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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, 31 Jan 2019 15:39:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Jan/31/t1548945592lw7fywzfjrxqk2m.htm/, Retrieved Sun, 05 May 2024 16:42:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318137, Retrieved Sun, 05 May 2024 16:42:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact19

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] [] [2019-01-31 14:39:30] [adb7236b59c3456f5dcd54db447fd65c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14 13 22
19 16 24
17 17 26
17 NA 21
15 NA 26
20 16 25
15 NA 21
19 NA 24
15 NA 27
15 17 28
19 17 23
NA 15 25
20 16 24
18 14 24
15 16 24
14 17 25
20 NA 25
NA NA NA
16 NA 25
16 NA 25
16 16 24
10 NA 26
19 16 26
19 NA 25
16 NA 26
15 NA 23
18 16 24
17 15 24
19 16 25
17 16 25
NA 13 24
19 15 28
20 17 27
5 NA NA
19 13 23
16 17 23
15 NA 24
16 14 24
18 14 22
16 18 25
15 NA 25
17 17 28
NA 13 22
20 16 28
19 15 25
7 15 24
13 NA 24
16 15 23
16 13 25
NA NA NA
18 17 26
18 NA 25
16 NA 27
17 11 26
19 14 23
16 13 25
19 NA 21
13 17 22
16 16 24
13 NA 25
12 17 27
17 16 24
17 16 26
17 16 21
16 15 27
16 12 22
14 17 23
16 14 24
13 14 25
16 16 24
14 NA 23
20 NA 28
12 NA NA
13 NA 24
18 NA 26
14 15 22
19 16 25
18 14 25
14 15 24
18 17 24
19 NA 26
15 10 21
14 NA 25
17 17 25
19 NA 26
13 20 25
19 17 26
18 18 27
20 NA 25
15 17 NA
15 14 20
15 NA 24
20 17 26
15 NA 25
19 17 25
18 NA 24
18 16 26
15 18 25
20 18 28
17 16 27
12 NA 25
18 NA 26
19 15 26
20 13 26
NA NA NA
17 NA 28
15 NA NA
16 NA 21
18 NA 25
18 16 25
14 NA 24
15 NA 24
12 NA 24
17 12 23
14 NA 23
18 16 24
17 16 24
17 NA 25
20 16 28
16 14 23
14 15 24
15 14 23
18 NA 24
20 15 25
17 NA 24
17 15 23
17 16 23
17 NA 25
15 NA 21
17 NA 22
18 11 19
17 NA 24
20 18 25
15 NA 21
16 11 22
15 NA 23
18 18 27
11 NA NA
15 15 26
18 19 29
20 17 28
19 NA 24
14 14 25
16 NA 25
15 13 22
17 17 25
18 14 26
20 19 26
17 14 24
18 NA 25
15 NA 19
16 16 25
11 16 23
15 15 25
18 12 25
17 NA 26
16 17 27
12 NA 24
19 NA 22
18 18 25
15 15 24
17 18 23
19 15 27
18 NA 24
19 NA 24
16 NA 21
16 16 25
16 NA 25
14 16 23

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time16 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time16 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318137&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]16 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318137&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time16 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)14.6541.9257.6120
X0.1410.1231.1430.256
- - -
Residual Std. Err. 2.281 on 97 df
Multiple R-sq. 0.013
95% CI Multiple R-sq. [0, 0.076]
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) & 14.654 & 1.925 & 7.612 & 0 \tabularnewline
X & 0.141 & 0.123 & 1.143 & 0.256 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.281  on  97 df \tabularnewline
Multiple R-sq.  & 0.013 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.076] \tabularnewline
Adjusted R-sq.  & 0.003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318137&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]14.654[/C][C]1.925[/C][C]7.612[/C][C]0[/C][/ROW]
[C]X[/C][C]0.141[/C][C]0.123[/C][C]1.143[/C][C]0.256[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.281  on  97 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.013[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.076][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318137&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)14.6541.9257.6120
X0.1410.1231.1430.256
- - -
Residual Std. Err. 2.281 on 97 df
Multiple R-sq. 0.013
95% CI Multiple R-sq. [0, 0.076]
Adjusted R-sq. 0.003






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TVDC16.7916.7911.3050.256
Residuals97504.6245.202 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TVDC & 1 & 6.791 & 6.791 & 1.305 & 0.256 \tabularnewline
Residuals & 97 & 504.624 & 5.202 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318137&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]TVDC[/C][C]1[/C][C]6.791[/C][C]6.791[/C][C]1.305[/C][C]0.256[/C][/ROW]
[ROW][C]Residuals[/C][C]97[/C][C]504.624[/C][C]5.202[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318137&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)
TVDC16.7916.7911.3050.256
Residuals97504.6245.202


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()