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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 computationMon, 30 Jan 2012 18:00:26 -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/2012/Jan/30/t1327964453cgt6nkteffcfdkk.htm/, Retrieved Mon, 29 Apr 2024 14:14:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161567, Retrieved Mon, 29 Apr 2024 14:14:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Simple Linear Regression] [Regression Example] [2012-01-24 12:40:19] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R  D    [Simple Linear Regression] [Question 1] [2012-01-30 23:00:26] [5639b887e38dee7c91ec122c5ed827df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84	40
84	55
85	55
85	35
85	50
86	45
86	55
88	45
88	20
88	30
89	60
89	34
90	50
91	14
91	54
91	45
92	70
92	46
93	65
93	40
94	55
95	60
95	45
95	55
95	30
95	60
95	25
96	60
96	20
97	54
98	20
98	15
99	26
100	70
100	60
100	48
101	60
101	60
102	55
102	68
102	20
103	35
103	40
104	54
105	26
105	35
105	35
106	55
106	55
106	75
106	75
107	40
107	78
107	40
108	80
108	65
108	50
109	45
109	26
109	70
110	50
111	52
111	45
111	60
111	60
112	60
114	70
115	80
115	75
118	60

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.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 & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161567&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161567&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161567&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 time3 seconds
R Server'AstonUniversity' @ aston.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)90.9223.22428.1980
X0.1760.0622.8520.006
- - -
Residual Std. Err. 8.573 on 68 df
Multiple R-sq. 0.107
Adjusted R-sq. 0.094

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 90.922 & 3.224 & 28.198 & 0 \tabularnewline
X & 0.176 & 0.062 & 2.852 & 0.006 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 8.573  on  68 df \tabularnewline
Multiple R-sq.  & 0.107 \tabularnewline
Adjusted R-sq.  & 0.094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161567&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]90.922[/C][C]3.224[/C][C]28.198[/C][C]0[/C][/ROW]
[C]X[/C][C]0.176[/C][C]0.062[/C][C]2.852[/C][C]0.006[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]8.573  on  68 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.107[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161567&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161567&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)90.9223.22428.1980
X0.1760.0622.8520.006
- - -
Residual Std. Err. 8.573 on 68 df
Multiple R-sq. 0.107
Adjusted R-sq. 0.094






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Grade1598.035598.0358.1360.006
Residuals684998.03773.501 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Grade & 1 & 598.035 & 598.035 & 8.136 & 0.006 \tabularnewline
Residuals & 68 & 4998.037 & 73.501 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161567&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]Grade[/C][C]1[/C][C]598.035[/C][C]598.035[/C][C]8.136[/C][C]0.006[/C][/ROW]
[ROW][C]Residuals[/C][C]68[/C][C]4998.037[/C][C]73.501[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161567&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161567&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)
Grade1598.035598.0358.1360.006
Residuals684998.03773.501


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):
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)
}# end cols
a<-table.row.end(a)
} #end rows
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()