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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, 04 Dec 2015 13:02:26 +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/04/t14492343422jiq9y3874pn4ed.htm/, Retrieved Thu, 16 May 2024 09:03:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285128, Retrieved Thu, 16 May 2024 09:03:10 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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] [simple regression...] [2015-12-04 13:02:26] [83287827dabe987cb447ff9f7ffea17c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9 1
12.2 1
12.8 1
7.4 1
6.7 1
12.6 1
14.8 1
13.3 1
11.1 1
8.2 1
11.4 1
6.4 1
10.6 1
12 1
6.3 1
11.3 0
11.9 1
9.3 1
9.6 0
10 1
6.4 1
13.8 1
10.8 1
13.8 1
11.7 1
10.9 1
16.1 0
13.4 0
9.9 1
11.5 1
8.3 1
11.7 1
9 1
9.7 1
10.8 1
10.3 1
10.4 1
12.7 0
9.3 1
11.8 1
5.9 1
11.4 1
13 1
10.8 1
12.3 0
11.3 1
11.8 1
7.9 0
12.7 1
12.3 0
11.6 0
6.7 0
10.9 1
12.1 0
13.3 1
10.1 1
5.7 0
14.3 1
8 0
13.3 0
9.3 1
12.5 1
7.6 1
15.9 1
9.2 1
9.1 0
11.1 1
13 1
14.5 1
12.2 0
12.3 1
11.4 1
8.8 0
14.6 0
12.6 1
13 1
12.6 0
13.2 1
9.9 0
7.7 1
10.5 0
13.4 0
10.9 0
4.3 0
10.3 0
11.8 0
11.2 0
11.4 0
8.6 0
13.2 0
12.6 0
5.6 0
9.9 0
8.8 0
7.7 0
9 0
7.3 0
11.4 0
13.6 0
7.9 0
10.7 0
10.3 0
8.3 0
9.6 0
14.2 0
8.5 0
13.5 0
4.9 0
6.4 0
9.6 0
11.6 0
11.1 0
4.35 1
12.7 1
18.1 1
17.85 1
16.6 0
12.6 0
17.1 1
19.1 1
16.1 1
13.35 1
18.4 1
14.7 1
10.6 1
12.6 1
16.2 1
13.6 1
18.9 0
14.1 1
14.5 1
16.15 1
14.75 1
14.8 1
12.45 1
12.65 1
17.35 1
8.6 1
18.4 1
16.1 1
11.6 0
17.75 1
15.25 1
17.65 1
16.35 1
17.65 1
13.6 1
14.35 1
14.75 1
18.25 1
9.9 1
16 1
18.25 1
16.85 1
14.6 0
13.85 0
18.95 1
15.6 1
14.85 0
11.75 0
18.45 0
15.9 0
17.1 1
16.1 1
19.9 0
10.95 0
18.45 0
15.1 0
15 0
11.35 0
15.95 0
18.1 0
14.6 0
15.4 1
15.4 1
17.6 0
13.35 1
19.1 1
15.35 0
7.6 1
13.4 0
13.9 0
19.1 1
15.25 0
12.9 0
16.1 0
17.35 0
13.15 0
12.15 0
12.6 0
10.35 0
15.4 0
9.6 0
18.2 0
13.6 0
14.85 0
14.75 1
14.1 0
14.9 0
16.25 0
19.25 1
13.6 0
13.6 1
15.65 0
12.75 1
14.6 0
9.85 1
12.65 0
19.2 0
16.6 0
11.2 0
15.25 1
11.9 1
13.2 0
16.35 1
12.4 1
15.85 0
18.15 1
11.15 0
15.65 0
17.75 1
7.65 0
12.35 1
15.6 1
19.3 1
15.2 0
17.1 1
15.6 0
18.4 1
19.05 1
18.55 1
19.1 1
13.1 0
12.85 1
9.5 1
4.5 1
11.85 0
13.6 1
11.7 1
12.4 0
13.35 1
11.4 0
14.9 0
19.9 0
11.2 0
14.6 0
17.6 1
14.05 1
16.1 1
13.35 1
11.85 1
11.95 1
14.75 0
15.15 0
13.2 1
16.85 0
7.85 0
7.7 1
12.6 0
7.85 0
10.95 0
12.35 0
9.95 0
14.9 0
16.65 0
13.4 0
13.95 0
15.7 0
16.85 0
10.95 0
15.35 0
12.2 0
15.1 0
17.75 0
15.2 0
14.6 1
16.65 0
8.1 0

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285128&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285128&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'Herman Ole Andreas Wold' @ wold.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)12.7350.29143.780
X0.4690.4071.1530.25
- - -
Residual Std. Err. 3.392 on 276 df
Multiple R-sq. 0.005
95% CI Multiple R-sq. [0, 0.034]
Adjusted R-sq. 0.001

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 12.735 & 0.291 & 43.78 & 0 \tabularnewline
X & 0.469 & 0.407 & 1.153 & 0.25 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.392  on  276 df \tabularnewline
Multiple R-sq.  & 0.005 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.034] \tabularnewline
Adjusted R-sq.  & 0.001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285128&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]12.735[/C][C]0.291[/C][C]43.78[/C][C]0[/C][/ROW]
[C]X[/C][C]0.469[/C][C]0.407[/C][C]1.153[/C][C]0.25[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.392  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.005[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.034][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285128&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)12.7350.29143.780
X0.4690.4071.1530.25
- - -
Residual Std. Err. 3.392 on 276 df
Multiple R-sq. 0.005
95% CI Multiple R-sq. [0, 0.034]
Adjusted R-sq. 0.001






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
group115.29915.2991.3290.25
Residuals2763176.20511.508 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
group & 1 & 15.299 & 15.299 & 1.329 & 0.25 \tabularnewline
Residuals & 276 & 3176.205 & 11.508 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285128&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]group[/C][C]1[/C][C]15.299[/C][C]15.299[/C][C]1.329[/C][C]0.25[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3176.205[/C][C]11.508[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285128&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)
group115.29915.2991.3290.25
Residuals2763176.20511.508


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):
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()