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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, 15 Dec 2016 19:43:25 +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/2016/Dec/15/t1481827434lh2k55dig4p76rt.htm/, Retrieved Fri, 01 Nov 2024 03:35:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299953, Retrieved Fri, 01 Nov 2024 03:35:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [] [2016-12-15 18:43:25] [462f83e9ca944f1b841aaa868aea0854] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15	13
13	16
14	17
13	NA
12	NA
17	16
12	NA
13	NA
13	NA
16	17
12	17
12	15
13	16
16	14
15	16
12	17
NA	NA
NA	NA
15	NA
12	NA
15	16
11	NA
13	16
13	NA
14	NA
14	NA
14	16
15	15
16	16
16	16
16	13
13	15
13	17
14	NA
13	13
14	17
12	NA
17	14
14	14
15	18
13	NA
14	17
15	13
19	16
14	15
13	15
12	NA
NA	15
14	13
15	NA
15	17
12	NA
14	NA
11	11
12	14
10	13
NA	NA
14	17
14	16
15	NA
15	17
13	16
15	16
16	16
12	15
17	12
15	17
NA	14
12	14
16	16
15	NA
15	NA
12	NA
13	NA
10	NA
14	15
11	16
12	14
14	15
12	17
14	NA
12	10
13	NA
13	17
14	NA
12	20
15	17
13	18
13	NA
11	17
12	14
16	NA
11	17
13	NA
12	17
17	NA
14	16
15	18
8	18
13	16
13	NA
15	NA
14	15
13	13
14	NA
12	NA
19	NA
15	NA
14	NA
14	16
15	NA
13	NA
15	NA
14	12
11	NA
17	16
13	16
9	NA
12	16
13	14
17	15
14	14
13	NA
16	15
14	NA
14	15
14	16
10	NA
12	NA
13	NA
14	11
18	NA
14	18
14	NA
13	11
13	NA
16	18
NA	NA
13	15
14	19
8	17
13	NA
13	14
16	NA
14	13
13	17
14	14
12	19
16	14
18	NA
16	NA
15	16
18	16
15	15
14	12
14	NA
15	17
9	NA
17	NA
11	18
15	15
NA	18
15	15
13	NA
NA	NA
15	NA
15	16
14	NA
13	16

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299953&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]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299953&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 time6 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)16.2811.40711.5690
X-0.0590.101-0.5820.562
- - -
Residual Std. Err. 1.884 on 98 df
Multiple R-sq. 0.003
95% CI Multiple R-sq. [0, 0.037]
Adjusted R-sq. -0.007

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 16.281 & 1.407 & 11.569 & 0 \tabularnewline
X & -0.059 & 0.101 & -0.582 & 0.562 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 1.884  on  98 df \tabularnewline
Multiple R-sq.  & 0.003 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.037] \tabularnewline
Adjusted R-sq.  & -0.007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299953&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]16.281[/C][C]1.407[/C][C]11.569[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.059[/C][C]0.101[/C][C]-0.582[/C][C]0.562[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]1.884  on  98 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.003[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.037][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299953&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)16.2811.40711.5690
X-0.0590.101-0.5820.562
- - -
Residual Std. Err. 1.884 on 98 df
Multiple R-sq. 0.003
95% CI Multiple R-sq. [0, 0.037]
Adjusted R-sq. -0.007






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
EPSUM11.21.20.3380.562
Residuals98347.713.548 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
EPSUM & 1 & 1.2 & 1.2 & 0.338 & 0.562 \tabularnewline
Residuals & 98 & 347.71 & 3.548 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299953&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]EPSUM[/C][C]1[/C][C]1.2[/C][C]1.2[/C][C]0.338[/C][C]0.562[/C][/ROW]
[ROW][C]Residuals[/C][C]98[/C][C]347.71[/C][C]3.548[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299953&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299953&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)
EPSUM11.21.20.3380.562
Residuals98347.713.548


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; 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()