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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 12:18:55 +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/t1513338574j8lge0xkrgrop7g.htm/, Retrieved Wed, 15 May 2024 04:06:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309660, Retrieved Wed, 15 May 2024 04:06:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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 11:18:55] [deec28e763260dad9f228be262d61467] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36.43	10.81
38.72	11.46
49.66	14.65
37.7	11.09
34.72	10.15
51.52	14.98
32.26	9.35
51.88	15.04
50.13	14.41
144.69	5.14
159.08	5.65
146.64	5.21
121.21	4.23
116.45	4.07
117.19	4.09
133.82	4.67
136.98	4.78
121.07	4.23
90.99	3.17
91.51	3.19
116.48	4.06
120.43	3.82
125.72	3.99
114.31	3.62
116.63	3.7
157.88	5.01
115.46	3.46
152.5	4.58
147.38	4.42
147.38	4.42
127.7	3.83
129.52	3.73
120.51	3.47
114.97	3.31
116.23	3.35
117.8	3.39
146.61	3.9
148.85	3.96
114.77	3.05
127.83	3.4
153.35	4.08
154.94	4
148.37	3.83
152.96	3.95
161.02	4.16
154.34	3.99
144.24	3.73
178.7	4.62
121.86	3.15
150.66	3.89
196.75	2.69
250.12	3.42
228.32	3.12
238.36	3.26
198.25	2.71
324.08	2.26
431.54	3.01
267.83	1.87
331.21	2.31
248.52	1.73
367.71	2.56
320.22	2.23
51.87	6.72
51.3	6.65
69.23	8.97
57.51	7.45
58.3	7.55
55.8	7.23
68.21	8.84
66.63	8.63
49.41	6.37
49.34	6.36
49.02	6.32
50.24	6.47
49.81	6.42
49.25	6.35
49.25	6.35
49.81	6.42
49.25	13.03
49.34	13.05
48.54	12.84
44.97	11.87
52.31	13.8
53.5	6.01
52.35	5.88
65.47	7.36
68	7.64
66.05	7.42
62.11	6.97
114.06	4.46
97.89	3.82
112.57	4.4
112.42	4.39
118.16	4.62
129.41	5.05
120.64	4.71
326.84	1.83
328.86	1.84
332.35	1.86
296.16	1.66
89.47	4.73
100.05	5.29
93.24	4.93
92.74	4.91
113.08	5.98
113.8	6.02
83.81	4.43
113.16	5.99
81.89	4.33
97.53	5.16
89.43	4.73
88.18	4.66
87.7	4.64
91.17	4.82
113.59	4.12
116.72	4.23
115.92	4.2
118.11	4.28
114.45	4.15
115.78	4.17

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 time7 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309660&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]7 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309660&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 time7 seconds
R ServerBig Analytics Cloud Computing Center






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)214.38111.56318.540
X-16.4271.838-8.9370
- - -
Residual Std. Err. 61.243 on 118 df
Multiple R-sq. 0.404
95% CI Multiple R-sq. [0.327, 0.461]
Adjusted R-sq. 0.399

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 214.381 & 11.563 & 18.54 & 0 \tabularnewline
X & -16.427 & 1.838 & -8.937 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 61.243  on  118 df \tabularnewline
Multiple R-sq.  & 0.404 \tabularnewline
95% CI Multiple R-sq.  & [0.327, 0.461] \tabularnewline
Adjusted R-sq.  & 0.399 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309660&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]214.381[/C][C]11.563[/C][C]18.54[/C][C]0[/C][/ROW]
[C]X[/C][C]-16.427[/C][C]1.838[/C][C]-8.937[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]61.243  on  118 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.404[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.327, 0.461][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.399[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309660&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)214.38111.56318.540
X-16.4271.838-8.9370
- - -
Residual Std. Err. 61.243 on 118 df
Multiple R-sq. 0.404
95% CI Multiple R-sq. [0.327, 0.461]
Adjusted R-sq. 0.399






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
PUV1299567.936299567.93679.870
Residuals118442581.433750.69 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
PUV & 1 & 299567.936 & 299567.936 & 79.87 & 0 \tabularnewline
Residuals & 118 & 442581.43 & 3750.69 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309660&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]PUV[/C][C]1[/C][C]299567.936[/C][C]299567.936[/C][C]79.87[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]118[/C][C]442581.43[/C][C]3750.69[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309660&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)
PUV1299567.936299567.93679.870
Residuals118442581.433750.69


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):
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()