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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, 14 Dec 2016 18:42:20 +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/14/t1481737550v3z6koz9msk9bwg.htm/, Retrieved Sat, 18 May 2024 01:29:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299661, Retrieved Sat, 18 May 2024 01:29:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

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] [2016-12-14 17:42:20] [462f83e9ca944f1b841aaa868aea0854] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15	25
13	23
14	23
13	NA
12	NA
17	29
12	NA
13	NA
13	NA
16	27
12	20
12	22
13	21
16	28
15	25
12	20
NA	NA
NA	NA
15	NA
12	NA
15	26
11	NA
13	21
13	NA
14	NA
14	NA
14	23
15	25
16	27
16	27
16	27
13	21
13	21
14	NA
13	21
14	24
12	NA
17	29
14	23
15	25
13	NA
14	23
15	25
19	33
14	23
13	21
12	NA
NA	1
14	24
15	NA
15	25
12	NA
14	NA
11	19
12	20
10	17
NA	NA
14	23
14	23
15	NA
15	25
13	21
15	25
16	27
12	20
17	29
15	26
NA	9
12	22
16	28
15	NA
15	NA
12	NA
13	NA
10	NA
14	23
11	19
12	20
14	24
12	19
14	NA
12	20
13	NA
13	21
14	NA
12	20
15	25
13	21
13	NA
11	18
12	20
16	NA
11	19
13	NA
12	19
17	NA
14	24
15	25
8	14
13	21
13	NA
15	NA
14	25
13	21
14	NA
12	NA
19	NA
15	NA
14	NA
14	23
15	NA
13	NA
15	NA
14	23
11	NA
17	29
13	21
9	NA
12	19
13	21
17	29
14	23
13	NA
16	27
14	NA
14	23
14	24
10	NA
12	NA
13	NA
14	23
18	NA
14	24
14	NA
13	22
13	NA
16	28
NA	NA
13	22
14	23
8	14
13	NA
13	22
16	NA
14	23
13	22
14	23
12	20
16	27
18	NA
16	NA
15	26
18	31
15	25
14	23
14	NA
15	25
9	NA
17	NA
11	19
15	25
NA	7
15	25
13	NA
NA	NA
15	NA
15	25
14	NA
13	21

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=299661&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=299661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299661&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)-0.9280.477-1.9460.055
X1.7430.03451.0460
- - -
Residual Std. Err. 0.638 on 98 df
Multiple R-sq. 0.964
95% CI Multiple R-sq. [0.941, 0.976]
Adjusted R-sq. 0.963

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -0.928 & 0.477 & -1.946 & 0.055 \tabularnewline
X & 1.743 & 0.034 & 51.046 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 0.638  on  98 df \tabularnewline
Multiple R-sq.  & 0.964 \tabularnewline
95% CI Multiple R-sq.  & [0.941, 0.976] \tabularnewline
Adjusted R-sq.  & 0.963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299661&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]-0.928[/C][C]0.477[/C][C]-1.946[/C][C]0.055[/C][/ROW]
[C]X[/C][C]1.743[/C][C]0.034[/C][C]51.046[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]0.638  on  98 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.964[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.941, 0.976][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299661&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)-0.9280.477-1.9460.055
X1.7430.03451.0460
- - -
Residual Std. Err. 0.638 on 98 df
Multiple R-sq. 0.964
95% CI Multiple R-sq. [0.941, 0.976]
Adjusted R-sq. 0.963






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
EPSUM11062.0551062.0552605.6450
Residuals9839.9450.408 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
EPSUM & 1 & 1062.055 & 1062.055 & 2605.645 & 0 \tabularnewline
Residuals & 98 & 39.945 & 0.408 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299661&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]1062.055[/C][C]1062.055[/C][C]2605.645[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]98[/C][C]39.945[/C][C]0.408[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299661&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)
EPSUM11062.0551062.0552605.6450
Residuals9839.9450.408


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()