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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 computationMon, 18 Dec 2017 12:00:49 +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/2017/Dec/18/t15135949323byyavm9widbbqd.htm/, Retrieved Tue, 14 May 2024 13:56:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310131, Retrieved Tue, 14 May 2024 13:56:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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] [home goals and aw...] [2017-12-18 11:00:49] [a09809e4bbd86c4423fe007414812000] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3	13
10	12
15	7
15	13
4	16
11	11
12	14
13	11
15	2
12	20
9	9
16	8
21	4
15	2
18	3
14	6
18	12
6	10
16	3
9	9
14	8
20	7
15	12
20	8
11	1
14	7
11	0
10	9
9	6
16	7
11	13
15	8
13	10
11	9
10	12
9	11
18	8
9	2
11	12
7	5
6	13
15	13
10	11
10	9
12	7
14	14
13	13
11	16
9	10
14	3
11	13
17	4
9	4
17	5
11	10
11	4
4	14
11	6
18	3
14	11
27	10
8	8
18	8
6	8
20	4
9	8
20	6
9	13
11	11
10	6
16	6
16	2
13	13
11	7
14	5
16	13
17	4
19	4
14	9
11	15
7	8
5	14
12	11
8	4
22	6
14	13
4	7
16	6
11	3
6	14
13	9
15	11
19	2
4	24
12	10
15	19
18	11
7	11
19	6
17	4
7	13
5	5
11	10
12	7
8	11
13	11
12	1
6	10
9	10
9	4
10	9
7	7
10	10
12	17
10	21
9	9
18	13
12	3
15	7
12	5
8	16
11	11
11	13
20	9
15	8
13	15
16	5
3	8
6	12
4	10
11	7
14	16
10	5
13	9
10	16
8	15
15	8
10	8
17	10
16	10
19	8
8	9
14	5
5	8
10	17
14	10
11	7
14	6
13	6
14	14
11	4
23	6
8	6
11	8
21	7
16	8
12	7
12	15
11	17
13	7
8	10
17	6
5	4
11	10
18	5
7	11
11	8
12	10
8	18
15	9
21	2
17	5
8	7
11	14
11	8
9	7
10	21
6	6
11	11
10	12
6	9
5	11
6	7
4	8
11	10
14	8
12	9
27	4
18	4
12	8
17	9
13	9
13	9
9	13
8	6
12	8
12	15
13	11
12	10
10	8
9	13
6	17
8	16
13	8
24	5
14	10
18	3
11	14
12	6
16	6
12	13
14	9
10	21
27	7
9	10
11	9
9	14
7	16
12	6
21	4
10	7
12	9
7	11
9	12
12	12
12	7
14	7
14	8
16	4
6	11
7	12
24	3
14	4
13	8
13	9
12	7
10	7
21	10
9	10
14	3
9	10
11	7
10	12
14	7
6	13
16	5
13	9
5	18
11	11
7	17
15	6
5	7
16	12
9	10
13	17
22	6
12	5
10	8
13	7
14	8
6	10
13	11
17	5
18	12
13	10
20	6
17	5
17	11
7	18
21	3
12	14
9	11
6	7
7	13
15	6
10	6
18	9
6	10
12	12
19	9
13	4
15	8
12	9
13	5
11	8
5	9
28	5
19	8
16	2
6	9
5	7
16	6
12	9
7	10
8	20
13	12
7	10
8	12
10	9
19	5
17	8
10	7
12	5
11	15
8	7
15	11
11	13
23	9
20	9
4	13
7	14
16	16
10	10
14	10
8	13
9	16
16	8
11	12
7	8
9	7
22	4
23	14
13	11
6	7
14	6
17	7
14	10
13	14
10	9
24	12
16	8
7	5
8	10
6	10
11	13
16	12
8	6
9	12
6	7
16	11
15	4
12	14
12	9
15	11
9	8
18	9
12	12
9	9
13	5
17	6
14	5
23	7
12	21
10	15
11	13
15	4
7	10
11	7
15	7
19	12
11	8
13	16
9	14
17	10
7	7
16	10
6	7
17	5
10	17
3	10
13	8
16	14
6	11
16	5
22	6
8	6
20	8
16	10
6	8
12	14

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 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 time9 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310131&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]9 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310131&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310131&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 time9 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)15.7580.57627.3750
X-0.3710.057-6.4680
- - -
Residual Std. Err. 4.445 on 378 df
Multiple R-sq. 0.1
95% CI Multiple R-sq. [0.054, 0.156]
Adjusted R-sq. 0.097

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 15.758 & 0.576 & 27.375 & 0 \tabularnewline
X & -0.371 & 0.057 & -6.468 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 4.445  on  378 df \tabularnewline
Multiple R-sq.  & 0.1 \tabularnewline
95% CI Multiple R-sq.  & [0.054, 0.156] \tabularnewline
Adjusted R-sq.  & 0.097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310131&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]15.758[/C][C]0.576[/C][C]27.375[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.371[/C][C]0.057[/C][C]-6.468[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]4.445  on  378 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.1[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.054, 0.156][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310131&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310131&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)15.7580.57627.3750
X-0.3710.057-6.4680
- - -
Residual Std. Err. 4.445 on 378 df
Multiple R-sq. 0.1
95% CI Multiple R-sq. [0.054, 0.156]
Adjusted R-sq. 0.097






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
AS1826.606826.60641.8360
Residuals3787468.60219.758 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
AS & 1 & 826.606 & 826.606 & 41.836 & 0 \tabularnewline
Residuals & 378 & 7468.602 & 19.758 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310131&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]AS[/C][C]1[/C][C]826.606[/C][C]826.606[/C][C]41.836[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]378[/C][C]7468.602[/C][C]19.758[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310131&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310131&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)
AS1826.606826.60641.8360
Residuals3787468.60219.758


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()