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Author

*Unverified author*

R Software Module

rwasp_Simple Regression Y ~ X.wasp

Title produced by software

Simple Linear Regression

Date of computation

Tue, 11 Mar 2014 10:51:45 -0400

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/2014/Mar/11/t1394549537i2lq1o0wqpda09v.htm/, Retrieved Wed, 15 May 2024 17:50:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234187, Retrieved Wed, 15 May 2024 17:50:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

239

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

-     [CARE Data - Boxplots and Scatterplot Matrix] [Kirpatrick and Fe...] [2013-01-29 22:26:12] [98fd0e87c3eb04e0cc2efde01dbafab6]
- RMP   [Simple Linear Regression] [Multiple Regression] [2014-02-25 21:33:43] [4f81ca23f967d3f23787758b4d63f412]
- R  D      [Simple Linear Regression] [] [2014-03-11 14:51:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

7.00	.00	109.00	13.10	68.00	32.00	258.00	183.00	137.00	95.00
7.00	1.00	112.00	12.90	65.00	19.00	449.00	245.00	134.00	85.00
8.00	.00	124.00	14.10	64.00	22.00	441.00	268.00	147.00	100.00
8.00	1.00	125.00	16.20	67.00	41.00	234.00	146.00	124.00	85.00
8.00	.00	127.00	21.50	93.00	52.00	202.00	131.00	104.00	95.00
9.00	.00	130.00	17.50	68.00	44.00	308.00	155.00	118.00	80.00
11.00	1.00	139.00	30.70	89.00	28.00	305.00	179.00	119.00	65.00
12.00	1.00	150.00	28.40	69.00	18.00	369.00	198.00	103.00	110.00
12.00	.00	146.00	25.10	67.00	24.00	312.00	194.00	128.00	70.00
13.00	1.00	155.00	31.50	68.00	23.00	413.00	225.00	136.00	95.00
13.00	.00	156.00	39.90	89.00	39.00	206.00	142.00	95.00	110.00
14.00	1.00	153.00	42.10	90.00	26.00	253.00	191.00	121.00	90.00
14.00	.00	160.00	45.60	93.00	45.00	174.00	139.00	108.00	100.00
15.00	1.00	158.00	51.20	93.00	45.00	158.00	124.00	90.00	80.00
16.00	1.00	160.00	35.90	66.00	31.00	302.00	133.00	101.00	134.00
17.00	1.00	153.00	34.80	70.00	29.00	204.00	118.00	120.00	134.00
17.00	.00	174.00	44.70	70.00	49.00	187.00	104.00	103.00	165.00
17.00	1.00	176.00	60.10	92.00	29.00	188.00	129.00	130.00	120.00
17.00	.00	171.00	42.60	69.00	38.00	172.00	130.00	103.00	130.00
19.00	1.00	156.00	37.20	72.00	21.00	216.00	119.00	81.00	85.00
19.00	.00	174.00	54.60	86.00	37.00	184.00	118.00	101.00	85.00
20.00	.00	178.00	64.00	86.00	34.00	225.00	148.00	135.00	160.00
23.00	.00	180.00	73.80	97.00	57.00	171.00	108.00	98.00	165.00
23.00	.00	175.00	51.10	71.00	33.00	224.00	131.00	113.00	95.00
23.00	.00	179.00	71.50	95.00	52.00	225.00	127.00	101.00	195.00

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	'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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234187&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234187&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234187&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	'Gertrude Mary Cox' @ cox.wessa.net

Linear Regression Model
Y ~ X
coefficients:
	Estimate	Std. Error	t value	Pr(>\|t\|)
(Intercept)	15.214	1.362	11.173	0
X	-1.669	2.053	-0.813	0.425
- - -
Residual Std. Err.	5.095 on 23 df
Multiple R-sq.	0.028
Adjusted R-sq.	-0.014

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 15.214 & 1.362 & 11.173 & 0 \tabularnewline
X & -1.669 & 2.053 & -0.813 & 0.425 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 5.095  on  23 df \tabularnewline
Multiple R-sq.  & 0.028 \tabularnewline
Adjusted R-sq.  & -0.014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234187&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]15.214[/C][C]1.362[/C][C]11.173[/C][C]0[/C][/ROW]
[C]X[/C][C]-1.669[/C][C]2.053[/C][C]-0.813[/C][C]0.425[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]5.095  on  23 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.028[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234187&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234187&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)	15.214	1.362	11.173	0
X	-1.669	2.053	-0.813	0.425
- - -
Residual Std. Err.	5.095 on 23 df
Multiple R-sq.	0.028
Adjusted R-sq.	-0.014

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Sex	1	17.156	17.156	0.661	0.425
Residuals	23	597.084	25.96

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Sex & 1 & 17.156 & 17.156 & 0.661 & 0.425 \tabularnewline
Residuals & 23 & 597.084 & 25.96 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234187&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]Sex[/C][C]1[/C][C]17.156[/C][C]17.156[/C][C]0.661[/C][C]0.425[/C][/ROW]
[ROW][C]Residuals[/C][C]23[/C][C]597.084[/C][C]25.96[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234187&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234187&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)
Sex	1	17.156	17.156	0.661	0.425
Residuals	23	597.084	25.96

Figure 1

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Postscript link

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Figure 2

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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)
}
a<-table.row.end(a)
}
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