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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, 01 Dec 2013 14:26:50 -0500

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/2013/Dec/01/t1385926041uh1snu6gza7bjgd.htm/, Retrieved Thu, 25 Apr 2024 07:25:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229852, Retrieved Thu, 25 Apr 2024 07:25:13 +0000

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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] [Regression Example] [2012-01-24 12:40:19] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R  D    [Simple Linear Regression] [Q1- week 8] [2013-12-01 19:26:50] [c1654cd6aa8f8bba86e6a3468d90f5b5] [Current]

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Dataseries X:

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Boxplots

111	45	27	52
102	50	18	55
108	49	19	45
109	55	20	60
118	39	29	34
88	68	46	45
102	69	27	68
105	56	23	26
92	58	29	70
104	48	38	85
83	34	20	54
84	50	37	55
85	76	32	40
110	49	26	55
121	51	40	50
120	53	30	71
100	36	26	55
94	62	23	70
89	46	27	55
93	50	38	60
128	47	25	65
84	50	33	66
127	44	45	55
106	50	34	55
129	29	20	60
106	49	24	35
109	26	26	55
91	79	26	26
111	53	39	45
105	53	27	35
118	72	18	65
103	35	34	35
101	42	25	60
101	37	26	60
95	46	28	60
108	48	21	65
95	46	39	45
98	49	25	50
100	65	29	60
100	52	37	48
107	75	34	40
95	58	30	55
97	43	28	54
93	60	25	40
89	43	27	40
111	51	33	34
95	70	30	60
106	69	26	30
83	65	18	24
115	63	21	30
112	44	39	60
92	61	36	46
85	40	32	35
95	62	23	60
115	59	27	54
91	47	45	45
107	50	24	60
102	50	29	70
86	65	21	35
96	54	28	60
114	44	37	50
105	66	22	50
120	34	31	70
88	74	32	45
90	57	20	50
85	60	33	55
106	36	32	26
109	50	18	25
91	60	44	30
96	45	24	60
108	55	21	40
86	44	29	40
98	57	30	50
99	33	37	
95	30	33	
88	64	25	
111	49	19	
103	76	16	
107	40	31	
118	48	29	
	65	37
	50	41
	70	28
	78	19
	44	28
	48	33
	52	32
	40	28

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229852&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229852&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	127.461	7.605	16.759	0
X	-0.627	0.128	-4.919	0
- - -
Residual Std. Err.	22.601 on 86 df
Multiple R-sq.	0.22
Adjusted R-sq.	0.21

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 127.461 & 7.605 & 16.759 & 0 \tabularnewline
X & -0.627 & 0.128 & -4.919 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 22.601  on  86 df \tabularnewline
Multiple R-sq.  & 0.22 \tabularnewline
Adjusted R-sq.  & 0.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229852&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]127.461[/C][C]7.605[/C][C]16.759[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.627[/C][C]0.128[/C][C]-4.919[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]22.601  on  86 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.22[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229852&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)	127.461	7.605	16.759	0
X	-0.627	0.128	-4.919	0
- - -
Residual Std. Err.	22.601 on 86 df
Multiple R-sq.	0.22
Adjusted R-sq.	0.21

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Add	1	12359.84	12359.84	24.196	0
Residuals	86	43930.114	510.815

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Add & 1 & 12359.84 & 12359.84 & 24.196 & 0 \tabularnewline
Residuals & 86 & 43930.114 & 510.815 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229852&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]Add[/C][C]1[/C][C]12359.84[/C][C]12359.84[/C][C]24.196[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]86[/C][C]43930.114[/C][C]510.815[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229852&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229852&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)
Add	1	12359.84	12359.84	24.196	0
Residuals	86	43930.114	510.815

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 = 1 ; par2 = 2 ; par3 = TRUE ;

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)
}# 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()

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code