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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 computationFri, 16 Dec 2016 17:10:02 +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/16/t1481904619ibbxi19qup1b0ld.htm/, Retrieved Thu, 02 May 2024 22:36:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300409, Retrieved Thu, 02 May 2024 22:36:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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] [2016-12-16 16:10:02] [33f2a624cfeb2efbc43d2c77b7c0dad6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18	13
19	16
18	17
15	NA
19	NA
19	16
19	NA
NA	NA
18	NA
20	17
14	17
15	15
18	16
19	14
16	16
18	17
18	NA
NA	NA
17	NA
19	NA
19	16
17	NA
18	16
16	NA
20	NA
13	NA
19	16
15	15
17	16
17	16
16	13
17	15
19	17
18	NA
19	13
20	17
16	NA
17	14
16	14
16	18
16	NA
16	17
14	13
17	16
18	15
16	15
16	NA
NA	15
16	13
15	NA
19	17
16	NA
17	NA
19	11
17	14
17	13
15	NA
16	17
16	16
16	NA
17	17
18	16
18	16
18	16
19	15
14	12
13	17
18	14
16	14
15	16
18	NA
18	NA
16	NA
19	NA
17	NA
17	15
19	16
19	14
20	15
19	17
18	NA
16	10
16	NA
15	17
20	NA
16	20
16	17
20	18
20	NA
18	17
15	14
14	NA
16	17
14	NA
18	17
20	NA
20	16
18	18
20	18
14	16
20	NA
17	NA
20	15
14	13
16	NA
20	NA
19	NA
18	NA
17	NA
17	16
19	NA
15	NA
18	NA
15	12
16	NA
16	16
20	16
18	NA
20	16
18	14
17	15
19	14
18	NA
19	15
17	NA
18	15
17	16
16	NA
19	NA
18	NA
17	11
18	NA
16	18
20	NA
14	11
17	NA
13	18
13	NA
17	15
18	19
16	17
NA	NA
19	14
NA	NA
17	13
16	17
17	14
17	19
17	14
20	NA
14	NA
20	16
19	16
16	15
19	12
17	NA
19	17
20	NA
19	NA
19	18
16	15
18	18
16	15
17	NA
18	NA
16	NA
17	16
15	NA
18	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=300409&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=300409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300409&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)15.2461.43910.5930
X0.1320.0921.4270.157
- - -
Residual Std. Err. 1.745 on 100 df
Multiple R-sq. 0.02
95% CI Multiple R-sq. [0, 0.104]
Adjusted R-sq. 0.01

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 15.246 & 1.439 & 10.593 & 0 \tabularnewline
X & 0.132 & 0.092 & 1.427 & 0.157 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 1.745  on  100 df \tabularnewline
Multiple R-sq.  & 0.02 \tabularnewline
95% CI Multiple R-sq.  & [0, 0.104] \tabularnewline
Adjusted R-sq.  & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300409&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]15.246[/C][C]1.439[/C][C]10.593[/C][C]0[/C][/ROW]
[C]X[/C][C]0.132[/C][C]0.092[/C][C]1.427[/C][C]0.157[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]1.745  on  100 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.02[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0, 0.104][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300409&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)15.2461.43910.5930
X0.1320.0921.4270.157
- - -
Residual Std. Err. 1.745 on 100 df
Multiple R-sq. 0.02
95% CI Multiple R-sq. [0, 0.104]
Adjusted R-sq. 0.01






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TVDCSUM16.1986.1982.0350.157
Residuals100304.5573.046 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TVDCSUM & 1 & 6.198 & 6.198 & 2.035 & 0.157 \tabularnewline
Residuals & 100 & 304.557 & 3.046 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300409&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]TVDCSUM[/C][C]1[/C][C]6.198[/C][C]6.198[/C][C]2.035[/C][C]0.157[/C][/ROW]
[ROW][C]Residuals[/C][C]100[/C][C]304.557[/C][C]3.046[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300409&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)
TVDCSUM16.1986.1982.0350.157
Residuals100304.5573.046


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()