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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 computationWed, 10 Nov 2010 18:18:07 +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/10/t128941299613dz43iyh5gg5c4.htm/, Retrieved Mon, 29 Apr 2024 09:59:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=93105, Retrieved Mon, 29 Apr 2024 09:59:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
225,18
233,09
226,83
221,81
229,61
235,41
222,29
226,04
209,75
203,66
223,57
217,38
217,38
222,84
221,72
216,14
208,2
199,41
186,55
175,42
179,87
192,57
201,11
201,77
202,76
207,37
194,98
186,47
186,91
183,51
175,73
178,13
191,34
201,46
197,8
211,58
216,85
205,25
197,78
203,64
200,69
187,41
193,83
200,44
214,49
260,26
347,84
361,09
428,75
372,07
367,2
353,67
355,45
317,71
287,61
293,13
341,72
361,89
343,13
325,73
315,33
279,72
243,02
219,12
165,59
164,07
156,44
158,75
161,91
173,46
177,52
165,46
180,18
188,8
201,5
201,22
188,89
175,51
176,26
190,68
202,76
207,32
206,26
194,81
197,78
184,05
183,2
149,53
144,15
134,05
153,25
158,35
160,21
184,91
192,41
207,03
212,32
193,7
191,66
184,29
170,76
166,29
146,2
148,12
164,59
181,34
192,64
195,76
193,03
181,69
178
171,83
169,1
176,81
193,73
184
214,74
261,53
235,31
254,33
252,93
211,29
192,6
194,81
187,02
181,49
189,79
174,55
185,25
220,2
228,6
219,95
236,19
200,35
184,74
182,04
173,49
163,71
152,35
162,12
174,29
185,85
197,07
198,63
175,28
162,51
165,44
192,87
211,22
201,56
206,41
221,06
221,01
200,79
203,64
235,12
239,49
203,56
190,48
177,75
172,86
166,67
165,19
166,61
180,02
196,49
182,2
186,3
164,45
173,63
186,5
186,31
183,96
196,7
181,78
183,82
201,2
190,79
178,32
172,36
163,56
169,04
172,09
167,97
164,39
145,5
143,37
150,37
163,39
176,91
173,62
179,66
174,42
177,03
168,66
172,37
176,12
171,24
160,17
167,97
187,38
183,51
189,37
197,74
189,36
193,57
213,18
240,29
252,76
224,81
244,77
257,76
247,53
252,51
264,69
265,05
317,37
329,13
261,48
234,06
190,3
218,15
226,2
237,75
225,25
209,8
206,75
206,5
225
225,25
231,75
236,75
222
207,25
205,6
209
239
280
278
228,68
228
234,25
253,08
249,4
252
240,64
247
261,35
262,43
253
250,82
245,43
236,09
230
224,82
212,35
195,57
191
196,09
197,74
190,9
177,26
162,09
163,57
172,91
169,9
195,19
185,64
164,09
168,5
175,43
181,86
193,43
181,09
178,48
183,73
182,39
192,25
192,19
188,5
182,09
196,95
204,48
191,95
195,41
200,48
200
205,22
202,82
198,1
191,78
177,95
186,62
186,59
190,73
206,45
240,73
201,76
192,5
201,78
236,67
258,1
241,52
190,71
200,32
223,41
201,38
211,83
224,41
211,57
194,77
201,86
225
278,9
259,74
230,45
238,26
250,14
263,81
247,22
229,81
224,27
213,23
239,57
249,7
212,5
203,27
192,05
190,04
202,05
211,91
210,39
231,25
224,3
209,64
206,05
229,7
264,67
246,29
260,91
265,14
284,52
287,48
321,9
321,59
282,39
241
228,48
261,59
270
262,86
277,41
288
287,14
337,65
328,38
374,41
344,77
361,05
374,22
321,95
317,55
317,52
314,64
271,71
261,95
259,18
315,09
337,18
Dataseries Y:
17,3
22,75
19,63
21,25
30,94
30,8
27,7
31,77
34,74
40,55
37,81
27,78
27,78
24,09
21,81
17,83
15,08
16,38
16,34
14,76
11,65
12,04
11,97
12,98
12,9
13,08
11,26
9,58
8,11
6,84
7,8
6,77
5,77
5,93
6,52
6,31
6,03
6,43
6,2
6,71
9,24
10,74
10,53
10,56
9,43
9,69
8,33
7,69
6,97
6,63
6,43
6
5,61
5,52
4,54
4,05
4,1
4,65
4,38
3,55
3,61
3,69
3,83
3,42
2,82
2,78
3,18
4,39
5,12
5,01
5,48
5,32
4,84
5,56
7,04
8,33
7,67
6,34
5,55
5,57
4,68
5,39
5,95
5,7
6,48
7,39
7,56
6,68
6,71
6,44
6,1
5,62
5,82
6,65
7,33
8,3
9,67
8,43
8,52
8,54
8,9
10,57
14,02
11,18
10,16
10,28
10,84
11,22
9,8
10,54
11,5
12,16
11,98
12,61
14,01
14,05
14,13
14,44
15,02
13,43
14,2
14,65
15,31
15,24
14,62
12,97
12
10,93
11,02
9,39
10,06
9,74
8,8
8,51
9,14
8,51
7,59
9,2
10,32
9,59
9,3
9,13
8,63
9
8,42
7,84
8,25
9,46
9,61
10,35
10,31
9,86
9,31
8,71
8,56
8,15
8,24
8,56
10,62
11,15
11,83
10,4
9,68
9,34
9,54
10,29
10,07
10,52
10,3
10,82
11,73
11,01
11,58
12,05
11,77
12,09
12,59
12,76
13,93
14,67
14,8
14,41
14,59
13,61
13,52
14,02
13,59
12,98
11,69
11,84
11,98
12,31
12,53
12,82
12,9
11,98
11,38
12,17
12,81
12,37
11,92
11,12
10,72
10,74
10,69
10,81
11,14
11,3
11,13
11,43
11,57
11,7
11,33
11,38
12,01
12,33
11,52
10,72
9,84
9,68
9,23
8,1
8,62
8,48
7,23
7,46
8,06
8,08
8,11
6,82
6,03
5,42
5,75
6,04
5,38
5,72
6,67
6,75
6,51
5,98
5,63
5,35
5,11
6,01
6,78
8,33
9,64
10,6
9,86
10,41
9,51
9,72
10,06
9,36
8,72
8,05
8,96
8,74
8,54
7,9
7,16
6,6
7,28
7,41
7,31
5,68
5,92
5,18
5,61
5,25
5,79
5,86
6,41
7,02
7,3
7,51
7,89
8,35
7,84
7,26
7,01
6,4
6,73
6,71
6,27
6,1
6,19
6,34
6,03
5,87
6,5
6,86
6,62
7,51
8,17
7,88
8,67
8,96
8,67
8,8
8,92
9,32
8,9
8,53
8,51
9,03
9,6
9,88
10,81
11,61
11,81
13,93
16,19
18,05
17,08
17,46
16,9
15,69
15,86
12,98
12,31
11,51
11,73
11,7
10,9
10,57
10,37
9,59
9,09
9,26
9,9
9,61
9,85
9,99
9,9
10,45
11,66
13,61
12,88
12,52
10,93
12,07
13,21
13,68
14,02
11,7
11,83
11,32
12,24
13,31
12,93
13,47
15,47
16,58
17,8
21,72
23,45
23,16
22,77
24,9
28,38
25,96
19,26
16,32
14,6
15,44
17,7
18,6
22,68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93105&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93105&T=0

As an alternative you can also use a 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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term5.758198118204581.239168686973634.646823454091314.70646373140760e-06
slope0.02291614201579040.005596106203617374.095015566533955.19638676590439e-05

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 5.75819811820458 & 1.23916868697363 & 4.64682345409131 & 4.70646373140760e-06 \tabularnewline
slope & 0.0229161420157904 & 0.00559610620361737 & 4.09501556653395 & 5.19638676590439e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93105&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]5.75819811820458[/C][C]1.23916868697363[/C][C]4.64682345409131[/C][C]4.70646373140760e-06[/C][/ROW]
[ROW][C]slope[/C][C]0.0229161420157904[/C][C]0.00559610620361737[/C][C]4.09501556653395[/C][C]5.19638676590439e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93105&T=1

As an alternative you can also use a 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 term5.758198118204581.239168686973634.646823454091314.70646373140760e-06
slope0.02291614201579040.005596106203617374.095015566533955.19638676590439e-05



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')