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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 computationThu, 10 Dec 2015 16:38:27 +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/2015/Dec/10/t1449766188rzmr3p61848ozu3.htm/, Retrieved Sat, 18 May 2024 14:46:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285821, Retrieved Sat, 18 May 2024 14:46:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

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] [Paper - SLR motiv...] [2015-12-10 16:38:27] [024df7c298481a95aca593c6dd9022cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18 12.9
23 12.2
22 12.8
22 7.4
19 6.7
25 12.6
28 14.8
16 13.3
28 11.1
21 8.2
22 11.4
24 6.4
24 10.6
26 12
28 6.3
24 11.3
20 11.9
26 9.3
21 9.6
28 10
27 6.4
23 13.8
24 10.8
24 13.8
22 11.7
21 10.9
25 16.1
20 13.4
21 9.9
26 11.5
23 8.3
21 11.7
27 9
25 9.7
23 10.8
25 10.3
23 10.4
19 12.7
22 9.3
24 11.8
19 5.9
21 11.4
27 13
25 10.8
25 12.3
23 11.3
17 11.8
28 7.9
25 12.7
20 12.3
25 11.6
21 6.7
24 10.9
28 12.1
20 13.3
19 10.1
24 5.7
21 14.3
24 8
23 13.3
18 9.3
27 12.5
25 7.6
20 15.9
21 9.2
23 9.1
27 11.1
24 13
27 14.5
24 12.2
23 12.3
24 11.4
21 8.8
23 14.6
27 12.6
25 13
19 12.6
24 13.2
25 9.9
23 7.7
23 10.5
25 13.4
26 10.9
26 4.3
16 10.3
23 11.8
26 11.2
25 11.4
23 8.6
26 13.2
22 12.6
20 5.6
27 9.9
20 8.8
22 7.7
24 9
21 7.3
24 11.4
26 13.6
24 7.9
24 10.7
27 10.3
25 8.3
27 9.6
19 14.2
22 8.5
22 13.5
25 4.9
23 6.4
24 9.6
24 11.6
23 11.1
22 4.35
24 12.7
19 18.1
25 17.85
26 16.6
18 12.6
24 17.1
28 19.1
23 16.1
19 13.35
19 18.4
27 14.7
24 10.6
26 12.6
21 16.2
25 13.6
28 18.9
19 14.1
20 14.5
26 16.15
27 14.75
23 14.8
18 12.45
23 12.65
21 17.35
23 8.6
22 18.4
21 16.1
14 11.6
24 17.75
26 15.25
24 17.65
22 16.35
20 17.65
20 13.6
18 14.35
18 14.75
25 18.25
28 9.9
23 16
20 18.25
22 16.85
27 14.6
24 13.85
23 18.95
20 15.6
22 14.85
21 11.75
24 18.45
26 15.9
24 17.1
18 16.1
17 19.9
23 10.95
21 18.45
21 15.1
24 15
22 11.35
24 15.95
24 18.1
24 14.6
23 15.4
21 15.4
24 17.6
19 13.35
19 19.1
23 15.35
25 7.6
24 13.4
21 13.9
18 19.1
23 15.25
20 12.9
23 16.1
23 17.35
23 13.15
23 12.15
27 12.6
19 10.35
25 15.4
25 9.6
21 18.2
25 13.6
17 14.85
22 14.75
23 14.1
27 14.9
27 16.25
5 19.25
19 13.6
24 13.6
23 15.65
28 12.75
25 14.6
27 9.85
16 12.65
25 19.2
26 16.6
24 11.2
23 15.25
24 11.9
27 13.2
25 16.35
19 12.4
19 15.85
24 18.15
20 11.15
21 15.65
28 17.75
26 7.65
19 12.35
23 15.6
23 19.3
21 15.2
26 17.1
25 15.6
25 18.4
24 19.05
23 18.55
22 19.1
27 13.1
26 12.85
23 9.5
22 4.5
26 11.85
22 13.6
17 11.7
25 12.4
22 13.35
28 11.4
22 14.9
21 19.9
24 11.2
26 14.6
26 17.6
24 14.05
27 16.1
22 13.35
23 11.85
22 11.95
23 14.75
15 15.15
20 13.2
22 16.85
25 7.85
27 7.7
24 12.6
21 7.85
17 10.95
26 12.35
20 9.95
22 14.9
24 16.65
23 13.4
22 13.95
28 15.7
21 16.85
24 10.95
28 15.35
25 12.2
24 15.1
24 17.75
21 15.2
20 14.6
26 16.65
16 8.1

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285821&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285821&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'George Udny Yule' @ yule.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)14.7521.5289.6530
X-0.0770.066-1.1730.242
- - -
Residual Std. Err. 3.392 on 276 df
Multiple R-sq. 0.005
95% CI Multiple R-sq. [0, 0.039]
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) & 14.752 & 1.528 & 9.653 & 0 \tabularnewline
X & -0.077 & 0.066 & -1.173 & 0.242 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.392  on  276 df \tabularnewline
Multiple R-sq.  & 0.005 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.039] \tabularnewline
Adjusted R-sq.  & 0.001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285821&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]14.752[/C][C]1.528[/C][C]9.653[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.077[/C][C]0.066[/C][C]-1.173[/C][C]0.242[/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, 0.039][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285821&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)14.7521.5289.6530
X-0.0770.066-1.1730.242
- - -
Residual Std. Err. 3.392 on 276 df
Multiple R-sq. 0.005
95% CI Multiple R-sq. [0, 0.039]
Adjusted R-sq. 0.001






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
AMS.E1115.83815.8381.3760.242
Residuals2763175.66611.506 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
AMS.E1 & 1 & 15.838 & 15.838 & 1.376 & 0.242 \tabularnewline
Residuals & 276 & 3175.666 & 11.506 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285821&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]AMS.E1[/C][C]1[/C][C]15.838[/C][C]15.838[/C][C]1.376[/C][C]0.242[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3175.666[/C][C]11.506[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285821&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285821&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)
AMS.E1115.83815.8381.3760.242
Residuals2763175.66611.506


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 <- '2'
par1 <- '1'
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()