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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, 17 Dec 2014 12:06:27 +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/17/t1418818119s85nq8w7xlnxnab.htm/, Retrieved Thu, 16 May 2024 13:29:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270101, Retrieved Thu, 16 May 2024 13:29:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

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] [] [2014-12-17 12:06:27] [e63466588bf3c49b37383cc70d2c7b07] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4	12,9
4	12,2
5	12,8
4	7,4
4	6,7
9	12,6
8	14,8
11	13,3
4	11,1
4	8,2
6	11,4
4	6,4
8	10,6
4	12,0
4	6,3
11	11,3
4	11,9
4	9,3
6	9,6
6	10,0
4	6,4
8	13,8
5	10,8
4	13,8
9	11,7
4	10,9
7	16,1
10	13,4
4	9,9
4	11,5
7	8,3
12	11,7
7	9,0
5	9,7
8	10,8
5	10,3
4	10,4
9	12,7
7	9,3
4	11,8
4	5,9
4	11,4
4	13,0
4	10,8
7	12,3
4	11,3
7	11,8
4	7,9
4	12,7
4	12,3
4	11,6
8	6,7
4	10,9
4	12,1
4	13,3
4	10,1
7	5,7
12	14,3
4	8,0
4	13,3
4	9,3
5	12,5
15	7,6
5	15,9
10	9,2
9	9,1
8	11,1
4	13,0
5	14,5
4	12,2
9	12,3
4	11,4
10	8,8
4	14,6
4	12,6
7	13,0
5	12,6
4	13,2
4	9,9
4	7,7
4	10,5
4	13,4
4	10,9
6	4,3
10	10,3
7	11,8
4	11,2
4	11,4
7	8,6
4	13,2
8	12,6
11	5,6
6	9,9
14	8,8
5	7,7
4	9,0
8	7,3
9	11,4
4	13,6
4	7,9
5	10,7
4	10,3
5	8,3
4	9,6
4	14,2
7	8,5
10	13,5
4	4,9
5	6,4
4	9,6
4	11,6
4	11,1
6	4,35
4	12,7
8	18,1
5	17,85
4	16,6
17	12,6
4	17,1
4	19,1
8	16,1
4	13,35
7	18,4
4	14,7
4	10,6
5	12,6
7	16,2
4	13,6
4	18,9
7	14,1
11	14,5
7	16,15
4	14,75
4	14,8
4	12,45
4	12,65
4	17,35
4	8,6
6	18,4
8	16,1
23	11,6
4	17,75
8	15,25
6	17,65
4	16,35
7	17,65
4	13,6
4	14,35
4	14,75
10	18,25
6	9,9
5	16
5	18,25
4	16,85
4	14,6
5	13,85
5	18,95
5	15,6
5	14,85
4	11,75
6	18,45
4	15,9
4	17,1
4	16,1
9	19,9
18	10,95
6	18,45
5	15,1
4	15
11	11,35
4	15,95
10	18,1
6	14,6
8	15,4
8	15,4
6	17,6
8	13,35
4	19,1
4	15,35
9	7,6
9	13,4
5	13,9
4	19,1
4	15,25
15	12,9
10	16,1
9	17,35
7	13,15
9	12,15
6	12,6
4	10,35
7	15,4
4	9,6
7	18,2
4	13,6
15	14,85
4	14,75
9	14,1
4	14,9
4	16,25
28	19,25
4	13,6
4	13,6
4	15,65
5	12,75
4	14,6
4	9,85
12	12,65
4	19,2
6	16,6
6	11,2
5	15,25
4	11,9
4	13,2
4	16,35
10	12,4
7	15,85
4	18,15
7	11,15
4	15,65
4	17,75
12	7,65
5	12,35
8	15,6
6	19,3
17	15,2
4	17,1
5	15,6
4	18,4
5	19,05
5	18,55
6	19,1
4	13,1
4	12,85
4	9,5
6	4,5
8	11,85
10	13,6
4	11,7
5	12,4
4	13,35
4	11,4
4	14,9
16	19,9
7	11,2
4	14,6
4	17,6
14	14,05
5	16,1
5	13,35
5	11,85
5	11,95
7	14,75
19	15,15
16	13,2
4	16,85
4	7,85
7	7,7
9	12,6
5	7,85
14	10,95
4	12,35
16	9,95
10	14,9
5	16,65
6	13,4
4	13,95
4	15,7
4	16,85
5	10,95
4	15,35
4	12,2
5	15,1
4	17,75
4	15,2
5	14,6
8	16,65
15	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'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=270101&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=270101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270101&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)12.9520.42130.7580
X0.0040.0590.0620.951
- - -
Residual Std. Err. 3.4 on 276 df
Multiple R-sq. 0
Adjusted R-sq. -0.004

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 12.952 & 0.421 & 30.758 & 0 \tabularnewline
X & 0.004 & 0.059 & 0.062 & 0.951 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.4  on  276 df \tabularnewline
Multiple R-sq.  & 0 \tabularnewline
Adjusted R-sq.  & -0.004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270101&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]12.952[/C][C]0.421[/C][C]30.758[/C][C]0[/C][/ROW]
[C]X[/C][C]0.004[/C][C]0.059[/C][C]0.062[/C][C]0.951[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.4  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270101&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)12.9520.42130.7580
X0.0040.0590.0620.951
- - -
Residual Std. Err. 3.4 on 276 df
Multiple R-sq. 0
Adjusted R-sq. -0.004






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Motivation10.0440.0440.0040.951
Residuals2763191.4611.563 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Motivation & 1 & 0.044 & 0.044 & 0.004 & 0.951 \tabularnewline
Residuals & 276 & 3191.46 & 11.563 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270101&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]Motivation[/C][C]1[/C][C]0.044[/C][C]0.044[/C][C]0.004[/C][C]0.951[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3191.46[/C][C]11.563[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270101&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270101&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)
Motivation10.0440.0440.0040.951
Residuals2763191.4611.563


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- '1'
par1 <- '2'
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()