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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationMon, 10 Dec 2012 05:37:07 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/10/t1355135909qq3own93nm1a18y.htm/, Retrieved Sat, 27 Apr 2024 03:35:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198083, Retrieved Sat, 27 Apr 2024 03:35:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2010-11-02 14:42:14] [b98453cac15ba1066b407e146608df68]
- RMPD    [Simple Linear Regression] [rg] [2012-12-10 10:37:07] [69fed4bf76000787e6433dea6d892b14] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
458,15	0
477,59	0,05
504,91	0,1
502,61	0,15
514,12	0,2
512,64	0,25
546,06	0,3
525,26	0,35
571,2	0,4
551,22	0,45
604,26	0,5
510,28	0,55
574,91	0,6
580,8	0,65
527,33	0,7
571,37	0,75
587,97	0,8
557,65	0,85
619,61	0,9
631,11	0,95
583,14	1
589,4	1,05
603,19	1,1
642,68	1,15
615,91	1,2
650,56	1,25
607,41	1,3
673,46	1,35
680,11	1,4
665,89	1,45
711,79	1,5
636,29	1,55
580,08	1,6
595,64	1,65
661,8	1,7
657,74	1,75
646,05	1,8
706,03	1,85
712,38	1,9
718,78	1,95
699,49	2
635,36	2,05
682,09	2,1
722,7	2,15
731,22	2,2
763,95	2,25
739,86	2,3
744,88	2,35
746,73	2,4
821,77	2,45
752,76	2,5
733,8	2,55
735,91	2,6
783,64	2,65
711,28	2,7
764,41	2,75
833,71	2,8
827,09	2,85
766,46	2,9
748,42	2,95
870,61	3
854,52	3,05
858,34	3,1
787,99	3,15
834,26	3,2
827,86	3,25
771,05	3,3
806,2	3,35
873,4	3,4
792,56	3,45
855,02	3,5
794,63	3,55
861,6	3,6
859,6	3,65
856,97	3,7
905,18	3,75
933	3,8
838,89	3,85
903,42	3,9
889,5	3,95
914,18	4
863,96	4,05
937,39	4,1
948,76	4,15
900,66	4,2
947,49	4,25
904,22	4,3
861,64	4,35
918,5	4,4
906,68	4,45
966,54	4,5
997,92	4,55
965,9	4,6
969,3	4,65
904,8	4,7
957,8	4,75
1026,98	4,8
1048,42	4,85
953,19	4,9
1020,25	4,95

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198083&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198083&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)499.2086.97771.550
X100.1262.43541.1170
- - -
Residual Std. Err. 35.147 on 98 df
Multiple R-sq. 0.945
Adjusted R-sq. 0.945

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 499.208 & 6.977 & 71.55 & 0 \tabularnewline
X & 100.126 & 2.435 & 41.117 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 35.147  on  98 df \tabularnewline
Multiple R-sq.  & 0.945 \tabularnewline
Adjusted R-sq.  & 0.945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198083&T=1

[TABLE]
[ROW][C]Linear Regression Model[/C][/ROW]
[ROW][C]Y ~ X[/C][/ROW]
[ROW][C]coefficients:[/C][C] [/C][/ROW]
[ROW][C] [/C][C]Estimate[/C][C]Std. Error[/C][C]t value[/C][C]Pr(>|t|)[/C][/ROW]
[C](Intercept)[/C][C]499.208[/C][C]6.977[/C][C]71.55[/C][C]0[/C][/ROW]
[C]X[/C][C]100.126[/C][C]2.435[/C][C]41.117[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]35.147  on  98 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.945[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198083&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:

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)499.2086.97771.550
X100.1262.43541.1170
- - -
Residual Std. Err. 35.147 on 98 df
Multiple R-sq. 0.945
Adjusted R-sq. 0.945






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
mest12088392.4762088392.4761690.5740
Residuals98121060.9491235.316 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
mest & 1 & 2088392.476 & 2088392.476 & 1690.574 & 0 \tabularnewline
Residuals & 98 & 121060.949 & 1235.316 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198083&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]mest[/C][C]1[/C][C]2088392.476[/C][C]2088392.476[/C][C]1690.574[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]98[/C][C]121060.949[/C][C]1235.316[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198083&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
mest12088392.4762088392.4761690.5740
Residuals98121060.9491235.316


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = 3 ; par3 = 5 ; par4 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'coefficients')
nr <- nrow(sumlmxdf$'coefficients')
a<-table.row.start(a)
a<-table.element(a,'Linear Regression Model', nc+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],nc+1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'coefficients:',1,TRUE)
a<-table.element(a, ' ',nc,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
for(i in 1 : nc){
a<-table.element(a, dimnames(sumlmxdf$'coefficients')[[2]][i],1,TRUE)
}#end header
a<-table.row.end(a)
for(i in 1: nr){
a<-table.element(a,dimnames(sumlmxdf$'coefficients')[[1]][i] ,1,TRUE)
for(j in 1 : nc){
a<-table.element(a, round(sumlmxdf$coefficients[i, j], digits=3), 1 ,FALSE)
}
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, '- - - ',1,TRUE)
a<-table.element(a, ' ',nc,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Std. Err. ',1,TRUE)
a<-table.element(a, paste(round(sumlmxdf$'sigma', digits=3), ' on ', sumlmxdf$'df'[2], 'df') ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'adj.r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
a<-table.element(a, 'Df',1,TRUE)
a<-table.element(a, 'Sum Sq',1,TRUE)
a<-table.element(a, 'Mean Sq',1,TRUE)
a<-table.element(a, 'F value',1,TRUE)
a<-table.element(a, 'Pr(>F)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,1,TRUE)
a<-table.element(a, anova.xdf$Df[1])
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',1,TRUE)
a<-table.element(a, anova.xdf$Df[2])
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qq.plot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot.lm(lmxdf, which=4)
dev.off()