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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 computationFri, 15 Dec 2017 11:54:53 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/15/t15133361432wns18avne6imxp.htm/, Retrieved Thu, 31 Oct 2024 22:46:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309648, Retrieved Thu, 31 Oct 2024 22:46:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

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] [] [2017-12-15 10:54:53] [f44dd4af88e8b85f25b182ab83c3a44e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36,43	2
38,72	-1
49,66	-3
37,7	-3
34,72	1
51,52	-3
32,26	2
51,88	2
50,13	-2
144,69	-3
159,08	1
146,64	-1
121,21	1
116,45	2
117,19	2
133,82	2
136,98	-2
121,07	3
90,99	3
91,51	3
116,48	2
120,43	0
125,72	0
114,31	1
116,63	1
157,88	-3
115,46	3
152,5	1
147,38	-2
147,38	-2
127,7	2
129,52	1
120,51	2
114,97	3
116,23	3
117,8	2
146,61	2
148,85	0
114,77	0
127,83	3
153,35	1
154,94	0
148,37	3
152,96	1
161,02	3
154,34	-1
144,24	-2
178,7	2
121,86	2
150,66	2
196,75	0
250,12	-1
228,32	-3
238,36	1
198,25	0
324,08	-1
431,54	-1
267,83	0
331,21	-2
248,52	0
367,71	-1
320,22	-2
51,87	-1
51,3	-1
69,23	2
57,51	3
58,3	3
55,8	3
68,21	0
66,63	3
49,41	0
49,34	0
49,02	0
50,24	0
49,81	0
49,25	0
49,25	0
49,81	0
49,25	-1
49,34	-1
48,54	-1
44,97	-2
52,31	-2
53,5	2
52,35	2
65,47	3
68	3
66,05	1
62,11	2
114,06	2
97,89	1
112,57	2
112,42	3
118,16	1
129,41	0
120,64	-2
326,84	-2
328,86	-1
332,35	-1
296,16	0
89,47	3
100,05	2
93,24	0
92,74	1
113,08	-2
113,8	-2
83,81	2
113,16	1
81,89	1
97,53	0
89,43	3
88,18	3
87,7	3
91,17	3
113,59	2
116,72	3
115,92	3
118,11	3
114,45	3
115,78	3

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309648&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309648&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309648&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)131.4947.45917.6280
X-11.0773.802-2.9140.004
- - -
Residual Std. Err. 76.598 on 118 df
Multiple R-sq. 0.067
95% CI Multiple R-sq. [0.01, 0.171]
Adjusted R-sq. 0.059

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 131.494 & 7.459 & 17.628 & 0 \tabularnewline
X & -11.077 & 3.802 & -2.914 & 0.004 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 76.598  on  118 df \tabularnewline
Multiple R-sq.  & 0.067 \tabularnewline
95% CI Multiple R-sq.  & [0.01, 0.171] \tabularnewline
Adjusted R-sq.  & 0.059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309648&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]131.494[/C][C]7.459[/C][C]17.628[/C][C]0[/C][/ROW]
[C]X[/C][C]-11.077[/C][C]3.802[/C][C]-2.914[/C][C]0.004[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]76.598  on  118 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.067[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.01, 0.171][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309648&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309648&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)131.4947.45917.6280
X-11.0773.802-2.9140.004
- - -
Residual Std. Err. 76.598 on 118 df
Multiple R-sq. 0.067
95% CI Multiple R-sq. [0.01, 0.171]
Adjusted R-sq. 0.059






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
COLOR149811.9549811.958.490.004
Residuals118692337.4175867.266 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
COLOR & 1 & 49811.95 & 49811.95 & 8.49 & 0.004 \tabularnewline
Residuals & 118 & 692337.417 & 5867.266 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309648&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]COLOR[/C][C]1[/C][C]49811.95[/C][C]49811.95[/C][C]8.49[/C][C]0.004[/C][/ROW]
[ROW][C]Residuals[/C][C]118[/C][C]692337.417[/C][C]5867.266[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309648&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309648&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)
COLOR149811.9549811.958.490.004
Residuals118692337.4175867.266


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = 50 ; par3 = 0 ; par4 = 0 ; par5 = 0 ; par6 = Y ; par7 = Y ; par8 = terrain.colors ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
library(boot)
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- na.omit(t(x))
rsq <- function(formula, data, indices) {
d <- data[indices,] # allows boot to select sample
fit <- lm(formula, data=d)
return(summary(fit)$r.square)
}
xdf<-data.frame(na.omit(t(y)))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
(results <- boot(data=xdf, statistic=rsq, R=1000, formula=Y~X))
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'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, '95% CI Multiple R-sq. ',1,TRUE)
a<-table.element(a, paste('[',round(boot.ci(results,type='bca')$bca[1,4], digits=3),', ', round(boot.ci(results,type='bca')$bca[1,5], digits=3), ']',sep='') ,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$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qqPlot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot(lmxdf, which=4)
dev.off()