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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

Wed, 25 Aug 2010 22:12:21 +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/Aug/26/t1282775081r30hqqlm81j51ul.htm/, Retrieved Sun, 28 Apr 2024 21:32:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79470, Retrieved Sun, 28 Apr 2024 21:32:53 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

221

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

-     [Linear Regression with One Explanatory Variable- Free Statistics Software (Calculator)] [Regression of Gra...] [2009-12-14 19:19:44] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R     [Linear Regression with One Explanatory Variable- Free Statistics Software (Calculator)] [Regression of Gra...] [2009-12-15 17:16:56] [98fd0e87c3eb04e0cc2efde01dbafab6]
-         [Linear Regression with One Explanatory Variable- Free Statistics Software (Calculator)] [w11] [2009-12-17 13:10:07] [66f61a2d5ef80b1eafe31e5651ad0889]
-    D        [Simple Linear Regression] [] [2010-08-25 22:12:21] [7b3d06fa35998fc5178bedfec9e0d266] [Current]

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Dataseries X:

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Histogram

Boxplots

82	79	26	35
82	58	30	50
82	60	44	20
83	76	32	55
83	62	23	24
84	49	26	40
84	50	34	55
85	51	40	55
85	65	21	35
85	57	30	50
86	57	20	45
86	48	29	55
88	69	27	45
88	55	21	20
88	78	19	30
89	47	25	60
89	63	21	34
90	44	29	50
91	72	18	14
91	66	22	54
91	49	19	45
92	48	38	70
92	50	29	46
93	50	33	65
93	69	26	40
94	50	38	55
95	49	25	60
95	52	37	45
95	51	33	55
95	61	36	30
95	54	28	60
95	70	28	25
96	60	33	60
96	76	16	20
97	70	30	54
98	75	34	20
98	65	37	15
99	50	41	26
100	46	27	70
100	43	28	60
100	60	25	48
101	48	21	60
101	46	39	60
102	50	18	55
102	56	23	68
102	74	32	20
103	46	28	35
103	48	33	40
104	50	37	54
105	58	29	26
105	42	25	35
105	50	18	35
106	49	24	55
106	53	39	55
106	40	32	75
106	33	37	75
107	43	27	40
107	34	31	78
107	52	32	40
108	49	19	80
108	65	29	65
108	40	31	50
109	55	20	45
109	53	27	26
109	30	33	70
110	53	30	50
111	45	27	52
111	35	34	45
111	44	39	60
111	44	28	60
112	50	24	60
114	36	32	70
115	47	45	80
115	44	37	75
118	39	29	60
118	37	26	65
118	40	28	50
120	62	23	55
120	45	24	60

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79470&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79470&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-10.146	16.675	-0.608	0.545
X	0.595	0.167	3.572	0.001
- - -
Residual Std. Err.	15.439 on 77 df
Multiple R-sq.	0.142
Adjusted R-sq.	0.131

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -10.146 & 16.675 & -0.608 & 0.545 \tabularnewline
X & 0.595 & 0.167 & 3.572 & 0.001 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 15.439  on  77 df \tabularnewline
Multiple R-sq.  & 0.142 \tabularnewline
Adjusted R-sq.  & 0.131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79470&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]-10.146[/C][C]16.675[/C][C]-0.608[/C][C]0.545[/C][/ROW]
[C]X[/C][C]0.595[/C][C]0.167[/C][C]3.572[/C][C]0.001[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]15.439  on  77 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.142[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79470&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)	-10.146	16.675	-0.608	0.545
X	0.595	0.167	3.572	0.001
- - -
Residual Std. Err.	15.439 on 77 df
Multiple R-sq.	0.142
Adjusted R-sq.	0.131

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
IQ	1	3042.247	3042.247	12.762	0.001
Residuals	77	18354.943	238.376

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
IQ & 1 & 3042.247 & 3042.247 & 12.762 & 0.001 \tabularnewline
Residuals & 77 & 18354.943 & 238.376 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79470&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]IQ[/C][C]1[/C][C]3042.247[/C][C]3042.247[/C][C]12.762[/C][C]0.001[/C][/ROW]
[ROW][C]Residuals[/C][C]77[/C][C]18354.943[/C][C]238.376[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79470&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)
IQ	1	3042.247	3042.247	12.762	0.001
Residuals	77	18354.943	238.376

Figure 1

PNG link

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 = 1 ; par3 = TRUE ;

Parameters (R input):

par1 = 4 ; 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$call['formula'],nc+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'coefficients:',1,TRUE)
a<-table.element(a, ' ',nc-1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
for(i in 1 : nc){
a<-table.element(a, dimnames(sumlmxdf$'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, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3),,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$Df[2],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
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