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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 computationWed, 24 Nov 2010 18:27:12 +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/24/t12906235895vfd8esoey2ml6g.htm/, Retrieved Fri, 03 May 2024 10:31:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100497, Retrieved Fri, 03 May 2024 10:31:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

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] [] [2010-11-24 18:27:12] [b7dd4adfab743bef2d672ff51f950617] [Current]
-    D    [Linear Regression Graphical Model Validation] [Paper Statistiek] [2010-12-27 11:07:48] [b2f924a86c4fbfa8afa1027f3839f526]
-   PD    [Linear Regression Graphical Model Validation] [] [2010-12-27 12:55:37] [b2f924a86c4fbfa8afa1027f3839f526]
-   PD      [Linear Regression Graphical Model Validation] [Simple Linear Reg...] [2010-12-27 16:45:21] [fd57ceeb2f72ef497e1390930b11fced]
-             [Linear Regression Graphical Model Validation] [] [2010-12-27 20:22:09] [b2f924a86c4fbfa8afa1027f3839f526]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22631
23956
23284
24334
24319
25252
24427
25434
25496
26681
25624
26706
25834
26513
26005
27158
26521
27652
26566
27597
27605
28621
27090
27652
28440
29076
27326
28477
29303
29301
27972
29247
29871
30079
28873
30897
30902
31321
29714
32006
31338
32562
31024
32678
33031
34115
32574
33984
34795
35680
34342
36136
36226
36226
34736
36588
45176
38351
36629
38146
39232
39257
37869
38394
40681
40797
39500
41366
42270
43536
42109
45262
46406
46275
44171
47037
Dataseries Y:
Download CSV
Histogram 
186448
190530
194207
190855
200779
204428
207617
212071
214239
215883
223484
221529
225247
226699
231406
232324
237192
236727
240698
240688
245283
243556
247826
245798
250479
249216
251896
247616
249994
246552
248771
247551
249745
245742
249019
245841
248771
244723
246878
246014
248496
244351
248016
246509
249426
247840
251035
250161
254278
250801
253985
249174
251287
247947
249992
243805
255812
250417
253033
248705
253950
251484
251093
245996
252721
248019
250464
245571
252690
250183
253639
254436
265280
268705
270643
271480

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100497&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]6 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=100497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100497&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term176367.4164867847476.5467039219223.58942215853050
slope2.005374672126250.2252219649289838.903992435900222.52686760404686e-13

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 176367.416486784 & 7476.54670392192 & 23.5894221585305 & 0 \tabularnewline
slope & 2.00537467212625 & 0.225221964928983 & 8.90399243590022 & 2.52686760404686e-13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100497&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]176367.416486784[/C][C]7476.54670392192[/C][C]23.5894221585305[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]2.00537467212625[/C][C]0.225221964928983[/C][C]8.90399243590022[/C][C]2.52686760404686e-13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100497&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 term176367.4164867847476.5467039219223.58942215853050
slope2.005374672126250.2252219649289838.903992435900222.52686760404686e-13


Figures (Output of Computation)

Figure 1
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Figure 2
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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')