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Author

*The author of this computation has been verified*

R Software Module

rwasp_Simple Regression Y ~ X.wasp

Title produced by software

Simple Linear Regression

Date of computation

Sun, 19 Apr 2015 15:10:57 +0100

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/2015/Apr/19/t142945272253h0a8mfjxvg7lz.htm/, Retrieved Thu, 20 Feb 2025 19:08:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278728, Retrieved Thu, 20 Feb 2025 19:08:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

217

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]
- RM    [Simple Linear Regression] [Print] [2014-12-04 13:21:05] [2a42404c3b0fbfc7622e3301a77a3a9b]
-  MP     [Simple Linear Regression] [IQ (IV ) and Grad...] [2014-12-04 13:48:23] [2a42404c3b0fbfc7622e3301a77a3a9b]
-   PD        [Simple Linear Regression] [SA v GN] [2015-04-19 14:10:57] [81dd4e4e1a53547628b5dda76e98ea83] [Current]
-   P           [Simple Linear Regression] [SAS vs SG500] [2015-04-19 14:16:34] [2a42404c3b0fbfc7622e3301a77a3a9b] 
- R P           [Simple Linear Regression] [SAS vs SN500] [2015-04-19 14:18:53] [2a42404c3b0fbfc7622e3301a77a3a9b] 
- R PD            [Simple Linear Regression] [SAS vs GN1250] [2015-04-19 14:24:04] [2a42404c3b0fbfc7622e3301a77a3a9b] 
-   P               [Simple Linear Regression] [SAS vs SG1250] [2015-04-19 14:27:40] [2a42404c3b0fbfc7622e3301a77a3a9b] 

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Dataseries X:

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Histogram

Boxplots

 35	24	-26	21
37	43	-19	-67
9	65	50	26
100	36	52	18
21	38	8	86
34	-14	-59	-7
59	26	8	24
41	71	47	-46
69	277	200	63
20	-25	-34	64
57	105	412	-46
50	-13	-67	-67
35	97	4	0
19	126	34	74
4	60	127	95
76	212	117	475
40	1	-33	19
25	-11	-19	43
66	20	-15	53
56	51	-49	-17
37	-146	-67	-28
70	-12	-88	-130
37	-5	39	45
37	106	58	48
41	-53	8	-53
42	100	-30	92
26	-54	7	-35
47	50	70	20
38	19	-14	-65
18	12	39	127
50	26	43	56

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278728&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278728&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	-1.254	31.542	-0.04	0.969
X	0.981	0.678	1.446	0.159
- - -
Residual Std. Err.	76.923 on 29 df
Multiple R-sq.	0.067
Adjusted R-sq.	0.035

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -1.254 & 31.542 & -0.04 & 0.969 \tabularnewline
X & 0.981 & 0.678 & 1.446 & 0.159 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 76.923  on  29 df \tabularnewline
Multiple R-sq.  & 0.067 \tabularnewline
Adjusted R-sq.  & 0.035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278728&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]-1.254[/C][C]31.542[/C][C]-0.04[/C][C]0.969[/C][/ROW]
[C]X[/C][C]0.981[/C][C]0.678[/C][C]1.446[/C][C]0.159[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]76.923  on  29 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.067[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278728&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)	-1.254	31.542	-0.04	0.969
X	0.981	0.678	1.446	0.159
- - -
Residual Std. Err.	76.923 on 29 df
Multiple R-sq.	0.067
Adjusted R-sq.	0.035

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
SAS	1	12368.9	12368.9	2.09	0.159
Residuals	29	171599.036	5917.208

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
SAS & 1 & 12368.9 & 12368.9 & 2.09 & 0.159 \tabularnewline
Residuals & 29 & 171599.036 & 5917.208 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278728&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]SAS[/C][C]1[/C][C]12368.9[/C][C]12368.9[/C][C]2.09[/C][C]0.159[/C][/ROW]
[ROW][C]Residuals[/C][C]29[/C][C]171599.036[/C][C]5917.208[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278728&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)
SAS	1	12368.9	12368.9	2.09	0.159
Residuals	29	171599.036	5917.208

Figure 1

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Postscript link

PDF link

Figure 2

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Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

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()
bitmap(file='cooksDistanceLmplot.png')
plot.lm(lmxdf, which=4)
dev.off()

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code