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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, 01 Dec 2015 17:19:17 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/01/t1448990589gtrdct820zmvrlz.htm/, Retrieved Thu, 16 May 2024 22:15:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284757, Retrieved Thu, 16 May 2024 22:15:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [Lineair regressie...] [2015-12-01 17:19:17] [973db046713346d64b5601c33e0811b1] [Current]
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Dataseries X:
1050 1000
1150 1125
1213 1087
1275 1070
1300 1100
1300 1150
1400 1250
1400 1150
1250 1100
1830 1350
1350 1275
1450 1375
1300 1175
1300 1200
1275 1175
1375 1300
1285 1260
1400 1330
1400 1325
1285 1200
1275 1225
1135 1090
1250 1075
1275 1080
1150 1080
1250 1180
1275 1225
1225 1175
1280 1250
1300 1250
1250 750
1175 1125
1300 700
1250 900
1300 900
1200 850




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 6 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284757&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284757&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)867.604135.0716.4230
X0.3730.1183.1650.003
- - -
Residual Std. Err. 110.626 on 34 df
Multiple R-sq. 0.228
95% CI Multiple R-sq. [0.035, 0.395]
Adjusted R-sq. 0.205

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 867.604 & 135.071 & 6.423 & 0 \tabularnewline
X & 0.373 & 0.118 & 3.165 & 0.003 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 110.626  on  34 df \tabularnewline
Multiple R-sq.  & 0.228 \tabularnewline
95% CI Multiple R-sq.  & [0.035, 0.395] \tabularnewline
Adjusted R-sq.  & 0.205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284757&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]867.604[/C][C]135.071[/C][C]6.423[/C][C]0[/C][/ROW]
[C]X[/C][C]0.373[/C][C]0.118[/C][C]3.165[/C][C]0.003[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]110.626  on  34 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.228[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.035, 0.395][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284757&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:
EstimateStd. Errort valuePr(>|t|)
(Intercept)867.604135.0716.4230
X0.3730.1183.1650.003
- - -
Residual Std. Err. 110.626 on 34 df
Multiple R-sq. 0.228
95% CI Multiple R-sq. [0.035, 0.395]
Adjusted R-sq. 0.205







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
FranchiseFee1122565.383122565.38310.0150.003
Residuals34416098.50612238.191

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
FranchiseFee & 1 & 122565.383 & 122565.383 & 10.015 & 0.003 \tabularnewline
Residuals & 34 & 416098.506 & 12238.191 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284757&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]FranchiseFee[/C][C]1[/C][C]122565.383[/C][C]122565.383[/C][C]10.015[/C][C]0.003[/C][/ROW]
[ROW][C]Residuals[/C][C]34[/C][C]416098.506[/C][C]12238.191[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284757&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
DfSum SqMean SqF valuePr(>F)
FranchiseFee1122565.383122565.38310.0150.003
Residuals34416098.50612238.191



Parameters (Session):
par3 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- '2'
par1 <- '1'
library(boot)
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
rsq <- function(formula, data, indices) {
d <- data[indices,] # allows boot to select sample
fit <- lm(formula, data=d)
return(summary(fit)$r.square)
}
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
(results <- boot(data=xdf, statistic=rsq, R=1000, formula=Y~X))
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'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$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qq.plot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot(lmxdf, which=4)
dev.off()