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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 computationSun, 13 Dec 2015 18:56:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/13/t1450033201y287v1m45wpvbq0.htm/, Retrieved Thu, 16 May 2024 16:42:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286228, Retrieved Thu, 16 May 2024 16:42:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59

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] [Simple Linear Reg...] [2015-12-13 18:56:07] [2cd399ee29a1908c11c72d5dc5a57aee] [Current]
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Dataset

Dataseries X:
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Histogram
Boxplots 
1 24 12.6707633 86.45220101
1 24.5 12.74154396 86.86160934
1 25 12.81159383 87.25262954
1 25.5 12.88102276 87.65247282
1 26 12.94993386 88.03233804
1 26.5 13.01842382 88.42326434
1 27 13.08658317 88.79294174
1 27.5 13.1544966 89.17549228
1 28 13.22224319 89.53576998
1 28.5 13.28989667 89.91040853
1 29 13.3575257 90.26194439
1 29.5 13.42519408 90.62907762
1 30 13.49296097 90.97242937
1 30.5 13.56088113 91.33242379
1 31 13.62900513 91.66807639
1 31.5 13.69737858 92.02127167
1 32 13.76604628 92.34966005
1 32.5 13.83504622 92.69637946
1 33 13.90441401 93.01790703
1 33.5 13.97418299 93.35846546
1 34 14.04437938 93.67351901
1 34.5 14.1150324 94.00822923
1 35 14.18616443 94.31719279
1 35.5 14.25779618 94.64636981
1 36 14.32994444 94.94962511
1 36.5 14.40262749 95.27359106
1 37 14.47585763 95.59527537
1 37.5 14.54964614 95.91474929
1 38 14.62400225 96.23208252
1 38.5 14.69893326 96.54734328
1 39 14.77444466 96.86059835
1 39.5 14.85054151 97.17191309
1 40 14.92722304 97.48135324
1 40.5 15.00449143 97.78897727
1 41 15.08234595 98.09484897
1 41.5 15.16078454 98.3990283
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0 184.5 52.82298572 162.17518
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0 185.5 52.9807949 162.2346979
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0 186.5 53.13326946 162.2908474
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0 219.5 56.50095811 163.1685697
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0 221 56.63965769 163.1858708
0 221.5 56.68632619 163.1914194
0 222 56.73319989 163.1968627
0 222.5 56.78026364 163.202203
0 223 56.82750509 163.2074426
0 223.5 56.87490465 163.2125835
0 224 56.92244396 163.217628
0 224.5 56.97009856 163.2225779
0 225 57.01784381 163.2274354
0 225.5 57.06564989 163.2322024
0 226 57.1134856 163.2368807
0 226.5 57.16131528 163.2414722
0 227 57.20910091 163.2459787
0 227.5 57.25679821 163.2504019
0 228 57.30436885 163.2547435
0 228.5 57.35175792 163.2590052
0 229 57.39891295 163.2631886
0 229.5 57.44578172 163.2672954
0 230 57.49229864 163.2713269
0 230.5 57.53840429 163.2752848
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0 231.5 57.62910094 163.2829854
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0 235 57.92214864 163.307822
0 235.5 57.95967458 163.3111185
0 236 57.99579467 163.3143558
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0 237 58.06335008 163.320657
0 237.5 58.09453209 163.3237231
0 238 58.12380699 163.3267344
0 238.5 58.15103575 163.3296918
0 239 58.17607382 163.3325964
0 239.5 58.1987714 163.3354491
0 240 58.21897289 163.338251
0 240.5 58.23651745 163.341003

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'George Udny Yule' @ yule.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 & 12 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286228&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286228&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286228&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 time12 seconds
R Server'George Udny Yule' @ yule.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-52.260.736-70.9990
X0.6450.005125.1120
- - -
Residual Std. Err. 4.046 on 866 df
Multiple R-sq. 0.948
95% CI Multiple R-sq. [0.944, 0.951]
Adjusted R-sq. 0.948

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -52.26 & 0.736 & -70.999 & 0 \tabularnewline
X & 0.645 & 0.005 & 125.112 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 4.046  on  866 df \tabularnewline
Multiple R-sq.  & 0.948 \tabularnewline
95% CI Multiple R-sq.  & [0.944, 0.951] \tabularnewline
Adjusted R-sq.  & 0.948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286228&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]-52.26[/C][C]0.736[/C][C]-70.999[/C][C]0[/C][/ROW]
[C]X[/C][C]0.645[/C][C]0.005[/C][C]125.112[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]4.046  on  866 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.948[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.944, 0.951][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286228&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286228&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)-52.260.736-70.9990
X0.6450.005125.1120
- - -
Residual Std. Err. 4.046 on 866 df
Multiple R-sq. 0.948
95% CI Multiple R-sq. [0.944, 0.951]
Adjusted R-sq. 0.948






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
len01256303.221256303.22115653.0460
Residuals86614179.89716.374 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
len0 & 1 & 256303.221 & 256303.221 & 15653.046 & 0 \tabularnewline
Residuals & 866 & 14179.897 & 16.374 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286228&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]len0[/C][C]1[/C][C]256303.221[/C][C]256303.221[/C][C]15653.046[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]866[/C][C]14179.897[/C][C]16.374[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286228&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286228&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)
len01256303.221256303.22115653.0460
Residuals86614179.89716.374


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 3 ; par2 = 4 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- '4'
par1 <- '3'
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()