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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 computationTue, 19 Nov 2013 07:09:42 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/19/t1384862995qy8bi8ovsdsvsv5.htm/, Retrieved Sat, 04 May 2024 23:19:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226379, Retrieved Sat, 04 May 2024 23:19:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41 12 53 14 9 12 38
39 11 83 18 9 11 32
30 14 66 11 9 15 35
31 12 67 12 9 6 33
34 21 76 16 9 13 37
35 12 78 18 9 10 29
39 22 53 14 9 12 31
34 11 80 14 9 14 36
36 10 74 15 9 12 35
37 13 76 15 9 9 38
38 10 79 17 9 10 31
36 8 54 19 9 12 34
38 15 67 10 9 12 35
39 14 54 16 9 11 38
33 10 87 18 9 15 37
32 14 58 14 9 12 33
36 14 75 14 9 10 32
38 11 88 17 9 12 38
39 10 64 14 9 11 38
32 13 57 16 9 12 32
32 9.5 66 18 9 11 33
31 14 68 11 9 12 31
39 12 54 14 9 13 38
37 14 56 12 9 11 39
39 11 86 17 9 12 32
41 9 80 9 9 13 32
36 11 76 16 9 10 35
33 15 69 14 9 14 37
33 14 78 15 9 12 33
34 13 67 11 9 10 33
31 9 80 16 9 12 31
27 15 54 13 9 8 32
37 10 71 17 9 10 31
34 11 84 15 9 12 37
34 13 74 14 9 12 30
32 8 71 16 9 7 33
29 20 63 9 9 9 31
36 12 71 15 9 12 33
29 10 76 17 9 10 31
35 10 69 13 9 10 33
37 9 74 15 9 10 32
34 14 75 16 9 12 33
38 8 54 16 9 15 32
35 14 52 12 9 10 33
38 11 69 15 9 10 28
37 13 68 11 9 12 35
38 9 65 15 9 13 39
33 11 75 15 9 11 34
36 15 74 17 9 11 38
38 11 75 13 9 12 32
32 10 72 16 9 14 38
32 14 67 14 9 10 30
32 18 63 11 9 12 33
34 14 62 12 9 13 38
32 11 63 12 9 5 32
37 14.5 76 15 9 6 35
39 13 74 16 9 12 34
29 9 67 15 9 12 34
37 10 73 12 9 11 36
35 15 70 12 9 10 34
30 20 53 8 9 7 28
38 12 77 13 9 12 34
34 12 80 11 9 14 35
31 14 52 14 9 11 35
34 13 54 15 9 12 31
35 11 80 10 10 13 37
36 17 66 11 10 14 35
30 12 73 12 10 11 27
39 13 63 15 10 12 40
35 14 69 15 10 12 37
38 13 67 14 10 8 36
31 15 54 16 10 11 38
34 13 81 15 10 14 39
38 10 69 15 10 14 41
34 11 84 13 10 12 27
39 19 80 12 10 9 30
37 13 70 17 10 13 37
34 17 69 13 10 11 31
28 13 77 15 10 12 31
37 9 54 13 10 12 27
33 11 79 15 10 12 36
35 9 71 15 10 12 37
37 12 73 16 10 12 33
32 12 72 15 10 11 34
33 13 77 14 10 10 31
38 13 75 15 10 9 39
33 12 69 14 10 12 34
29 15 54 13 10 12 32
33 22 70 7 10 12 33
31 13 73 17 10 9 36
36 15 54 13 10 15 32
35 13 77 15 10 12 41
32 15 82 14 10 12 28
29 12.5 80 13 10 12 30
39 11 80 16 10 10 36
37 16 69 12 10 13 35
35 11 78 14 10 9 31
37 11 81 17 10 12 34
32 10 76 15 10 10 36
38 10 76 17 10 14 36
37 16 73 12 10 11 35
36 12 85 16 10 15 37
32 11 66 11 10 11 28
33 16 79 15 10 11 39
40 19 68 9 10 12 32
38 11 76 16 10 12 35
41 16 71 15 10 12 39
36 15 54 10 10 11 35
43 24 46 10 10 7 42
30 14 85 15 10 12 34
31 15 74 11 10 14 33
32 11 88 13 10 11 41
32 15 38 14 10 11 33
37 12 76 18 10 10 34
37 10 86 16 10 13 32
33 14 54 14 10 13 40
34 13 67 14 10 8 40
33 9 69 14 10 11 35
38 15 90 14 10 12 36
33 15 54 12 10 11 37
31 14 76 14 10 13 27
38 11 89 15 10 12 39
37 8 76 15 10 14 38
36 11 73 15 10 13 31
31 11 79 13 10 15 33
39 8 90 17 10 10 32
44 10 74 17 10 11 39
33 11 81 19 10 9 36
35 13 72 15 10 11 33
32 11 71 13 10 10 33
28 20 66 9 10 11 32
40 10 77 15 10 8 37
27 15 65 15 10 11 30
37 12 74 15 10 12 38
32 14 85 16 10 12 29
28 23 54 11 10 9 22
34 14 63 14 10 11 35
30 16 54 11 10 10 35
35 11 64 15 10 8 34
31 12 69 13 10 9 35
32 10 54 15 10 8 34
30 14 84 16 10 9 37
30 12 86 14 10 15 35
31 12 77 15 10 11 23
40 11 89 16 10 8 31
32 12 76 16 10 13 27
36 13 60 11 10 12 36
32 11 75 12 10 12 31
35 19 73 9 10 9 32
38 12 85 16 10 7 39
42 17 79 13 10 13 37
34 9 71 16 10 9 38
35 12 72 12 10 6 39
38 19 69 9 9 8 34
33 18 78 13 10 8 31
36 15 54 13 10 15 32
32 14 69 14 10 6 37
33 11 81 19 10 9 36
34 9 84 13 10 11 32
32 18 84 12 10 8 38
34 16 69 13 10 8 36
27 24 66 10 11 10 26
31 14 81 14 11 8 26
38 20 82 16 11 14 33
34 18 72 10 11 10 39
24 23 54 11 11 8 30
30 12 78 14 11 11 33
26 14 74 12 11 12 25
34 16 82 9 11 12 38
27 18 73 9 11 12 37
37 20 55 11 11 5 31
36 12 72 16 11 12 37
41 12 78 9 11 10 35
29 17 59 13 11 7 25
36 13 72 16 11 12 28
32 9 78 13 11 11 35
37 16 68 9 11 8 33
30 18 69 12 11 9 30
31 10 67 16 11 10 31
38 14 74 11 11 9 37
36 11 54 14 11 12 36
35 9 67 13 11 6 30
31 11 70 15 11 15 36
38 10 80 14 11 12 32
22 11 89 16 11 12 28
32 19 76 13 11 12 36
36 14 74 14 11 11 34
39 12 87 15 11 7 31
28 14 54 13 11 7 28
32 21 61 11 11 5 36
32 13 38 11 11 12 36
38 10 75 14 11 12 40
32 15 69 15 11 3 33
35 16 62 11 11 11 37
32 14 72 15 11 10 32
37 12 70 12 11 12 38
34 19 79 14 11 9 31
33 15 87 14 11 12 37
33 19 62 8 11 9 33
26 13 77 13 11 12 32
30 17 69 9 11 12 30
24 12 69 15 11 10 30
34 11 75 17 11 9 31
34 14 54 13 11 12 32
33 11 72 15 11 8 34
34 13 74 15 11 11 36
35 12 85 14 11 11 37
35 15 52 16 11 12 36
36 14 70 13 11 10 33
34 12 84 16 11 10 33
34 17 64 9 11 12 33
41 11 84 16 11 12 44
32 18 87 11 11 11 39
30 13 79 10 11 8 32
35 17 67 11 11 12 35
28 13 65 15 11 10 25
33 11 85 17 11 11 35
39 12 83 14 11 10 34
36 22 61 8 11 8 35
36 14 82 15 11 12 39
35 12 76 11 11 12 33
38 12 58 16 11 10 36
33 17 72 10 11 12 32
31 9 72 15 11 9 32
34 21 38 9 11 9 36
32 10 78 16 11 6 36
31 11 54 19 11 10 32
33 12 63 12 11 9 34
34 23 66 8 11 9 33
34 13 70 11 11 9 35
34 12 71 14 11 6 30
33 16 67 9 11 10 38
32 9 58 15 11 6 34
41 17 72 13 11 14 33
34 9 72 16 11 10 32
36 14 70 11 11 10 31
37 17 76 12 11 6 30
36 13 50 13 11 12 27
29 11 72 10 11 12 31
37 12 72 11 11 7 30
27 10 88 12 11 8 32
35 19 53 8 11 11 35
28 16 58 12 11 3 28
35 16 66 12 11 6 33
37 14 82 15 11 10 31
29 20 69 11 11 8 35
32 15 68 13 11 9 35
36 23 44 14 11 9 32
19 20 56 10 11 8 21
21 16 53 12 11 9 20
31 14 70 15 11 7 34
33 17 78 13 11 7 32
36 11 71 13 11 6 34
33 13 72 13 11 9 32
37 17 68 12 11 10 33
34 15 67 12 11 11 33
35 21 75 9 11 12 37
31 18 62 9 11 8 32
37 15 67 15 11 11 34
35 8 83 10 11 3 30
27 12 64 14 11 11 30
34 12 68 15 11 12 38
40 22 62 7 11 7 36
29 12 72 14 11 9 32

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226379&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226379&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'Gwilym Jenkins' @ jenkins.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)10.5361.387.6340
X0.0870.042.1690.031
- - -
Residual Std. Err. 2.481 on 262 df
Multiple R-sq. 0.018
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) & 10.536 & 1.38 & 7.634 & 0 \tabularnewline
X & 0.087 & 0.04 & 2.169 & 0.031 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.481  on  262 df \tabularnewline
Multiple R-sq.  & 0.018 \tabularnewline
Adjusted R-sq.  & 0.014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226379&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]10.536[/C][C]1.38[/C][C]7.634[/C][C]0[/C][/ROW]
[C]X[/C][C]0.087[/C][C]0.04[/C][C]2.169[/C][C]0.031[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.481  on  262 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.018[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226379&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)10.5361.387.6340
X0.0870.042.1690.031
- - -
Residual Std. Err. 2.481 on 262 df
Multiple R-sq. 0.018
Adjusted R-sq. 0.014






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Connected128.97228.9724.7060.031
Residuals2621612.9946.156 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Connected & 1 & 28.972 & 28.972 & 4.706 & 0.031 \tabularnewline
Residuals & 262 & 1612.994 & 6.156 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226379&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]Connected[/C][C]1[/C][C]28.972[/C][C]28.972[/C][C]4.706[/C][C]0.031[/C][/ROW]
[ROW][C]Residuals[/C][C]262[/C][C]1612.994[/C][C]6.156[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226379&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)
Connected128.97228.9724.7060.031
Residuals2621612.9946.156


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = 1 ; par3 = TRUE ;
Parameters (R input):
par1 = 4 ; par2 = 1 ; par3 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
xdf<-data.frame(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) )
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$'r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'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')
qq.plot(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.lm(lmxdf, which=4)
dev.off()