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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 computationWed, 10 Dec 2014 16:58:21 +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/10/t1418230768tkc0v3wsl4yn0ao.htm/, Retrieved Sun, 19 May 2024 14:44:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265510, Retrieved Sun, 19 May 2024 14:44:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54

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] [] [2014-12-10 16:58:21] [f8081e57f48fffedb891dd68b4ffae29] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13 12.9
8 12.2
14 12.8
16 7.4
14 6.7
13 12.6
15 14.8
13 13.3
20 11.1
17 8.2
15 11.4
16 6.4
12 10.6
17 12
11 6.3
16 11.3
16 11.9
15 9.3
13 9.6
14 10
19 6.4
16 13.8
17 10.8
10 13.8
15 11.7
14 10.9
14 16.1
16 13.4
15 9.9
17 11.5
14 8.3
16 11.7
15 9
16 9.7
16 10.8
10 10.3
8 10.4
17 12.7
14 9.3
10 11.8
14 5.9
12 11.4
16 13
16 10.8
16 12.3
8 11.3
16 11.8
15 7.9
8 12.7
13 12.3
14 11.6
13 6.7
16 10.9
19 12.1
19 13.3
14 10.1
15 5.7
13 14.3
10 8
16 13.3
15 9.3
11 12.5
9 7.6
16 15.9
12 9.2
12 9.1
14 11.1
14 13
13 14.5
15 12.2
17 12.3
14 11.4
11 8.8
9 14.6
7 12.6
15 13
12 12.6
15 13.2
14 9.9
16 7.7
14 10.5
13 13.4
16 10.9
13 4.3
16 10.3
16 11.8
16 11.2
10 11.4
12 8.6
12 13.2
12 12.6
12 5.6
19 9.9
14 8.8
13 7.7
16 9
15 7.3
12 11.4
8 13.6
10 7.9
16 10.7
16 10.3
10 8.3
18 9.6
12 14.2
16 8.5
10 13.5
14 4.9
12 6.4
11 9.6
15 11.6
7 11.1
16 4.35
16 12.7
16 18.1
16 17.85
12 16.6
15 12.6
14 17.1
15 19.1
16 16.1
13 13.35
10 18.4
17 14.7
15 10.6
18 12.6
16 16.2
20 13.6
16 18.9
17 14.1
16 14.5
15 16.15
13 14.75
16 14.8
16 12.45
16 12.65
17 17.35
20 8.6
14 18.4
17 16.1
6 11.6
16 17.75
15 15.25
16 17.65
16 16.35
14 17.65
16 13.6
16 14.35
16 14.75
14 18.25
14 9.9
16 16
16 18.25
15 16.85
16 14.6
16 13.85
18 18.95
15 15.6
16 14.85
16 11.75
16 18.45
17 15.9
14 17.1
18 16.1
9 19.9
15 10.95
14 18.45
15 15.1
13 15
16 11.35
20 15.95
14 18.1
12 14.6
15 15.4
15 15.4
15 17.6
16 13.35
11 19.1
16 15.35
7 7.6
11 13.4
9 13.9
15 19.1
16 15.25
14 12.9
15 16.1
13 17.35
13 13.15
12 12.15
16 12.6
14 10.35
16 15.4
14 9.6
15 18.2
10 13.6
16 14.85
14 14.75
16 14.1
12 14.9
16 16.25
16 19.25
15 13.6
14 13.6
16 15.65
11 12.75
15 14.6
18 9.85
13 12.65
7 19.2
7 16.6
17 11.2
18 15.25
15 11.9
8 13.2
13 16.35
13 12.4
15 15.85
18 18.15
16 11.15
14 15.65
15 17.75
19 7.65
16 12.35
12 15.6
16 19.3
11 15.2
16 17.1
15 15.6
19 18.4
15 19.05
14 18.55
14 19.1
17 13.1
16 12.85
20 9.5
16 4.5
9 11.85
13 13.6
15 11.7
19 12.4
16 13.35
17 11.4
16 14.9
9 19.9
11 11.2
14 14.6
19 17.6
13 14.05
14 16.1
15 13.35
15 11.85
14 11.95
16 14.75
17 15.15
12 13.2
15 16.85
17 7.85
15 7.7
10 12.6
16 7.85
15 10.95
11 12.35
16 9.95
16 14.9
16 16.65
14 13.4
14 13.95
16 15.7
16 16.85
18 10.95
14 15.35
20 12.2
15 15.1
16 17.75
16 15.2
16 14.6
12 16.65
8 8.1

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265510&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265510&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265510&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'George Udny Yule' @ yule.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)13.7150.6521.1110
X0.0520.0481.0660.287
- - -
Residual Std. Err. 2.737 on 276 df
Multiple R-sq. 0.004
Adjusted R-sq. 0

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 13.715 & 0.65 & 21.111 & 0 \tabularnewline
X & 0.052 & 0.048 & 1.066 & 0.287 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.737  on  276 df \tabularnewline
Multiple R-sq.  & 0.004 \tabularnewline
Adjusted R-sq.  & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265510&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]13.715[/C][C]0.65[/C][C]21.111[/C][C]0[/C][/ROW]
[C]X[/C][C]0.052[/C][C]0.048[/C][C]1.066[/C][C]0.287[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.737  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.004[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265510&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265510&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)13.7150.6521.1110
X0.0520.0481.0660.287
- - -
Residual Std. Err. 2.737 on 276 df
Multiple R-sq. 0.004
Adjusted R-sq. 0






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT18.5128.5121.1360.287
Residuals2762067.3047.49 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT & 1 & 8.512 & 8.512 & 1.136 & 0.287 \tabularnewline
Residuals & 276 & 2067.304 & 7.49 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265510&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]TOT[/C][C]1[/C][C]8.512[/C][C]8.512[/C][C]1.136[/C][C]0.287[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]2067.304[/C][C]7.49[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265510&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265510&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)
TOT18.5128.5121.1360.287
Residuals2762067.3047.49


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()