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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, 19 Dec 2018 20:53:39 +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/2018/Dec/19/t15452494093k4ibcl5okikpb9.htm/, Retrieved Mon, 29 Apr 2024 21:44:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316114, Retrieved Mon, 29 Apr 2024 21:44:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact23

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 
0.79 0.18
2.21 0.87
2.12 1.14
0.93 0.2
5.38 NA
3.14 1.08
2.23 0.89
11.88 NA
9.31 4.85
6.06 4.14
2.31 1.25
6.84 4.46
7.49 6.19
0.72 0.26
4.48 3.28
5.09 2.57
7.44 4.43
1.41 0.51
5.77 NA
4.84 0.63
2.96 0.67
3.12 1.74
3.83 2.36
3.11 0.91
2.86 NA
4.06 3.24
3.32 2.08
1.21 0.12
0.8 0.04
2.52 NA
1.21 NA
1.17 0.19
8.17 5
5.65 3.56
1.24 0.08
1.46 0.01
4.36 2.04
3.38 2.32
1.87 0.67
1.03 0.25
1.29 0.47
0.82 0.07
2.84 1.37
1.27 0.26
3.92 2.21
1.95 1.23
4.21 2.94
5.19 3.42
5.51 2.6
2.19 NA
2.57 1.47
1.53 0.86
2.17 1.08
2.15 1.02
2.07 0.84
3.97 3.17
0.42 0.03
6.86 NA
1.02 0.07
2.9 1.06
5.87 NA
5.14 2.71
2.34 1.58
4.73 2.39
2.02 0.43
1.03 0.21
1.58 0.83
5.3 3.28
1.97 0.43
4.38 2.58
2.98 NA
3.23 2.61
1.89 0.7
1.41 0.16
1.53 0.09
3.07 1.25
0.61 0.15
1.68 0.6
2.92 1.9
1.16 0.61
1.58 0.64
2.79 1.72
1.88 1.36
5.57 3.22
6.22 4.59
4.61 2.77
1.89 1.09
5.02 3.69
2.1 1.09
5.55 4.59
1.03 0.2
1.17 0.68
5.69 4.17
8.13 6.89
1.91 0.95
1.22 0.09
6.29 1.66
3.84 2.52
1.66 0.51
1.21 0.14
3.69 2.33
5.83 2.15
15.82 12.65
3.26 2.06
0.99 0.07
0.81 0.07
3.71 2.1
1.53 0.1
2.08 1.73
2.54 0.55
3.46 1.99
2.89 1.74
1.78 1.03
6.08 2.09
3.78 2.13
7.78 NA
1.68 0.67
0.87 0.17
1.43 0.09
2.48 1.02
2.94 NA
0.98 0.16
5.28 3.23
3.58 1.78
5.6 2.84
1.39 0.45
1.56 0.1
1.16 0.21
4.98 NA
7.52 5.8
0.79 0.38
2.79 1.44
1.91 0.35
4.16 0.97
2.28 0.67
1.1 0.34
4.44 2.64
3.88 2.15
10.8 9.57
3.65 3.27
2.71 1.46
5.69 3.87
0.87 0.07
4.94 3.34
2.45 1.56
3.11 NA
2.77 0.96
1.49 0.37
5.61 4.21
1.21 0.3
2.7 1.66
1.24 0.07
7.97 5.91
4.06 2.82
5.81 4.27
1.29 0
1.24 0.07
3.31 2.34
3.67 2.22
1.32 0.52
4.25 3.01
2.01 0.67
7.25 3.88
5.79 4.26
1.51 0.81
0.91 0.13
1.32 0.17
2.66 1.54
0.48 0.06
1.13 0.31
2.7 0.88
7.92 6.89
2.34 1.11
3.33 1.92
5.47 4.13
1.24 0.08
2.84 1.92
4.94 3.14
7.93 6.37
8.22 5.9
2.91 0.98
2.32 1.41
3.57 2.13
1.65 0.79
2.07 NA
1.03 0.42
0.99 0.24
1.37 0.53

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 time10 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316114&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]10 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316114&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 time10 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)1.1220.07515.0590
X1.1570.02840.6090
- - -
Residual Std. Err. 0.709 on 171 df
Multiple R-sq. 0.906
95% CI Multiple R-sq. [0.846, 0.947]
Adjusted R-sq. 0.906

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 1.122 & 0.075 & 15.059 & 0 \tabularnewline
X & 1.157 & 0.028 & 40.609 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 0.709  on  171 df \tabularnewline
Multiple R-sq.  & 0.906 \tabularnewline
95% CI Multiple R-sq.  & [0.846, 0.947] \tabularnewline
Adjusted R-sq.  & 0.906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316114&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]1.122[/C][C]0.075[/C][C]15.059[/C][C]0[/C][/ROW]
[C]X[/C][C]1.157[/C][C]0.028[/C][C]40.609[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]0.709  on  171 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.906[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.846, 0.947][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316114&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)1.1220.07515.0590
X1.1570.02840.6090
- - -
Residual Std. Err. 0.709 on 171 df
Multiple R-sq. 0.906
95% CI Multiple R-sq. [0.846, 0.947]
Adjusted R-sq. 0.906






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Carbon_Footprint1829.436829.4361649.1250
Residuals17186.0050.503 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Carbon_Footprint & 1 & 829.436 & 829.436 & 1649.125 & 0 \tabularnewline
Residuals & 171 & 86.005 & 0.503 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316114&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]Carbon_Footprint[/C][C]1[/C][C]829.436[/C][C]829.436[/C][C]1649.125[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]171[/C][C]86.005[/C][C]0.503[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316114&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316114&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)
Carbon_Footprint1829.436829.4361649.1250
Residuals17186.0050.503


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()