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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationTue, 03 Dec 2013 06:38:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/03/t13860707552f2yjtbfcocbpy8.htm/, Retrieved Wed, 24 Apr 2024 20:59:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230207, Retrieved Wed, 24 Apr 2024 20:59:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

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] [Question 1 ] [2013-12-03 11:38:38] [a907cfb4171037b3c525fe2d5462dffd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
111	45	27	52
102	50	18	55
108	49	19	80
109	55	20	45
118	39	29	60
88	68	46	34
102	69	27	45
105	56	23	68
92	58	29	26
104	48	38	70
83	34	20	54
84	50	37	55
85	76	32	40
110	49	26	55
100	51	40	50
94	53	30	55
89	36	26	70
93	62	23	55
84	46	27	60
106	50	38	65
82	47	25	66
106	50	33	55
109	44	45	55
91	50	34	60
111	29	20	35
105	49	24	55
118	26	26	26
103	79	26	14
101	53	39	45
101	53	27	35
95	72	18	65
108	35	34	35
95	42	25	60
98	37	26	60
82	46	28	60
100	48	21	65
100	46	39	45
107	49	25	20
95	65	29	50
97	52	37	60
93	75	34	48
81	58	30	40
89	43	28	55
111	60	25	54
95	43	27	40
106	51	33	40
83	70	30	34
81	69	26	60
115	65	18	30
112	63	21	24
92	44	39	30
85	61	36	60
95	40	32	46
115	62	23	35
91	59	27	60
107	47	45	54
102	50	24	20
86	50	29	45
96	65	21	60
114	54	28	70
105	44	37	35
120	66	22	20
88	34	31	60
90	74	32	20
85	57	20	50
106	60	33	50
109	36	32	70
91	50	18	20
96	60	44	45
108	45	24	20
86	55	21	50
98	44	29	55
99	57	30	15
95	33	37	26
88	30	33	25
111	64	25	30
103	49	19	60
107	76	16	40
118	40	31	40

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230207&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230207&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)103.9095.29419.6280
X-0.0940.099-0.9460.347
- - -
Residual Std. Err. 10.462 on 77 df
Multiple R-sq. 0.011
Adjusted R-sq. -0.001

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 103.909 & 5.294 & 19.628 & 0 \tabularnewline
X & -0.094 & 0.099 & -0.946 & 0.347 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 10.462  on  77 df \tabularnewline
Multiple R-sq.  & 0.011 \tabularnewline
Adjusted R-sq.  & -0.001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230207&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]103.909[/C][C]5.294[/C][C]19.628[/C][C]0[/C][/ROW]
[C]X[/C][C]-0.094[/C][C]0.099[/C][C]-0.946[/C][C]0.347[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]10.462  on  77 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.011[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230207&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)103.9095.29419.6280
X-0.0940.099-0.9460.347
- - -
Residual Std. Err. 10.462 on 77 df
Multiple R-sq. 0.011
Adjusted R-sq. -0.001






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Add198.00898.0080.8950.347
Residuals778427.941109.454 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Add & 1 & 98.008 & 98.008 & 0.895 & 0.347 \tabularnewline
Residuals & 77 & 8427.941 & 109.454 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230207&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]98.008[/C][C]98.008[/C][C]0.895[/C][C]0.347[/C][/ROW]
[ROW][C]Residuals[/C][C]77[/C][C]8427.941[/C][C]109.454[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230207&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Add198.00898.0080.8950.347
Residuals778427.941109.454


Figures (Output of Computation)

Input Parameters & R Code

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()