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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 computationWed, 21 Dec 2016 15:58:42 +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/21/t1482332334gii5l3nz4ra795h.htm/, Retrieved Mon, 06 May 2024 21:42:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302357, Retrieved Mon, 06 May 2024 21:42:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79

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] [] [2016-12-21 14:58:42] [563c2945bc7c763925d38f2fb19cdb55] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15	13
13	16
14	17
13	14.66666667
12	16
17	16
12	17.33333333
13	16
13	17.33333333
16	17
12	17
12	15
13	16
16	14
15	16
12	17
14.66666667	16
15	14.66666667
12	17.33333333
15	16
11	14.66666667
13	16
13	14.66666667
14	17.33333333
14	14.66666667
14	16
15	15
16	16
16	16
16	13
13	15
13	17
14	14.66666667
13	13
14	17
12	14.66666667
17	14
14	14
15	18
13	14.66666667
14	17
15	13
19	16
14	15
13	15
12	16
4	15
14	13
15	12
15	17
12	17.33333333
14	17.33333333
11	11
12	14
10	13
14.66666667	14.66666667
14	17
14	16
15	14.66666667
15	17
13	16
15	16
16	16
12	15
17	12
15	17
18.66666667	14
12	14
16	16
15	14.66666667
15	14.66666667
12	13.33333333
13	13.33333333
10	17.33333333
14	15
11	16
12	14
14	15
12	17
14	16
12	10
13	16
13	17
14	17.33333333
12	20
15	17
13	18
13	14.66666667
11	17
12	14
16	14.66666667
11	17
13	16
12	17
17	14.66666667
14	16
15	18
8	18
13	16
13	16
15	17.33333333
14	15
13	13
14	14.66666667
12	17.33333333
19	16
15	16
14	14.66666667
14	16
15	16
13	13.33333333
15	14.66666667
14	12
11	18.66666667
17	16
13	16
9	17.33333333
12	16
13	14
17	15
14	14
13	16
16	15
14	17.33333333
14	15
14	16
10	16
12	14.66666667
13	14.66666667
14	11
18	16
14	18
14	13.33333333
13	11
13	16
16	18
14	12
13	15
14	19
8	17
13	13.33333333
13	14
16	16
14	13
13	17
14	14
12	19
16	14
18	16
16	12
15	16
18	16
15	15
14	12
14	14.66666667
15	17
9	13.33333333
17	14.66666667
11	18
15	15
16	18
15	15
13	14.66666667
16	16
15	13.33333333
15	16
14	13.33333333
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 time7 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 time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302357&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]7 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302357&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 time7 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)16.360.89718.2360
X-0.0690.064-1.0730.285
- - -
Residual Std. Err. 1.732 on 166 df
Multiple R-sq. 0.007
95% CI Multiple R-sq. [0, 0.05]
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) & 16.36 & 0.897 & 18.236 & 0 \tabularnewline
X & -0.069 & 0.064 & -1.073 & 0.285 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 1.732  on  166 df \tabularnewline
Multiple R-sq.  & 0.007 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.05] \tabularnewline
Adjusted R-sq.  & 0.001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302357&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]16.36[/C][C]0.897[/C][C]18.236[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.069[/C][C]0.064[/C][C]-1.073[/C][C]0.285[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]1.732  on  166 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.007[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.05][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302357&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)16.360.89718.2360
X-0.0690.064-1.0730.285
- - -
Residual Std. Err. 1.732 on 166 df
Multiple R-sq. 0.007
95% CI Multiple R-sq. [0, 0.05]
Adjusted R-sq. 0.001






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
privacy13.4533.4531.1510.285
Residuals166498.0373 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
privacy & 1 & 3.453 & 3.453 & 1.151 & 0.285 \tabularnewline
Residuals & 166 & 498.037 & 3 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302357&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]privacy[/C][C]1[/C][C]3.453[/C][C]3.453[/C][C]1.151[/C][C]0.285[/C][/ROW]
[ROW][C]Residuals[/C][C]166[/C][C]498.037[/C][C]3[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302357&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)
privacy13.4533.4531.1510.285
Residuals166498.0373


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = 1 ; par3 = 2 ; par4 = FALSE ;
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()