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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 17:45:19 +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/t1449769885oxcwierrd07m5ph.htm/, Retrieved Thu, 16 May 2024 14:41:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285829, Retrieved Thu, 16 May 2024 14:41:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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 17:45:19] [024df7c298481a95aca593c6dd9022cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4 12.9
4 12.2
5 12.8
4 7.4
4 6.7
9 12.6
8 14.8
11 13.3
4 11.1
4 8.2
6 11.4
4 6.4
8 10.6
4 12
4 6.3
11 11.3
4 11.9
4 9.3
6 9.6
6 10
4 6.4
8 13.8
5 10.8
4 13.8
9 11.7
4 10.9
7 16.1
10 13.4
4 9.9
4 11.5
7 8.3
12 11.7
7 9
5 9.7
8 10.8
5 10.3
4 10.4
9 12.7
7 9.3
4 11.8
4 5.9
4 11.4
4 13
4 10.8
7 12.3
4 11.3
7 11.8
4 7.9
4 12.7
4 12.3
4 11.6
8 6.7
4 10.9
4 12.1
4 13.3
4 10.1
7 5.7
12 14.3
4 8
4 13.3
4 9.3
5 12.5
15 7.6
5 15.9
10 9.2
9 9.1
8 11.1
4 13
5 14.5
4 12.2
9 12.3
4 11.4
10 8.8
4 14.6
4 12.6
7 13
5 12.6
4 13.2
4 9.9
4 7.7
4 10.5
4 13.4
4 10.9
6 4.3
10 10.3
7 11.8
4 11.2
4 11.4
7 8.6
4 13.2
8 12.6
11 5.6
6 9.9
14 8.8
5 7.7
4 9
8 7.3
9 11.4
4 13.6
4 7.9
5 10.7
4 10.3
5 8.3
4 9.6
4 14.2
7 8.5
10 13.5
4 4.9
5 6.4
4 9.6
4 11.6
4 11.1
6 4.35
4 12.7
8 18.1
5 17.85
4 16.6
17 12.6
4 17.1
4 19.1
8 16.1
4 13.35
7 18.4
4 14.7
4 10.6
5 12.6
7 16.2
4 13.6
4 18.9
7 14.1
11 14.5
7 16.15
4 14.75
4 14.8
4 12.45
4 12.65
4 17.35
4 8.6
6 18.4
8 16.1
23 11.6
4 17.75
8 15.25
6 17.65
4 16.35
7 17.65
4 13.6
4 14.35
4 14.75
10 18.25
6 9.9
5 16
5 18.25
4 16.85
4 14.6
5 13.85
5 18.95
5 15.6
5 14.85
4 11.75
6 18.45
4 15.9
4 17.1
4 16.1
9 19.9
18 10.95
6 18.45
5 15.1
4 15
11 11.35
4 15.95
10 18.1
6 14.6
8 15.4
8 15.4
6 17.6
8 13.35
4 19.1
4 15.35
9 7.6
9 13.4
5 13.9
4 19.1
4 15.25
15 12.9
10 16.1
9 17.35
7 13.15
9 12.15
6 12.6
4 10.35
7 15.4
4 9.6
7 18.2
4 13.6
15 14.85
4 14.75
9 14.1
4 14.9
4 16.25
28 19.25
4 13.6
4 13.6
4 15.65
5 12.75
4 14.6
4 9.85
12 12.65
4 19.2
6 16.6
6 11.2
5 15.25
4 11.9
4 13.2
4 16.35
10 12.4
7 15.85
4 18.15
7 11.15
4 15.65
4 17.75
12 7.65
5 12.35
8 15.6
6 19.3
17 15.2
4 17.1
5 15.6
4 18.4
5 19.05
5 18.55
6 19.1
4 13.1
4 12.85
4 9.5
6 4.5
8 11.85
10 13.6
4 11.7
5 12.4
4 13.35
4 11.4
4 14.9
16 19.9
7 11.2
4 14.6
4 17.6
14 14.05
5 16.1
5 13.35
5 11.85
5 11.95
7 14.75
19 15.15
16 13.2
4 16.85
4 7.85
7 7.7
9 12.6
5 7.85
14 10.95
4 12.35
16 9.95
10 14.9
5 16.65
6 13.4
4 13.95
4 15.7
4 16.85
5 10.95
4 15.35
4 12.2
5 15.1
4 17.75
4 15.2
5 14.6
8 16.65
15 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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285829&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285829&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'Sir Maurice George Kendall' @ kendall.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)12.9520.42130.7580
X0.0040.0590.0620.951
- - -
Residual Std. Err. 3.4 on 276 df
Multiple R-sq. 0
95% CI Multiple R-sq. [0, 0]
Adjusted R-sq. -0.004

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 12.952 & 0.421 & 30.758 & 0 \tabularnewline
X & 0.004 & 0.059 & 0.062 & 0.951 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.4  on  276 df \tabularnewline
Multiple R-sq.  & 0 \tabularnewline
95% CI Multiple R-sq.  & [0, 0] \tabularnewline
Adjusted R-sq.  & -0.004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285829&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]12.952[/C][C]0.421[/C][C]30.758[/C][C]0[/C][/ROW]
[C]X[/C][C]0.004[/C][C]0.059[/C][C]0.062[/C][C]0.951[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.4  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285829&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)12.9520.42130.7580
X0.0040.0590.0620.951
- - -
Residual Std. Err. 3.4 on 276 df
Multiple R-sq. 0
95% CI Multiple R-sq. [0, 0]
Adjusted R-sq. -0.004






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
AMS.A10.0440.0440.0040.951
Residuals2763191.4611.563 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
AMS.A & 1 & 0.044 & 0.044 & 0.004 & 0.951 \tabularnewline
Residuals & 276 & 3191.46 & 11.563 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285829&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.A[/C][C]1[/C][C]0.044[/C][C]0.044[/C][C]0.004[/C][C]0.951[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]3191.46[/C][C]11.563[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285829&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.A10.0440.0440.0040.951
Residuals2763191.4611.563


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):
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()