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Author's title

Author

*The author of this computation has been verified*

R Software Module

Ian.Hollidayrwasp_Simple Regression Y ~ X.wasp

Title produced by software

Simple Linear Regression

Date of computation

Tue, 04 May 2010 13:39:46 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/04/t1272980502pt17zf7ek8plnjh.htm/, Retrieved Tue, 30 Apr 2024 18:52:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=75419, Retrieved Tue, 30 Apr 2024 18:52:55 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

153

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

-     [Simple Linear Regression] [PY2224 Mock Exam ...] [2010-04-28 07:33:16] [98fd0e87c3eb04e0cc2efde01dbafab6]
-    D  [Simple Linear Regression] [PY2224 May Mock E...] [2010-04-30 11:33:27] [98fd0e87c3eb04e0cc2efde01dbafab6]
-         [Simple Linear Regression] [PY2224 May Mock E...] [2010-04-30 11:37:32] [98fd0e87c3eb04e0cc2efde01dbafab6]
-   PD        [Simple Linear Regression] [Linear Regression] [2010-05-04 13:39:46] [8853a743cb4f0fc816ef95f18ccb07bb] [Current]

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Dataseries X:

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Histogram

Boxplots

133.1	130.8	212	156
85.0	80.0	268	250
83.8	77.9	111	107
104.5	98.3	132	117
76.8	73.2	165	96
90.5	88.9	57	63
106.9	103.7	163	131
81.5	78.9	111	54
96.5	94.9	300	241
103.0	97.2	192	124
127.5	124.7	176	215
103.2	102.0	146	138
113.5	115.0	446	795
107.0	99.2	232	63
106.0	103.5	255	204
114.9	105.3	187	144
103.4	96.0	154	96

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	75.101.192.8 @ 75.101.192.8

\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 & 75.101.192.8 @ 75.101.192.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75419&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]75.101.192.8 @ 75.101.192.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75419&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75419&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	3 seconds
R Server	75.101.192.8 @ 75.101.192.8

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-4.74	4.89	-0.969	0.348
X	1.007	0.047	21.277	0
- - -
Residual Std. Err.	2.93 on 15 df
Multiple R-sq.	0.968
Adjusted R-sq.	0.966

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -4.74 & 4.89 & -0.969 & 0.348 \tabularnewline
X & 1.007 & 0.047 & 21.277 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.93  on  15 df \tabularnewline
Multiple R-sq.  & 0.968 \tabularnewline
Adjusted R-sq.  & 0.966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75419&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]-4.74[/C][C]4.89[/C][C]-0.969[/C][C]0.348[/C][/ROW]
[C]X[/C][C]1.007[/C][C]0.047[/C][C]21.277[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.93  on  15 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.968[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75419&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75419&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)	-4.74	4.89	-0.969	0.348
X	1.007	0.047	21.277	0
- - -
Residual Std. Err.	2.93 on 15 df
Multiple R-sq.	0.968
Adjusted R-sq.	0.966

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Weight-at-bassline	1	3886.713	3886.713	452.727	0
Residuals	15	128.777	8.585

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Weight-at-bassline & 1 & 3886.713 & 3886.713 & 452.727 & 0 \tabularnewline
Residuals & 15 & 128.777 & 8.585 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75419&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]Weight-at-bassline[/C][C]1[/C][C]3886.713[/C][C]3886.713[/C][C]452.727[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]15[/C][C]128.777[/C][C]8.585[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75419&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75419&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)
Weight-at-bassline	1	3886.713	3886.713	452.727	0
Residuals	15	128.777	8.585

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ; par2 = 2 ; par3 = TRUE ;

Parameters (R input):

par1 = 4 ; 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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code