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R Software Module

rwasp_Simple Regression Y ~ X.wasp

Title produced by software

Simple Linear Regression

Date of computation

Sat, 09 Jan 2016 11:25:19 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/09/t1452338879u7mk0ma6aiwtpa7.htm/, Retrieved Sun, 05 May 2024 12:15:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287505, Retrieved Sun, 05 May 2024 12:15:53 +0000

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Estimated Impact

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

-       [Simple Linear Regression] [Vraag 5 Jenkins] [2016-01-09 11:25:19] [40755018184b88d6390872a4ca56a143] [Current]

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Dataseries X:

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Histogram

Boxplots

46.4 392 0.4
45.7 118 0.61
45.3 44 0.53
38.6 158 0.53
37.2 81 0.53
35 374 0.37
34 187 0.3
28.3 993 0.19
24.7 1723 0.12
24.7 287 0.2
24.4 970 0.19
22.7 885 0.12
22.3 200 0.53
21.7 575 0.14
21.6 688 0.34
21.3 48 0.69
21.2 572 0.49
20.8 239 0.42
20.3 244 0.48
18.9 472 0.25
18.8 134 0.52
18.6 633 0.19
18 295 0.44
17.6 906 0.24
17 1045 0.16
16.7 775 0.1
15.9 619 0.15
15.3 901 0.05
15 910 0.24
14.8 556 0.22

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287505&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287505&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	16.31	3.307	4.932	0
X	26.027	8.979	2.899	0.007
- - -
Residual Std. Err.	8.549 on 28 df
Multiple R-sq.	0.231
95% CI Multiple R-sq.	[0.051, 0.543]
Adjusted R-sq.	0.203

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 16.31 & 3.307 & 4.932 & 0 \tabularnewline
X & 26.027 & 8.979 & 2.899 & 0.007 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 8.549  on  28 df \tabularnewline
Multiple R-sq.  & 0.231 \tabularnewline
95% CI Multiple R-sq.  & [0.051, 0.543] \tabularnewline
Adjusted R-sq.  & 0.203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287505&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]16.31[/C][C]3.307[/C][C]4.932[/C][C]0[/C][/ROW]
[C]X[/C][C]26.027[/C][C]8.979[/C][C]2.899[/C][C]0.007[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]8.549  on  28 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.231[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.051, 0.543][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287505&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	16.31	3.307	4.932	0
X	26.027	8.979	2.899	0.007
- - -
Residual Std. Err.	8.549 on 28 df
Multiple R-sq.	0.231
95% CI Multiple R-sq.	[0.051, 0.543]
Adjusted R-sq.	0.203

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Prop_Population_on_Farms	1	613.97	613.97	8.402	0.007
Residuals	28	2046.162	73.077

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Prop_Population_on_Farms & 1 & 613.97 & 613.97 & 8.402 & 0.007 \tabularnewline
Residuals & 28 & 2046.162 & 73.077 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287505&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]Prop_Population_on_Farms[/C][C]1[/C][C]613.97[/C][C]613.97[/C][C]8.402[/C][C]0.007[/C][/ROW]
[ROW][C]Residuals[/C][C]28[/C][C]2046.162[/C][C]73.077[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287505&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287505&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Prop_Population_on_Farms	1	613.97	613.97	8.402	0.007
Residuals	28	2046.162	73.077

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

Parameters (R input):

par1 = 1 ; par2 = 3 ; 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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code