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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 computationSat, 13 Nov 2010 12:17:57 +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/13/t1289650592tu2wpou7azv34rm.htm/, Retrieved Wed, 15 Jan 2025 08:01:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94359, Retrieved Wed, 15 Jan 2025 08:01:26 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact250

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] [workshop 6 tutorial] [2010-11-12 10:13:29] [87d60b8864dc39f7ed759c345edfb471]
-    D    [Linear Regression Graphical Model Validation] [workshop 6 mini-t...] [2010-11-12 14:05:27] [87d60b8864dc39f7ed759c345edfb471]
-    D      [Linear Regression Graphical Model Validation] [W6-mini tutorial] [2010-11-12 20:02:51] [48146708a479232c43a8f6e52fbf83b4]
-               [Linear Regression Graphical Model Validation] [WS 6 - mini-tutorial] [2010-11-13 12:17:57] [a948b7c78e10e31abd3f68e640bbd8ba] [Current]
-   P             [Linear Regression Graphical Model Validation] [ws 6 mini tutorial] [2010-11-14 12:47:04] [af8eb90b4bf1bcfcc4325c143dbee260]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24
25
17
18
18
16
20
16
18
17
23
30
23
18
15
12
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15
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31
27
34
21
31
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16
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21
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17
24
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26
25
17
32
33
13
32
25
29
22
18
17
20
15
20
33
29
23
26
18
20
11
28
26
22
17
12
14
17
21
19
18
10
29
31
19
9
20
28
19
30
29
26
23
13
21
19
28
23
18
21
20
23
21
21
15
28
19
26
10
16
22
19
31
31
29
19
22
23
15
20
18
23
25
21
24
25
17
13
28
21
25
9
16
19
17
25
20
29
14
22
15
19
20
15
20
18
33
22
16
17
16
21
26
18
18
17
22
30
30
24
21
21
29
31
20
16
22
20
28
38
22
20
17
28
22
31
Dataseries Y:
Download CSV
Histogram 
26
23
25
23
19
29
25
21
22
25
24
18
22
15
22
28
20
12
24
20
21
20
21
23
28
24
24
24
23
23
29
24
18
25
21
26
22
22
22
23
30
23
17
23
23
25
24
24
23
21
24
24
28
16
20
29
27
22
28
16
25
24
28
24
23
30
24
21
25
25
22
23
26
23
25
21
25
24
29
22
27
26
22
24
27
24
24
29
22
21
24
24
23
20
27
26
25
21
21
19
21
21
16
22
29
15
17
15
21
21
19
24
20
17
23
24
14
19
24
13
22
16
19
25
25
23
24
26
26
25
18
21
26
23
23
22
20
13
24
15
14
22
10
24
22
24
19
20
13
20
22
24
29
12
20
21
24
22
20

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94359&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94359&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term21.53661204576781.2140477539616417.73950981375340
slope0.03691103867217970.05437806339808220.678785458061780.498273172762898

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 21.5366120457678 & 1.21404775396164 & 17.7395098137534 & 0 \tabularnewline
slope & 0.0369110386721797 & 0.0543780633980822 & 0.67878545806178 & 0.498273172762898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94359&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]21.5366120457678[/C][C]1.21404775396164[/C][C]17.7395098137534[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]0.0369110386721797[/C][C]0.0543780633980822[/C][C]0.67878545806178[/C][C]0.498273172762898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94359&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 term21.53661204576781.2140477539616417.73950981375340
slope0.03691103867217970.05437806339808220.678785458061780.498273172762898


Figures (Output of Computation)

Figure 1
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Figure 2
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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')