Free Statistics

of Irreproducible Research!

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 computationTue, 16 Nov 2010 15:08:10 +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/16/t1289920011noqrmwdl6ynvzzy.htm/, Retrieved Sat, 04 May 2024 22:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95892, Retrieved Sat, 04 May 2024 22:00:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Linear Regression Graphical Model Validation] [Workshop 6 Mini T...] [2010-11-16 14:24:31] [945bcebba5e7ac34a41d6888338a1ba9]
F    D    [Linear Regression Graphical Model Validation] [workshop 6 Mini T...] [2010-11-16 15:08:10] [514029464b0621595fe21c9fa38c7009] [Current]
Feedback Forum
2010-11-20 18:56:16 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply
We zien hier bij 'slope' ofwel β in de formule 'Yt = α + β Xt + ... + et' inderdaad een negatief getal. Dit zou kunnen wijzen op een negatief verband tussen beiden. Zoals de student terecht heeft opgemerkt is de P waarde zeer klein, dit betekent inderdaad dat we de nulhypothese (β = 0) mogen verwerpen en de alternatieve hypothese (β = -0.93) mogen aanvaarden.

Echter vooraleer men voorspellingen mag doen op basis van dit model, dient men eerst na te gaan of alle onderliggende assumpties zijn voldaan. Dit wordt naar mijn mening niet voldoende behandeld door de student. Zo is een van de voorwaarden dat de residu's normaal moeten verdeeld zijn. Wanneer we de normal QQ plot bekijken blijkt het hier niet te gaan om een normaalverdeling (ondanks wat de student wel schrijft in zijn of haar conclusie). Naar de finale paper toe zou ik dus aanraden hier meer aandacht aan te besteden.

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Dataseries X:
12
11
14
12
21
12
22
11
10
13
10
8
15
14
10
14
14
11
10
13
7
14
12
14
11
9
11
15
14
13
9
15
10
11
13
8
20
12
10
10
9
14
8
14
11
13
9
11
15
11
10
14
18
14
11
12
13
9
10
15
20
12
12
14
13
11
17
12
13
14
13
15
13
10
11
19
13
17
13
9
11
10
9
12
12
13
13
12
15
22
13
15
13
15
10
11
16
11
11
10
10
16
12
11
16
19
11
16
15
24
14
15
11
15
12
10
14
13
9
15
15
14
11
8
11
11
8
10
11
13
11
20
10
15
12
14
23
14
16
11
12
10
14
12
12
11
12
13
11
19
12
17
9
12
19
18
15
14
11
9
18
16
Dataseries Y:
53
86
66
67
76
78
53
80
74
76
79
54
67
54
87
58
75
88
64
57
66
68
54
56
86
80
76
69
78
67
80
54
71
84
74
71
63
71
76
69
74
75
54
52
69
68
65
75
74
75
72
67
63
62
63
76
74
67
73
70
53
77
77
52
54
80
66
73
63
69
67
54
81
69
84
80
70
69
77
54
79
30
71
73
72
77
75
69
54
70
73
54
77
82
80
80
69
78
81
76
76
73
85
66
79
68
76
71
54
46
82
74
88
38
76
86
54
70
69
90
54
76
89
76
73
79
90
74
81
72
71
66
77
65
74
82
54
63
54
64
69
54
84
86
77
89
76
60
75
73
85
79
71
72
69
78
54
69
81
84
84
69




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=95892&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=95892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95892&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 term82.69956513590943.4247741188226124.14745097534790
slope-0.92801220832170.257507115295105-3.603831324265310.000418289983261211

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 82.6995651359094 & 3.42477411882261 & 24.1474509753479 & 0 \tabularnewline
slope & -0.9280122083217 & 0.257507115295105 & -3.60383132426531 & 0.000418289983261211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95892&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]82.6995651359094[/C][C]3.42477411882261[/C][C]24.1474509753479[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]-0.9280122083217[/C][C]0.257507115295105[/C][C]-3.60383132426531[/C][C]0.000418289983261211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95892&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 term82.69956513590943.4247741188226124.14745097534790
slope-0.92801220832170.257507115295105-3.603831324265310.000418289983261211



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')