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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 01:11:26 +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/t14817630822mz8eowzj56l3g7.htm/, Retrieved Fri, 03 May 2024 13:02:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299759, Retrieved Fri, 03 May 2024 13:02:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

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] [simple regression] [2016-12-15 00:11:26] [11b61e09f442d73f657668491c17a736] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10	10
15	13
13	14
13	NA
11	NA
15	13
12	NA
15	NA
14	NA
12	14
15	14
NA	12
15	12
14	11
11	12
11	14
15	NA
NA	NA
12	NA
11	NA
12	13
8	NA
14	13
14	NA
14	NA
12	NA
14	12
13	12
14	13
14	13
NA	10
14	12
15	13
3	NA
14	10
13	14
12	NA
12	10
14	10
13	14
12	NA
13	14
NA	10
15	13
15	12
5	12
9	NA
11	12
12	10
NA	NA
14	14
15	NA
12	NA
13	8
15	11
12	10
14	NA
12	14
12	12
10	NA
11	14
13	13
13	13
13	13
13	12
12	10
10	14
12	11
10	10
13	13
11	NA
15	NA
9	NA
10	NA
14	NA
10	12
15	13
13	11
10	10
13	14
15	NA
12	7
11	NA
13	13
15	NA
11	15
14	13
14	14
15	NA
13	13
12	11
12	NA
15	14
12	NA
15	14
14	NA
14	12
12	13
15	14
15	13
9	NA
14	NA
15	12
15	10
NA	NA
13	NA
12	NA
12	NA
15	NA
14	12
10	NA
11	NA
10	NA
13	9
11	NA
14	12
13	13
13	NA
15	13
13	11
11	12
11	11
14	NA
15	12
13	NA
13	12
13	13
13	NA
11	NA
14	NA
14	8
13	NA
15	13
12	NA
12	8
12	NA
13	13
7	NA
12	12
14	15
15	14
15	NA
12	11
13	NA
13	10
13	14
14	10
15	15
13	11
14	NA
12	NA
13	12
9	13
11	12
13	9
13	NA
11	14
10	NA
15	NA
14	14
13	12
13	15
15	11
14	NA
15	NA
14	NA
12	12
13	NA
11	11

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=299759&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=299759&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299759&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)11.0781.2199.0910
X0.1550.0991.5670.12
- - -
Residual Std. Err. 1.678 on 98 df
Multiple R-sq. 0.024
95% CI Multiple R-sq. [0, 0.11]
Adjusted R-sq. 0.014

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 11.078 & 1.219 & 9.091 & 0 \tabularnewline
X & 0.155 & 0.099 & 1.567 & 0.12 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 1.678  on  98 df \tabularnewline
Multiple R-sq.  & 0.024 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.11] \tabularnewline
Adjusted R-sq.  & 0.014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299759&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]11.078[/C][C]1.219[/C][C]9.091[/C][C]0[/C][/ROW]
[C]X[/C][C]0.155[/C][C]0.099[/C][C]1.567[/C][C]0.12[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]1.678  on  98 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.024[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.11][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299759&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299759&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)11.0781.2199.0910
X0.1550.0991.5670.12
- - -
Residual Std. Err. 1.678 on 98 df
Multiple R-sq. 0.024
95% CI Multiple R-sq. [0, 0.11]
Adjusted R-sq. 0.014






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
tvdc16.9186.9182.4560.12
Residuals98275.9922.816 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
tvdc & 1 & 6.918 & 6.918 & 2.456 & 0.12 \tabularnewline
Residuals & 98 & 275.992 & 2.816 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299759&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]6.918[/C][C]6.918[/C][C]2.456[/C][C]0.12[/C][/ROW]
[ROW][C]Residuals[/C][C]98[/C][C]275.992[/C][C]2.816[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299759&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299759&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)
tvdc16.9186.9182.4560.12
Residuals98275.9922.816


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()