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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

Tue, 16 Nov 2010 19:46:58 +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/16/t1289936991qxbv6yiy897d3v3.htm/, Retrieved Sun, 05 May 2024 08:05:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96348, Retrieved Sun, 05 May 2024 08:05:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

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] [8081b8996d5947580de3eb171e82db4f]
-    D      [Linear Regression Graphical Model Validation] [WS6 Tutorial Hypo...] [2010-11-16 19:46:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

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Dataseries Y:

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Histogram

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96348&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96348&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Simple Linear Regression
Statistics	Estimate	S.D.	T-STAT (H0: coeff=0)	P-value (two-sided)
constant term	2.84353245698624	0.373925314716286	7.60454653663595	2.45448106284130e-12
slope	0.358520022331624	0.0665044316894927	5.39091926994496	2.52796717337134e-07

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 2.84353245698624 & 0.373925314716286 & 7.60454653663595 & 2.45448106284130e-12 \tabularnewline
slope & 0.358520022331624 & 0.0665044316894927 & 5.39091926994496 & 2.52796717337134e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96348&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]2.84353245698624[/C][C]0.373925314716286[/C][C]7.60454653663595[/C][C]2.45448106284130e-12[/C][/ROW]
[ROW][C]slope[/C][C]0.358520022331624[/C][C]0.0665044316894927[/C][C]5.39091926994496[/C][C]2.52796717337134e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96348&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	2.84353245698624	0.373925314716286	7.60454653663595	2.45448106284130e-12
slope	0.358520022331624	0.0665044316894927	5.39091926994496	2.52796717337134e-07

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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PDF link

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code