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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 computationTue, 09 Dec 2014 12:47:37 +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/09/t1418129283etcccvdw63vxrce.htm/, Retrieved Thu, 16 May 2024 11:35:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=264536, Retrieved Thu, 16 May 2024 11:35:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Blocked Bootstrap Plot - Central Tendency] [] [2014-11-02 13:37:17] [cc401d1001c65f55a3dfc6f2420e9570]
- RMPD  [Simple Linear Regression] [] [2014-11-02 15:26:26] [cc401d1001c65f55a3dfc6f2420e9570]
- RM      [Simple Linear Regression] [] [2014-11-05 18:55:35] [e296091fd6311efcd9175c015e8e9c4e]
-  MPD        [Simple Linear Regression] [] [2014-12-09 12:47:37] [72ee53c6f28232e74174360ca89644de] [Current]
-   PD          [Simple Linear Regression] [] [2014-12-14 12:39:34] [36c866d94170840abc594fd3e7d5794f]
-   PD          [Simple Linear Regression] [] [2014-12-14 12:50:11] [36c866d94170840abc594fd3e7d5794f]
-    D            [Simple Linear Regression] [] [2014-12-14 12:55:18] [36c866d94170840abc594fd3e7d5794f]
-    D              [Simple Linear Regression] [] [2014-12-14 12:59:02] [36c866d94170840abc594fd3e7d5794f]
-    D                [Simple Linear Regression] [] [2014-12-14 13:02:17] [36c866d94170840abc594fd3e7d5794f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9 21
12.2 26
12.8 22
7.4 22
6.7 18
12.6 23
14.8 12
13.3 20
11.1 22
8.2 21
11.4 19
6.4 22
10.6 15
12 20
6.3 19
11.3 18
11.9 15
9.3 20
9.6 21
10 21
6.4 15
13.8 16
10.8 23
13.8 21
11.7 18
10.9 25
16.1 9
13.4 30
9.9 20
11.5 23
8.3 16
11.7 16
9 19
9.7 25
10.8 25
10.3 18
10.4 23
12.7 21
9.3 10
11.8 14
5.9 22
11.4 26
13 23
10.8 23
12.3 24
11.3 24
11.8 18
7.9 23
12.7 15
12.3 19
11.6 16
6.7 25
10.9 23
12.1 17
13.3 19
10.1 21
5.7 18
14.3 27
8 21
13.3 13
9.3 8
12.5 29
7.6 28
15.9 23
9.2 21
9.1 19
11.1 19
13 20
14.5 18
12.2 19
12.3 17
11.4 19
8.8 25
14.6 19
12.6 22
13 26
12.6 14
13.2 28
9.9 16
7.7 24
10.5 20
13.4 12
10.9 24
4.3 22
10.3 12
11.8 22
11.2 20
11.4 10
8.6 23
13.2 17
12.6 22
5.6 24
9.9 18
8.8 21
7.7 20
9 20
7.3 22
11.4 19
13.6 20
7.9 26
10.7 23
10.3 24
8.3 21
9.6 21
14.2 19
8.5 8
13.5 17
4.9 20
6.4 11
9.6 8
11.6 15
11.1 18
4.35 18
12.7 19
18.1 19
17.85 23
16.6 22
12.6 21
17.1 25
19.1 30
16.1 17
13.35 27
18.4 23
14.7 23
10.6 18
12.6 18
16.2 23
13.6 19
18.9 15
14.1 20
14.5 16
16.15 24
14.75 25
14.8 25
12.45 19
12.65 19
17.35 16
8.6 19
18.4 19
16.1 23
11.6 21
17.75 22
15.25 19
17.65 20
16.35 20
17.65 3
13.6 23
14.35 14
14.75 23
18.25 20
9.9 15
16 13
18.25 16
16.85 7
14.6 24
13.85 17
18.95 24
15.6 24
14.85 19
11.75 25
18.45 20
15.9 28
17.1 23
16.1 27
19.9 18
10.95 28
18.45 21
15.1 19
15 23
11.35 27
15.95 22
18.1 28
14.6 25
15.4 21
15.4 22
17.6 28
13.35 20
19.1 29
15.35 25
7.6 25
13.4 20
13.9 20
19.1 16
15.25 20
12.9 20
16.1 23
17.35 18
13.15 25
12.15 18
12.6 19
10.35 25
15.4 25
9.6 25
18.2 24
13.6 19
14.85 26
14.75 10
14.1 17
14.9 13
16.25 17
19.25 30
13.6 25
13.6 4
15.65 16
12.75 21
14.6 23
9.85 22
12.65 17
19.2 20
16.6 20
11.2 22
15.25 16
11.9 23
13.2 16
16.35 0
12.4 18
15.85 25
18.15 23
11.15 12
15.65 18
17.75 24
7.65 11
12.35 18
15.6 14
19.3 23
15.2 24
17.1 29
15.6 18
18.4 15
19.05 29
18.55 16
19.1 19
13.1 22
12.85 16
9.5 23
4.5 23
11.85 19
13.6 4
11.7 20
12.4 24
13.35 20
11.4 4
14.9 24
19.9 22
11.2 16
14.6 3
17.6 15
14.05 24
16.1 17
13.35 20
11.85 27
11.95 23
14.75 26
15.15 23
13.2 17
16.85 20
7.85 22
7.7 19
12.6 24
7.85 19
10.95 23
12.35 15
9.95 27
14.9 26
16.65 22
13.4 22
13.95 18
15.7 15
16.85 22
10.95 27
15.35 10
12.2 20
15.1 17
17.75 23
15.2 19
14.6 13
16.65 27
8.1 23

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264536&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264536&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)19.5031.20616.1760
X0.0390.090.4360.663
- - -
Residual Std. Err. 5.079 on 276 df
Multiple R-sq. 0.001
Adjusted R-sq. -0.003

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 19.503 & 1.206 & 16.176 & 0 \tabularnewline
X & 0.039 & 0.09 & 0.436 & 0.663 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 5.079  on  276 df \tabularnewline
Multiple R-sq.  & 0.001 \tabularnewline
Adjusted R-sq.  & -0.003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264536&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]19.503[/C][C]1.206[/C][C]16.176[/C][C]0[/C][/ROW]
[C]X[/C][C]0.039[/C][C]0.09[/C][C]0.436[/C][C]0.663[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]5.079  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.001[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264536&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)19.5031.20616.1760
X0.0390.090.4360.663
- - -
Residual Std. Err. 5.079 on 276 df
Multiple R-sq. 0.001
Adjusted R-sq. -0.003






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOTAL14.8984.8980.190.663
Residuals2767120.0725.797 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOTAL & 1 & 4.898 & 4.898 & 0.19 & 0.663 \tabularnewline
Residuals & 276 & 7120.07 & 25.797 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=264536&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]TOTAL[/C][C]1[/C][C]4.898[/C][C]4.898[/C][C]0.19[/C][C]0.663[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]7120.07[/C][C]25.797[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=264536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=264536&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)
TOTAL14.8984.8980.190.663
Residuals2767120.0725.797


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; 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()