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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, 18 Dec 2015 19:44:04 +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/2015/Dec/18/t1450468173k5ao42vq6y2tdaa.htm/, Retrieved Thu, 16 May 2024 23:36:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286928, Retrieved Thu, 16 May 2024 23:36:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [regression 2] [2015-12-18 19:44:04] [2dd7367b8030d78c01d18163d124e067] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9 11
12.2 19
12.8 16
7.4 24
6.7 15
12.6 17
14.8 19
13.3 19
11.1 28
8.2 26
11.4 15
6.4 26
10.6 16
12 24
6.3 25
11.3 22
11.9 15
9.3 21
9.6 22
10 27
6.4 26
13.8 26
10.8 22
13.8 21
11.7 22
10.9 20
16.1 21
13.4 20
9.9 22
11.5 21
8.3 8
11.7 22
9 20
9.7 24
10.8 17
10.3 20
10.4 23
12.7 20
9.3 22
11.8 19
5.9 15
11.4 20
13 22
10.8 17
12.3 14
11.3 24
11.8 17
7.9 23
12.7 25
12.3 16
11.6 18
6.7 20
10.9 18
12.1 23
13.3 24
10.1 23
5.7 13
14.3 20
8 20
13.3 19
9.3 22
12.5 22
7.6 15
15.9 17
9.2 19
9.1 20
11.1 22
13 21
14.5 21
12.2 16
12.3 20
11.4 21
8.8 20
14.6 23
12.6 18
13 16
12.6 17
13.2 24
9.9 13
7.7 19
10.5 20
13.4 22
10.9 19
4.3 21
10.3 15
11.8 21
11.2 24
11.4 22
8.6 20
13.2 21
12.6 19
5.6 14
9.9 25
8.8 11
7.7 17
9 22
7.3 20
11.4 22
13.6 15
7.9 23
10.7 20
10.3 22
8.3 16
9.6 25
14.2 18
8.5 19
13.5 25
4.9 21
6.4 22
9.6 21
11.6 22
11.1 23
4.35 20
12.7 6
18.1 15
17.85 18
16.6 24
12.6 22
17.1 21
19.1 23
16.1 20
13.35 20
18.4 18
14.7 25
10.6 16
12.6 20
16.2 14
13.6 22
18.9 26
14.1 20
14.5 17
16.15 22
14.75 22
14.8 20
12.45 17
12.65 22
17.35 17
8.6 22
18.4 21
16.1 25
11.6 11
17.75 19
15.25 24
17.65 17
16.35 22
17.65 17
13.6 26
14.35 20
14.75 19
18.25 21
9.9 24
16 21
18.25 19
16.85 13
14.6 24
13.85 28
18.95 27
15.6 22
14.85 23
11.75 19
18.45 18
15.9 23
17.1 21
16.1 22
19.9 17
10.95 15
18.45 21
15.1 20
15 26
11.35 19
15.95 28
18.1 21
14.6 19
15.4 22
15.4 21
17.6 20
13.35 19
19.1 11
15.35 17
7.6 19
13.4 20
13.9 17
19.1 21
15.25 21
12.9 12
16.1 23
17.35 22
13.15 22
12.15 21
12.6 20
10.35 18
15.4 21
9.6 24
18.2 22
13.6 20
14.85 17
14.75 19
14.1 16
14.9 19
16.25 23
19.25 8
13.6 22
13.6 23
15.65 15
12.75 17
14.6 21
9.85 25
12.65 18
19.2 20
16.6 21
11.2 21
15.25 24
11.9 22
13.2 22
16.35 23
12.4 17
15.85 15
18.15 22
11.15 19
15.65 18
17.75 21
7.65 20
12.35 19
15.6 19
19.3 16
15.2 18
17.1 23
15.6 22
18.4 23
19.05 20
18.55 24
19.1 25
13.1 25
12.85 20
9.5 23
4.5 21
11.85 23
13.6 23
11.7 11
12.4 21
13.35 27
11.4 19
14.9 21
19.9 16
11.2 21
14.6 22
17.6 16
14.05 18
16.1 23
13.35 24
11.85 20
11.95 20
14.75 18
15.15 4
13.2 14
16.85 22
7.85 17
7.7 23
12.6 20
7.85 18
10.95 19
12.35 20
9.95 15
14.9 24
16.65 21
13.4 19
13.95 19
15.7 27
16.85 23
10.95 23
15.35 20
12.2 17
15.1 21
17.75 23
15.2 22
14.6 16
16.65 20
8.1 16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286928&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]7 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=286928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286928&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 time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)19.6740.88322.2790
X0.0290.0660.4360.663
- - -
Residual Std. Err. 3.72 on 276 df
Multiple R-sq. 0.001
95% CI Multiple R-sq. [0, 0.007]
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) & 19.674 & 0.883 & 22.279 & 0 \tabularnewline
X & 0.029 & 0.066 & 0.436 & 0.663 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.72  on  276 df \tabularnewline
Multiple R-sq.  & 0.001 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.007] \tabularnewline
Adjusted R-sq.  & -0.003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286928&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]19.674[/C][C]0.883[/C][C]22.279[/C][C]0[/C][/ROW]
[C]X[/C][C]0.029[/C][C]0.066[/C][C]0.436[/C][C]0.663[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.72  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.001[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.007][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286928&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)19.6740.88322.2790
X0.0290.0660.4360.663
- - -
Residual Std. Err. 3.72 on 276 df
Multiple R-sq. 0.001
95% CI Multiple R-sq. [0, 0.007]
Adjusted R-sq. -0.003






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT12.632.630.190.663
Residuals2763819.76213.84 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT & 1 & 2.63 & 2.63 & 0.19 & 0.663 \tabularnewline
Residuals & 276 & 3819.762 & 13.84 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286928&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]2.63[/C][C]2.63[/C][C]0.19[/C][C]0.663[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3819.762[/C][C]13.84[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286928&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)
TOT12.632.630.190.663
Residuals2763819.76213.84


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'
library(boot)
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- na.omit(t(x))
rsq <- function(formula, data, indices) {
d <- data[indices,] # allows boot to select sample
fit <- lm(formula, data=d)
return(summary(fit)$r.square)
}
xdf<-data.frame(na.omit(t(y)))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
(results <- boot(data=xdf, statistic=rsq, R=1000, formula=Y~X))
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'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, '95% CI Multiple R-sq. ',1,TRUE)
a<-table.element(a, paste('[',round(boot.ci(results,type='bca')$bca[1,4], digits=3),', ', round(boot.ci(results,type='bca')$bca[1,5], digits=3), ']',sep='') ,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$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qqPlot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot(lmxdf, which=4)
dev.off()