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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 computationSat, 13 Dec 2014 08:21:21 +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/2014/Dec/13/t14184590191ffqzr3qdf7lolg.htm/, Retrieved Thu, 16 May 2024 11:39:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266905, Retrieved Thu, 16 May 2024 11:39:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

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] [Lineair regressio...] [2014-12-13 08:21:21] [d0ee3c98d5e00815b38c7c808f1992f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149 18
139 31
148 39
158 46
128 31
224 67
159 35
105 52
159 77
167 37
165 32
159 36
119 38
176 69
54 21
91 26
163 54
124 36
137 42
121 23
153 34
148 112
221 35
188 47
149 47
244 37
148 109
92 24
150 20
153 22
94 23
156 32
132 30
161 92
105 43
97 55
151 16
131 49
166 71
157 43
111 29
145 56
162 46
163 19
59 23
187 59
109 30
90 61
105 7
83 38
116 32
42 16
148 19
155 22
125 48
116 23
128 26
138 33
49 9
96 24
164 34
162 48
99 18
202 43
186 33
66 28
183 71
214 26
188 67
104 34
177 80
126 29
76 16
99 59
139 32
162 43
108 38
159 29
74 36
110 32
96 35
116 21
87 29
97 12
127 37
106 37
80 47
74 51
91 32
133 21
74 13
114 14
140 -2
95 20
98 24
121 11
126 23
98 24
95 14
110 52
70 15
102 23
86 19
130 35
96 24
102 39
100 29
94 13
52 8
98 18
118 24
99 19
48 23
50 16
150 33
154 32
109 37
68 14
194 52
158 75
159 72
67 15
147 29
39 13
100 40
111 19
138 24
101 121
131 93
101 36
114 23
165 85
114 41
111 46
75 18
82 35
121 17
32 4
150 28
117 44
71 10
165 38
154 57
126 23
149 36
145 22
120 40
109 31
132 11
172 38
169 24
114 37
156 37
172 22
68 15
89 2
167 43
113 31
115 29
78 45
118 25
87 4
173 31
2 -4
162 66
49 61
122 32
96 31
100 39
82 19
100 31
115 36
141 42
165 21
165 21
110 25
118 32
158 26
146 28
49 32
90 41
121 29
155 33
104 17
147 13
110 32
108 30
113 34
115 59
61 13
60 23
109 10
68 5
111 31
77 19
73 32
151 30
89 25
78 48
110 35
220 67
65 15
141 22
117 18
122 33
63 46
44 24
52 14
131 12
101 38
42 12
152 28
107 41
77 12
154 31
103 33
96 34
175 21
57 20
112 44
143 52
49 7
110 29
131 11
167 26
56 24
137 7
86 60
121 13
149 20
168 52
140 28
88 25
168 39
94 9
51 19
48 13
145 60
66 19
85 34
109 14
63 17
102 45
162 66
86 48
114 29
164 -2
119 51
126 2
132 24
142 40
83 20
94 19
81 16
166 20
110 40
64 27
93 25
104 49
105 39
49 61
88 19
95 67
102 45
99 30
63 8
76 19
109 52
117 22
57 17
120 33
73 34
91 22
108 30
105 25
117 38
119 26

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'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266905&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266905&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266905&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'Herman Ole Andreas Wold' @ wold.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)91.1114.4220.6130
X0.7850.1176.6870
- - -
Residual Std. Err. 36.768 on 275 df
Multiple R-sq. 0.14
Adjusted R-sq. 0.137

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 91.111 & 4.42 & 20.613 & 0 \tabularnewline
X & 0.785 & 0.117 & 6.687 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 36.768  on  275 df \tabularnewline
Multiple R-sq.  & 0.14 \tabularnewline
Adjusted R-sq.  & 0.137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266905&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]91.111[/C][C]4.42[/C][C]20.613[/C][C]0[/C][/ROW]
[C]X[/C][C]0.785[/C][C]0.117[/C][C]6.687[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]36.768  on  275 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.14[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266905&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266905&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)91.1114.4220.6130
X0.7850.1176.6870
- - -
Residual Std. Err. 36.768 on 275 df
Multiple R-sq. 0.14
Adjusted R-sq. 0.137






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
PRH160453.69660453.69644.7190
Residuals275371763.1991351.866 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
PRH & 1 & 60453.696 & 60453.696 & 44.719 & 0 \tabularnewline
Residuals & 275 & 371763.199 & 1351.866 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266905&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]PRH[/C][C]1[/C][C]60453.696[/C][C]60453.696[/C][C]44.719[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]275[/C][C]371763.199[/C][C]1351.866[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266905&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266905&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)
PRH160453.69660453.69644.7190
Residuals275371763.1991351.866


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()