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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 computationFri, 12 Dec 2014 13:39:48 +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/2014/Dec/12/t1418391604p4vc9jr5mskrsuw.htm/, Retrieved Thu, 16 May 2024 07:29:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266690, Retrieved Thu, 16 May 2024 07:29:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [jfh] [2014-12-12 13:39:48] [cf34f1111566f5ca061ad80c95189d56] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13 12
8 8
14 11
16 13
14 11
13 10
15 7
13 10
20 15
17 12
15 12
16 10
12 10
17 14
11 6
16 12
16 14
15 11
13 8
14 12
19 15
16 13
17 11
10 12
15 7
14 11
14 7
16 12
15 12
17 13
14 9
16 11
15 12
16 15
16 12
10 6
8 5
17 13
14 11
10 6
14 12
12 10
16 6
16 12
16 11
8 6
16 12
15 12
8 8
13 10
14 11
13 7
16 12
19 13
19 14
14 12
15 6
13 14
10 10
16 12
15 11
11 10
9 7
16 12
12 7
12 12
14 12
14 10
13 10
15 12
17 12
14 12
11 8
9 10
7 5
15 10
12 12
15 11
14 9
16 12
14 11
13 10
16 12
13 10
16 9
16 11
16 12
10 7
12 11
12 12
12 6
12 9
19 15
14 10
13 11
16 12
15 12
12 12
8 11
10 9
16 11
16 12
10 12
18 14
12 8
16 10
10 9
14 10
12 9
11 10
15 12
7 11
16 9
16 11
16 12
16 12
12 7
15 12
14 12
15 12
16 10
13 15
10 10
17 15
15 10
18 15
16 9
20 15
16 12
17 13
16 12
15 12
13 8
16 9
16 15
16 12
17 12
20 15
14 11
17 12
6 6
16 14
15 12
16 12
16 12
14 11
16 12
16 12
16 12
14 12
14 8
16 8
16 12
15 12
16 11
16 10
18 11
15 12
16 13
16 12
16 12
17 10
14 10
18 11
9 8
15 12
14 9
15 12
13 9
16 11
20 15
14 8
12 8
15 11
15 11
15 11
16 13
11 7
16 12
7 8
11 8
9 4
15 11
16 10
14 7
15 12
13 11
13 9
12 10
16 8
14 8
16 11
14 12
15 10
10 10
16 12
14 8
16 11
12 8
16 10
16 14
15 9
14 9
16 10
11 13
15 12
18 13
13 8
7 3
7 8
17 12
18 11
15 9
8 12
13 12
13 12
15 10
18 13
16 9
14 12
15 11
19 14
16 11
12 9
16 12
11 8
16 15
15 12
19 14
15 12
14 9
14 9
17 13
16 13
20 15
16 11
9 7
13 10
15 11
19 14
16 14
17 13
16 12
9 8
11 13
14 9
19 12
13 13
14 11
15 11
15 13
14 12
16 12
17 10
12 9
15 10
17 13
15 13
10 9
16 11
15 12
11 8
16 12
16 12
16 12
14 9
14 12
16 12
16 11
18 12
14 6
20 7
15 10
16 12
16 10
16 12
12 9
8 3

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266690&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266690&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)6.3310.61710.2690
X0.750.05613.3540
- - -
Residual Std. Err. 2.137 on 276 df
Multiple R-sq. 0.393
Adjusted R-sq. 0.39

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 6.331 & 0.617 & 10.269 & 0 \tabularnewline
X & 0.75 & 0.056 & 13.354 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.137  on  276 df \tabularnewline
Multiple R-sq.  & 0.393 \tabularnewline
Adjusted R-sq.  & 0.39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266690&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]6.331[/C][C]0.617[/C][C]10.269[/C][C]0[/C][/ROW]
[C]X[/C][C]0.75[/C][C]0.056[/C][C]13.354[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.137  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.393[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266690&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)6.3310.61710.2690
X0.750.05613.3540
- - -
Residual Std. Err. 2.137 on 276 df
Multiple R-sq. 0.393
Adjusted R-sq. 0.39






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
CONFSOFTTOT1814.808814.808178.3390
Residuals2761261.0094.569 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
CONFSOFTTOT & 1 & 814.808 & 814.808 & 178.339 & 0 \tabularnewline
Residuals & 276 & 1261.009 & 4.569 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266690&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]CONFSOFTTOT[/C][C]1[/C][C]814.808[/C][C]814.808[/C][C]178.339[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]1261.009[/C][C]4.569[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266690&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266690&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)
CONFSOFTTOT1814.808814.808178.3390
Residuals2761261.0094.569


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 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()