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]30863.0689428911[/C][C]7553.98958157867[/C][C]4.08566474835423[/C][C]7.7341559866273e-05[/C][/ROW]
[ROW][C]slope[/C][C]0.00430653334885068[/C][C]0.0140483423543246[/C][C]0.306550996568287[/C][C]0.759687171990939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94100&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94100&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 term30863.06894289117553.989581578674.085664748354237.7341559866273e-05
slope0.004306533348850680.01404834235432460.3065509965682870.759687171990939


Figures (Output of Computation)

Figure 1
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Figure 2
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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')