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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, 01 Jun 2012 05:31:32 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jun/01/t13385431110mgu43gw98fw7jp.htm/, Retrieved Thu, 02 May 2024 10:40:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168325, Retrieved Thu, 02 May 2024 10:40:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

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] [Triglyceridge Reg...] [2011-07-07 15:11:49] [74be16979710d4c4e7c6647856088456]
- R     [Simple Linear Regression] [Triglyceride] [2012-05-04 19:33:41] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R       [Simple Linear Regression] [Tricglyceride vs ...] [2012-06-01 08:48:24] [ac59e217462c4b907248e97ba2ac8ba3]
- R PD        [Simple Linear Regression] [Weight against re...] [2012-06-01 09:31:32] [1fa2eba2cf8100b3350d01270322fdcf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58	51
53	54
59	59
57	56
51	52
64	64
52	57
65	66
62	62
61	61
61	61
54	59
50	50
63	61
58	60
39	41
71	71
52	52
68	63
56	54
54	53
63	59
54	55
54	56
75	75
56	57
78	75
60	59
64	63
64	62
52	51
62	61
55	54
56	57
50	50
50	55
63	64
61	60
53	52
60	55
56	56
53	53
57	59
57	56
56	56
56	57
50	50
52	52
55	55
47	47
45	45
62	63
53	51
52	51
57	55
64	64
59	55
55	57
76	77
62	62
68	68
55	55
45	45
68	68
44	44
62	61
56	53
50	47
53	53
64	62
52	53
53	55
54	55
64	66
55	55
55	55
59	55
70	67
57	58
47	47
47	45
48	44
57	56
51	50
54	54
53	52
59	58
59	59
63	62
66	66
53	50
63	59
56	56
60	55
58	54
50	49
59	59
51	51
62	61

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168325&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168325&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)1.9281.7291.1150.267
X0.9750.0332.1910
- - -
Residual Std. Err. 2.025 on 97 df
Multiple R-sq. 0.914
Adjusted R-sq. 0.914

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 1.928 & 1.729 & 1.115 & 0.267 \tabularnewline
X & 0.975 & 0.03 & 32.191 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.025  on  97 df \tabularnewline
Multiple R-sq.  & 0.914 \tabularnewline
Adjusted R-sq.  & 0.914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168325&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]1.928[/C][C]1.729[/C][C]1.115[/C][C]0.267[/C][/ROW]
[C]X[/C][C]0.975[/C][C]0.03[/C][C]32.191[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.025  on  97 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.914[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168325&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)1.9281.7291.1150.267
X0.9750.0332.1910
- - -
Residual Std. Err. 2.025 on 97 df
Multiple R-sq. 0.914
Adjusted R-sq. 0.914






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
rptwt14251.4074251.4071036.2850
Residuals97397.9474.103 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
rptwt & 1 & 4251.407 & 4251.407 & 1036.285 & 0 \tabularnewline
Residuals & 97 & 397.947 & 4.103 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168325&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]rptwt[/C][C]1[/C][C]4251.407[/C][C]4251.407[/C][C]1036.285[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]97[/C][C]397.947[/C][C]4.103[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168325&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168325&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)
rptwt14251.4074251.4071036.2850
Residuals97397.9474.103


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)
}
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()