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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationFri, 21 Dec 2012 16:08:27 -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/21/t1356124139areiln1gvjiqps5.htm/, Retrieved Tue, 10 Feb 2026 13:15:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204295, Retrieved Tue, 10 Feb 2026 13:15:48 +0000
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User-defined keywords
Estimated Impact358

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [Workshop 5: Taak 6] [2012-10-26 10:39:07] [7bed0d115000febeef05f886574a3dac]
- RMPD  [Simple Linear Regression] [Simple Regression] [2012-12-17 14:18:08] [7bed0d115000febeef05f886574a3dac]
- R P       [Simple Linear Regression] [Paper - Deel 5: S...] [2012-12-21 21:08:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4	'Yes'	'Treatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'NoTreatment'	NA	0	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'Treatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'Yes'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'Treatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	1	0	1	'Bad'
4	'Yes'	'Treatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	1	0	1	'Good'
4	'No'	'Treatment'	NA	1	0	1	'Good'
4	'Yes'	'Treatment'	NA	1	1	1	'Bad'
4	'Yes'	'Treatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'Treatment'	NA	1	1	1	'Good'
4	'Yes'	'NoTreatment'	NA	0	0	1	'Bad'
4	'Yes'	'NoTreatment'	NA	1	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	1	'Good'
4	'Yes'	'NoTreatment'	NA	0	0	1	'Good'
4	'No'	'Treatment'	NA	1	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	1	'Bad'
4	'Yes'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	1	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'NoTreatment'	NA	0	0	1	'Bad'
4	'No'	'Treatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'Treatment'	NA	1	0	1	'Bad'
4	'No'	'NoTreatment'	NA	1	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	1	'Good'
4	'No'	'Treatment'	NA	0	0	1	'Bad'
4	'No'	'NoTreatment'	NA	1	1	1	'Good'
4	'No'	'NoTreatment'	NA	1	0	0	'Good'
4	'Yes'	'NoTreatment'	NA	0	0	1	'Good'
4	'Yes'	'Treatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	1	'Bad'
4	'No'	'NoTreatment'	NA	0	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'Treatment'	NA	1	0	0	'Bad'
4	'Yes'	'Treatment'	NA	1	1	1	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	1	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'Treatment'	NA	1	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'Yes'	'Treatment'	NA	1	1	1	'Good'
4	'Yes'	'Treatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	1	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'Treatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'Treatment'	NA	1	1	1	'Bad'
4	'Yes'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	0	'Good'
4	'Yes'	'NoTreatment'	NA	1	0	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'Treatment'	NA	0	0	1	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Good'
4	'No'	'NoTreatment'	NA	1	0	1	'Good'
4	'No'	'Treatment'	NA	1	1	0	'Good'
4	'No'	'Treatment'	NA	0	0	1	'Bad'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'Yes'	'NoTreatment'	NA	1	0	0	'Good'
4	'No'	'NoTreatment'	NA	0	0	0	'Bad'
4	'No'	'NoTreatment'	NA	1	1	0	'Bad'
4	'No'	'NoTreatment'	NA	0	0	1	'Good'
4	'Yes'	'NoTreatment'	NA	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'Treatment'	1	0	0	'Good'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'No'	NA	'NoTreatment'	0	0	1	'Bad'
2	'Yes'	NA	'Treatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	1	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'Treatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'Treatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Good'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'Treatment'	1	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'Treatment'	1	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'Treatment'	1	0	1	'Bad'
2	'No'	NA	'Treatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	1	0	0	'Bad'
2	'Yes'	NA	'Treatment'	1	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'Treatment'	1	0	0	'Bad'
2	'No'	NA	'NoTreatment'	1	0	1	'Good'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'No'	NA	'Treatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	1	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	1	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	1	0	1	'Good'
2	'Yes'	NA	'Treatment'	1	0	1	'Good'
2	'No'	NA	'Treatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	1	1	0	'Good'
2	'No'	NA	'Treatment'	1	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	1	'Good'
2	'No'	NA	'NoTreatment'	0	0	1	'Bad'
2	'No'	NA	'Treatment'	0	0	0	'Good'
2	'No'	NA	'Treatment'	1	0	0	'Bad'
2	'No'	NA	'Treatment'	0	0	0	'Bad'
2	'Yes'	NA	'NoTreatment'	0	0	0	'Bad'
2	'No'	NA	'NoTreatment'	0	0	1	'Good'
2	'No'	NA	'NoTreatment'	0	0	0	'Good'
2	'Yes'	NA	'NoTreatment'	1	1	0	'Bad'
2	'Yes'	NA	'NoTreatment'	1	1	1	'Bad'
2	'Yes'	NA	'NoTreatment'	1	0	0	'Bad'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204295&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204295&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204295&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)00.02301
X0.2670.0436.2550
- - -
Residual Std. Err. 0.241 on 152 df
Multiple R-sq. 0.205
Adjusted R-sq. 0.199

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 0 & 0.023 & 0 & 1 \tabularnewline
X & 0.267 & 0.043 & 6.255 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 0.241  on  152 df \tabularnewline
Multiple R-sq.  & 0.205 \tabularnewline
Adjusted R-sq.  & 0.199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204295&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]0[/C][C]0.023[/C][C]0[/C][C]1[/C][/ROW]
[C]X[/C][C]0.267[/C][C]0.043[/C][C]6.255[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]0.241  on  152 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.205[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204295&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204295&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)00.02301
X0.2670.0436.2550
- - -
Residual Std. Err. 0.241 on 152 df
Multiple R-sq. 0.205
Adjusted R-sq. 0.199






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Used12.2652.26539.1220
Residuals1528.80.058 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Used & 1 & 2.265 & 2.265 & 39.122 & 0 \tabularnewline
Residuals & 152 & 8.8 & 0.058 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204295&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]Used[/C][C]1[/C][C]2.265[/C][C]2.265[/C][C]39.122[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]152[/C][C]8.8[/C][C]0.058[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204295&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204295&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)
Used12.2652.26539.1220
Residuals1528.80.058


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 6 ; par2 = 5 ; par3 = TRUE ;
Parameters (R input):
par1 = 6 ; par2 = 5 ; 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()