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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, 17 Dec 2010 13:47:08 +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/t1292593522ujeh7kw9jl81t6m.htm/, Retrieved Fri, 09 May 2025 18:38:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111463, Retrieved Fri, 09 May 2025 18:38:46 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact252

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] [aeb27d5c05332f2e597ad139ee63fbe4]
-    D        [Linear Regression Graphical Model Validation] [Simple Linear Reg...] [2010-12-17 13:47:08] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
211868
229527
229139
198563
195722
202196
205816
212588
214320
220375
204442
206903
214126
226899
223532
195309
186005
188906
191563
189226
186413
178037
166827
169362
174330
187069
186530
158114
151001
159612
161914
164182
169701
171297
166444
173476
182516
202388
202300
168053
167302
172608
178106
185686
194581
194596
197922
208795
230580
240636
240048
211457
211142
214771
212610
219313
219277
231805
229245
241114
248624
265845
256446
219452
217142
221678
227184
230354
235243
237217
233575
244460
243324
260307
241476
203666
200237
204045
209465
213586
216234
213188
208679
217859
227247
243477
232571
191531
186029
189733
190420
194163
198770
195198
193111
195411
202108
215706
206348
166972
166070
169292
175041
177876
181140
179566
175335
184128
189917
194690
179612
150605
150569
153745
155511
159044
163095
159585
158644
166618
176512
200765
182698
153730
156145
161570
165688
173666
180144
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 time5 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 & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111463&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]5 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=111463&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111463&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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term47538.3927425364963.543865829629.577510348967230
slope-0.07278687044774540.0249057465795051-2.922493016436680.00411190354097579

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 47538.392742536 & 4963.54386582962 & 9.57751034896723 & 0 \tabularnewline
slope & -0.0727868704477454 & 0.0249057465795051 & -2.92249301643668 & 0.00411190354097579 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111463&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]47538.392742536[/C][C]4963.54386582962[/C][C]9.57751034896723[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]-0.0727868704477454[/C][C]0.0249057465795051[/C][C]-2.92249301643668[/C][C]0.00411190354097579[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111463&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111463&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 term47538.3927425364963.543865829629.577510348967230
slope-0.07278687044774540.0249057465795051-2.922493016436680.00411190354097579


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')