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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_linear_regression.wasp

Title produced by software

Linear Regression Graphical Model Validation

Date of computation

Sun, 14 Nov 2010 15:45:15 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/14/t12897497155atpdoyrprjk3m0.htm/, Retrieved Fri, 26 Apr 2024 12:24:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94572, Retrieved Fri, 26 Apr 2024 12:24:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

161

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Paired and Unpaired Two Samples Tests about the Mean] [WS 5 Question 3] [2010-11-01 07:38:26] [00b18f0d8e13a2047ccd266ce7bab24a]
F RMPD    [Linear Regression Graphical Model Validation] [WS 6 Tutorial Hyp...] [2010-11-14 15:45:15] [4d0f7ea43b071af5c75b527ee1ef14c2] [Current]
-    D      [Linear Regression Graphical Model Validation] [WS6 Tutorial Hypo...] [2010-11-16 19:46:58] [74be16979710d4c4e7c6647856088456] 
F    D      [Linear Regression Graphical Model Validation] [WS6 Tutorial Hypo...] [2010-11-16 19:46:58] [8081b8996d5947580de3eb171e82db4f] 

Feedback Forum

2010-11-21 08:44:52 [48eb36e2c01435ad7e4ea7854a9d98fe] [reply] 
We zien hier bij 'slope' inderdaad een positief getal. Dit zou kunnen wijzen op een positief verband tussen beiden. Zoals de student terecht heeft opgemerkt is de bijhorende P waarde zeer klein, dit betekent inderdaad dat we de nulhypothese (beta = 0) mogen verwerpen en de alternatieve hypothese (beta = 0,33) 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 er geen autocorrelatie mag zijn, hieraan besteed de student geen aandacht.  
 
Voor de finale paper zou ik aanraden om hieraan meer aandacht te besteden en die onderliggende assumpties duidelijker te omschrijven. Daarnaast zou ik ook een duidelijkere definitie geven van de X variabele en de Y variabele.

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Dataseries X:

Download CSV

Histogram

Boxplots

5,3
5,6
3,8
4,0
4,0
3,6
4,4
3,6
4,0
3,8
5,1
6,7
5,1
4,0
3,3
2,7
4,7
3,3
4,4
6,9
6,0
7,6
4,7
6,9
4,2
3,6
4,4
4,7
4,9
3,8
5,3
5,6
5,8
5,6
3,8
7,1
7,3
2,9
7,1
5,6
6,4
4,9
4,0
3,8
4,4
3,3
4,4
7,3
6,4
5,1
5,8
4,0
4,4
2,4
6,2
5,8
4,9
3,8
2,7
3,1
3,8
4,7
4,2
4,0
2,2
6,4
6,9
4,2
2,0
4,4
6,2
4,2
6,7
6,4
5,8
5,1
2,9
4,7
4,2
6,2
5,1
4,0
4,7
4,4
5,1
4,7
4,7
3,3
6,2
4,2
5,8
2,2
3,6
4,9
4,2
6,9
6,9
6,4
4,2
4,9
5,1
3,3
4,4
4,0
5,1
5,6
4,7
5,3
5,6
3,8
2,9
6,2
4,7
5,6
2,0
3,6
4,2
3,8
5,6
4,4
6,4
3,1
4,9
3,3
4,2
4,4
3,3
4,4
4,0
7,3
4,9
3,6
3,8
3,6
4,7
5,8
4,0
4,0
3,8
4,9
6,7
6,7
5,3
4,7
4,7
6,4
6,9
4,4
3,6
4,9
4,4
6,2
8,4
4,9
4,4
3,8
6,2
4,9
6,9

Dataseries Y:

Download CSV

Histogram

6,0
4,0
4,0
4,0
4,5
3,5
2,0
5,5
3,5
3,5
6,0
5,0
5,0
4,0
4,0
2,0
4,5
4,0
3,5
5,5
4,5
5,5
6,5
4,0
4,0
4,5
3,0
4,5
4,5
3,0
3,0
8,0
2,5
3,5
4,5
3,0
3,0
2,5
6,0
3,5
5,0
4,5
4,0
2,5
4,0
4,0
5,0
3,0
4,0
3,5
2,0
4,0
4,0
2,0
10,0
4,0
4,0
3,0
2,0
4,0
4,5
3,0
3,5
4,5
2,5
2,5
4,0
4,0
3,0
4,0
3,5
3,5
4,5
5,5
3,0
4,0
3,0
4,5
4,0
3,0
5,0
4,0
4,0
5,0
2,5
3,5
2,5
4,0
7,0
3,5
4,0
3,0
2,5
3,0
5,0
6,0
4,5
6,0
3,5
4,0
5,0
3,0
5,0
5,0
5,0
2,5
3,5
5,0
5,5
3,0
3,5
6,0
5,5
5,5
5,5
2,5
4,0
3,0
4,5
2,0
2,0
3,5
5,5
3,0
3,5
4,0
2,0
4,0
4,5
4,0
5,5
4,0
2,5
2,0
4,0
5,0
3,0
4,5
4,5
6,5
4,5
5,0
10,0
2,5
5,5
3,0
4,5
3,5
4,5
5,0
4,5
4,0
3,5
3,0
6,5
3,0
4,0
5,0
8,0

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94572&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94572&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Simple Linear Regression
Statistics	Estimate	S.D.	T-STAT (H0: coeff=0)	P-value (two-sided)
constant term	2.52314438597660	0.400914800782363	6.29346779179225	2.96110469477640e-09
slope	0.331523790492684	0.0808204485600044	4.10197909563131	6.5595747021252e-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 & 2.52314438597660 & 0.400914800782363 & 6.29346779179225 & 2.96110469477640e-09 \tabularnewline
slope & 0.331523790492684 & 0.0808204485600044 & 4.10197909563131 & 6.5595747021252e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94572&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]2.52314438597660[/C][C]0.400914800782363[/C][C]6.29346779179225[/C][C]2.96110469477640e-09[/C][/ROW]
[ROW][C]slope[/C][C]0.331523790492684[/C][C]0.0808204485600044[/C][C]4.10197909563131[/C][C]6.5595747021252e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94572&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
Statistics	Estimate	S.D.	T-STAT (H0: coeff=0)	P-value (two-sided)
constant term	2.52314438597660	0.400914800782363	6.29346779179225	2.96110469477640e-09
slope	0.331523790492684	0.0808204485600044	4.10197909563131	6.5595747021252e-05

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Figure 4

PNG link

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Figure 5

PNG link

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Figure 6

PNG link

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Figure 7

PNG link

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Figure 8

PNG link

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Figure 9

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code