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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 computationThu, 18 Dec 2014 12:56:53 +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/2014/Dec/18/t1418907461zpwmr35kuimbwt0.htm/, Retrieved Sun, 19 May 2024 20:24:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270883, Retrieved Sun, 19 May 2024 20:24:14 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [] [2014-12-18 12:56:53] [578aae52f3152e8435e37fe3b2f57a45] [Current]
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Dataseries X:
325.87 3.40
302.25 4.80
294.00 6.50
285.43 8.50
286.19 13.60
276.70 15.70
267.77 18.80
267.03 19.20
257.87 12.90
257.19 14.40
275.60 6.20
305.68 2.40
358.06 4.60
320.07 7.10
295.90 7.80
291.27 9.90
272.87 13.90
269.27 17.10
271.32 17.80
267.45 18.30
260.33 14.70
277.94 10.50
277.07 8.60
312.65 4.40
319.71 2.30
318.39 2.80
304.90 8.80
303.73 10.70
273.29 12.80
274.33 19.30
270.45 19.50
278.23 20.30
274.03 15.30
279.00 7.90
287.50 8.30
336.87 4.50
334.10 3.20
296.07 5.00
286.84 6.60
277.63 11.10
261.32 13.40
264.07 16.30
261.94 17.40
252.84 18.90
257.83 15.80
271.16 11.70
273.63 6.40
304.87 2.90
323.90 4.70
336.11 2.40
335.65 7.00
282.23 10.60
273.03 12.80
270.07 17.70
246.03 18.20
242.35 16.50
250.33 16.20
267.45 13.90
268.80 6.60
302.68 3.60
313.10 1.40
306.39 2.60
305.61 4.30
277.27 8.80
264.94 14.50
268.63 16.80
293.90 22.70
248.65 15.70
256.00 18.20
258.52 14.20
266.90 9.10
281.23 5.90
306.00 7.00
325.46 6.20
291.13 7.80
282.53 14.30
256.52 14.60
258.63 17.30
252.74 17.10
245.16 17.00
255.03 13.90
268.35 10.30
293.73 6.70
278.39 3.90




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270883&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]2 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=270883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270883&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)320.0324.01479.7320
X-3.3490.326-10.2880
- - -
Residual Std. Err. 16.697 on 82 df
Multiple R-sq. 0.563
Adjusted R-sq. 0.558

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 320.032 & 4.014 & 79.732 & 0 \tabularnewline
X & -3.349 & 0.326 & -10.288 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 16.697  on  82 df \tabularnewline
Multiple R-sq.  & 0.563 \tabularnewline
Adjusted R-sq.  & 0.558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270883&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]320.032[/C][C]4.014[/C][C]79.732[/C][C]0[/C][/ROW]
[C]X[/C][C]-3.349[/C][C]0.326[/C][C]-10.288[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]16.697  on  82 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.563[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270883&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)320.0324.01479.7320
X-3.3490.326-10.2880
- - -
Residual Std. Err. 16.697 on 82 df
Multiple R-sq. 0.563
Adjusted R-sq. 0.558







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Tt129506.94329506.943105.8360
Residuals8222861.454278.798

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Tt & 1 & 29506.943 & 29506.943 & 105.836 & 0 \tabularnewline
Residuals & 82 & 22861.454 & 278.798 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270883&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]Tt[/C][C]1[/C][C]29506.943[/C][C]29506.943[/C][C]105.836[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]82[/C][C]22861.454[/C][C]278.798[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270883&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270883&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)
Tt129506.94329506.943105.8360
Residuals8222861.454278.798



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):
par3 <- 'TRUE'
par2 <- '2'
par1 <- '1'
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()