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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 11:59:05 +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/t1418817554r3axwkcfo6o3d6r.htm/, Retrieved Thu, 16 May 2024 09:47:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270093, Retrieved Thu, 16 May 2024 09:47:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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 11:59:05] [4511a3627978005d3fb0dfa0eb9854e9] [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=270093&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=270093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270093&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)6.210.8257.5230
X0.0040.0620.0620.951
- - -
Residual Std. Err. 3.477 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) & 6.21 & 0.825 & 7.523 & 0 \tabularnewline
X & 0.004 & 0.062 & 0.062 & 0.951 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.477  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=270093&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]6.21[/C][C]0.825[/C][C]7.523[/C][C]0[/C][/ROW]
[C]X[/C][C]0.004[/C][C]0.062[/C][C]0.062[/C][C]0.951[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.477  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=270093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270093&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)6.210.8257.5230
X0.0040.0620.0620.951
- - -
Residual Std. Err. 3.477 on 276 df
Multiple R-sq. 0
Adjusted R-sq. -0.004






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT10.0460.0460.0040.951
Residuals2763337.30612.092 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT & 1 & 0.046 & 0.046 & 0.004 & 0.951 \tabularnewline
Residuals & 276 & 3337.306 & 12.092 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270093&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]0.046[/C][C]0.046[/C][C]0.004[/C][C]0.951[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3337.306[/C][C]12.092[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270093&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)
TOT10.0460.0460.0040.951
Residuals2763337.30612.092


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):
par3 <- 'FALSE'
par2 <- '2'
par1 <- '1'
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()