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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, 15 Dec 2014 12:57:22 +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/15/t1418648252h8sulrytzkmklwd.htm/, Retrieved Thu, 16 May 2024 11:20:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268290, Retrieved Thu, 16 May 2024 11:20:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49

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] [] [2014-12-15 12:57:22] [e4f070d9a53956de258aedfd2fe319be] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9 2011
12.2 2011
12.8 2011
7.4 2011
6.7 2011
12.6 2011
14.8 2011
13.3 2011
11.1 2011
8.2 2011
11.4 2011
6.4 2011
10.6 2011
12 2011
6.3 2011
11.3 2011
11.9 2011
9.3 2011
9.6 2011
10 2011
6.4 2011
13.8 2011
10.8 2011
13.8 2011
11.7 2011
10.9 2011
16.1 2011
13.4 2011
9.9 2011
11.5 2011
8.3 2011
11.7 2011
9 2011
9.7 2011
10.8 2011
10.3 2011
10.4 2011
12.7 2011
9.3 2011
11.8 2011
5.9 2011
11.4 2011
13 2011
10.8 2011
12.3 2011
11.3 2011
11.8 2011
7.9 2011
12.7 2011
12.3 2011
11.6 2011
6.7 2011
10.9 2011
12.1 2011
13.3 2011
10.1 2011
5.7 2011
14.3 2011
8 2011
13.3 2011
9.3 2011
12.5 2011
7.6 2011
15.9 2011
9.2 2011
9.1 2011
11.1 2011
13 2011
14.5 2011
12.2 2011
12.3 2011
11.4 2011
8.8 2011
14.6 2011
12.6 2011
13 2011
12.6 2011
13.2 2011
9.9 2011
7.7 2011
10.5 2011
13.4 2011
10.9 2011
4.3 2011
10.3 2011
11.8 2011
11.2 2011
11.4 2011
8.6 2011
13.2 2011
12.6 2011
5.6 2011
9.9 2011
8.8 2011
7.7 2011
9 2011
7.3 2011
11.4 2011
13.6 2011
7.9 2011
10.7 2011
10.3 2011
8.3 2011
9.6 2011
14.2 2011
8.5 2011
13.5 2011
4.9 2011
6.4 2011
9.6 2011
11.6 2011
11.1 2011
4.35 2012
12.7 2012
18.1 2012
17.85 2012
16.6 2012
12.6 2012
17.1 2012
19.1 2012
16.1 2012
13.35 2012
18.4 2012
14.7 2012
10.6 2012
12.6 2012
16.2 2012
13.6 2012
18.9 2012
14.1 2012
14.5 2012
16.15 2012
14.75 2012
14.8 2012
12.45 2012
12.65 2012
17.35 2012
8.6 2012
18.4 2012
16.1 2012
11.6 2012
17.75 2012
15.25 2012
17.65 2012
16.35 2012
17.65 2012
13.6 2012
14.35 2012
14.75 2012
18.25 2012
9.9 2012
16 2012
18.25 2012
16.85 2012
14.6 2012
13.85 2012
18.95 2012
15.6 2012
14.85 2012
11.75 2012
18.45 2012
15.9 2012
17.1 2012
16.1 2012
19.9 2012
10.95 2012
18.45 2012
15.1 2012
15 2012
11.35 2012
15.95 2012
18.1 2012
14.6 2012
15.4 2012
15.4 2012
17.6 2012
13.35 2012
19.1 2012
15.35 2012
7.6 2012
13.4 2012
13.9 2012
19.1 2012
15.25 2012
12.9 2012
16.1 2012
17.35 2012
13.15 2012
12.15 2012
12.6 2012
10.35 2012
15.4 2012
9.6 2012
18.2 2012
13.6 2012
14.85 2012
14.75 2012
14.1 2012
14.9 2012
16.25 2012
19.25 2012
13.6 2012
13.6 2012
15.65 2012
12.75 2012
14.6 2012
9.85 2012
12.65 2012
19.2 2012
16.6 2012
11.2 2012
15.25 2012
11.9 2012
13.2 2012
16.35 2012
12.4 2012
15.85 2012
18.15 2012
11.15 2012
15.65 2012
17.75 2012
7.65 2012
12.35 2012
15.6 2012
19.3 2012
15.2 2012
17.1 2012
15.6 2012
18.4 2012
19.05 2012
18.55 2012
19.1 2012
13.1 2012
12.85 2012
9.5 2012
4.5 2012
11.85 2012
13.6 2012
11.7 2012
12.4 2012
13.35 2012
11.4 2012
14.9 2012
19.9 2012
11.2 2012
14.6 2012
17.6 2012
14.05 2012
16.1 2012
13.35 2012
11.85 2012
11.95 2012
14.75 2012
15.15 2012
13.2 2012
16.85 2012
7.85 2012
7.7 2012
12.6 2012
7.85 2012
10.95 2012
12.35 2012
9.95 2012
14.9 2012
16.65 2012
13.4 2012
13.95 2012
15.7 2012
16.85 2012
10.95 2012
15.35 2012
12.2 2012
15.1 2012
17.75 2012
15.2 2012
14.6 2012
16.65 2012
8.1 2012

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268290&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268290&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-7690.191696.178-11.0460
X3.8290.34611.0650
- - -
Residual Std. Err. 2.83 on 276 df
Multiple R-sq. 0.307
Adjusted R-sq. 0.305

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -7690.191 & 696.178 & -11.046 & 0 \tabularnewline
X & 3.829 & 0.346 & 11.065 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.83  on  276 df \tabularnewline
Multiple R-sq.  & 0.307 \tabularnewline
Adjusted R-sq.  & 0.305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268290&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]-7690.191[/C][C]696.178[/C][C]-11.046[/C][C]0[/C][/ROW]
[C]X[/C][C]3.829[/C][C]0.346[/C][C]11.065[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.83  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.307[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268290&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)-7690.191696.178-11.0460
X3.8290.34611.0650
- - -
Residual Std. Err. 2.83 on 276 df
Multiple R-sq. 0.307
Adjusted R-sq. 0.305






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Course_id_year1980.704980.704122.4330
Residuals2762210.88.01 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Course_id_year & 1 & 980.704 & 980.704 & 122.433 & 0 \tabularnewline
Residuals & 276 & 2210.8 & 8.01 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268290&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]Course_id_year[/C][C]1[/C][C]980.704[/C][C]980.704[/C][C]122.433[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]2210.8[/C][C]8.01[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268290&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268290&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)
Course_id_year1980.704980.704122.4330
Residuals2762210.88.01


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = FALSE ;
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)
}
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()