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Author

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R Software Module

Ian.Hollidayrwasp_Simple Regression Y ~ X.wasp

Title produced by software

Simple Linear Regression

Date of computation

Thu, 05 May 2011 11:05:35 +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/2011/May/05/t1304593328qolwmjkjo1c3n86.htm/, Retrieved Fri, 10 May 2024 07:44:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121083, Retrieved Fri, 10 May 2024 07:44:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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]
- R  D        [Simple Linear Regression] [linear regression] [2011-05-05 11:05:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

84.0	90	82.4	131	
88.8	137	87.0	82	
87.0	182	81.8	152	
84.5	72	80.4	72	
69.4	143	69.0	126	
104.7	96	102.0	157	
90.0	115	87.6	88	
89.4	124	86.8	123	
95.2	188	92.8	255	
108.1	167	100.9	87	
93.9	143	90.2	213	
83.4	143	75.0	102	
104.4	276	102.9	313	
103.7	84	95.7	84	
99.2	142	99.2	135	
95.6	64	88.5	114	
126.0	226	123.2	152	
103.7	199	95.5	120	
133.1	212	130.8	156	
85.0	268	80.0	250	
83.8	111	77.9	107	
104.5	132	98.3	117	
76.8	165	73.2	96	
90.5	57	88.9	63	
106.9	163	103.7	131	
81.5	111	78.9	54	
96.5	300	94.9	241	
103.0	192	97.2	124	
127.5	176	124.7	215	
103.2	146	102.0	138	
113.5	446	115.0	795	
107.0	232	99.2	63	
106.0	255	103.5	204	
114.9	187	105.3	144	
103.4	154	96.0	96

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121083&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121083&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-39.622	86.341	-0.459	0.649
X	2.113	0.868	2.435	0.02
- - -
Residual Std. Err.	72.27 on 33 df
Multiple R-sq.	0.152
Adjusted R-sq.	0.127

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -39.622 & 86.341 & -0.459 & 0.649 \tabularnewline
X & 2.113 & 0.868 & 2.435 & 0.02 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 72.27  on  33 df \tabularnewline
Multiple R-sq.  & 0.152 \tabularnewline
Adjusted R-sq.  & 0.127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121083&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]-39.622[/C][C]86.341[/C][C]-0.459[/C][C]0.649[/C][/ROW]
[C]X[/C][C]2.113[/C][C]0.868[/C][C]2.435[/C][C]0.02[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]72.27  on  33 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.152[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121083&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)	-39.622	86.341	-0.459	0.649
X	2.113	0.868	2.435	0.02
- - -
Residual Std. Err.	72.27 on 33 df
Multiple R-sq.	0.152
Adjusted R-sq.	0.127

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
weightbase	1	30971.65	30971.65	5.93	0.02
Residuals	33	172357.093	5222.942

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
weightbase & 1 & 30971.65 & 30971.65 & 5.93 & 0.02 \tabularnewline
Residuals & 33 & 172357.093 & 5222.942 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121083&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]weightbase[/C][C]1[/C][C]30971.65[/C][C]30971.65[/C][C]5.93[/C][C]0.02[/C][/ROW]
[ROW][C]Residuals[/C][C]33[/C][C]172357.093[/C][C]5222.942[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121083&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)
weightbase	1	30971.65	30971.65	5.93	0.02
Residuals	33	172357.093	5222.942

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = 1 ; par3 = TRUE ;

Parameters (R input):

par1 = 2 ; par2 = 1 ; 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