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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, 14 Dec 2014 12:59:02 +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/14/t1418561961s2r84m90vrjs9s7.htm/, Retrieved Tue, 10 Feb 2026 14:24:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267531, Retrieved Tue, 10 Feb 2026 14:24:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact410

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Blocked Bootstrap Plot - Central Tendency] [] [2014-11-02 13:37:17] [cc401d1001c65f55a3dfc6f2420e9570]
- RMPD  [Simple Linear Regression] [] [2014-11-02 15:26:26] [cc401d1001c65f55a3dfc6f2420e9570]
- RM      [Simple Linear Regression] [] [2014-11-05 18:55:35] [e296091fd6311efcd9175c015e8e9c4e]
-  MPD      [Simple Linear Regression] [] [2014-12-09 12:47:37] [36c866d94170840abc594fd3e7d5794f]
-   PD        [Simple Linear Regression] [] [2014-12-14 12:50:11] [36c866d94170840abc594fd3e7d5794f]
-    D          [Simple Linear Regression] [] [2014-12-14 12:55:18] [36c866d94170840abc594fd3e7d5794f]
-    D              [Simple Linear Regression] [] [2014-12-14 12:59:02] [72ee53c6f28232e74174360ca89644de] [Current]
-    D                [Simple Linear Regression] [] [2014-12-14 13:02:17] [36c866d94170840abc594fd3e7d5794f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68	12.9
39	12.2
32	12.8
62	7.4
33	6.7
52	12.6
62	14.8
77	13.3
76	11.1
41	8.2
48	11.4
63	6.4
30	10.6
78	12
19	6.3
31	11.3
66	11.9
35	9.3
42	9.6
45	10
21	6.4
25	13.8
44	10.8
69	13.8
54	11.7
74	10.9
80	16.1
42	13.4
61	9.9
41	11.5
46	8.3
39	11.7
34	9
51	9.7
42	10.8
31	10.3
39	10.4
20	12.7
49	9.3
53	11.8
31	5.9
39	11.4
54	13
49	10.8
34	12.3
46	11.3
55	11.8
42	7.9
50	12.7
13	12.3
37	11.6
25	6.7
30	10.9
28	12.1
45	13.3
35	10.1
28	5.7
41	14.3
6	8
45	13.3
73	9.3
17	12.5
40	7.6
64	15.9
37	9.2
25	9.1
65	11.1
100	13
28	14.5
35	12.2
56	12.3
29	11.4
43	8.8
59	14.6
50	12.6
59	13
27	12.6
61	13.2
28	9.9
51	7.7
35	10.5
29	13.4
48	10.9
25	4.3
44	10.3
64	11.8
32	11.2
20	11.4
28	8.6
34	13.2
31	12.6
26	5.6
58	9.9
23	8.8
21	7.7
21	9
33	7.3
16	11.4
20	13.6
37	7.9
35	10.7
33	10.3
27	8.3
41	9.6
40	14.2
35	8.5
28	13.5
32	4.9
22	6.4
44	9.6
27	11.6
17	11.1
12	4.35
45	12.7
37	18.1
37	17.85
108	16.6
10	12.6
68	17.1
72	19.1
143	16.1
9	13.35
55	18.4
17	14.7
37	10.6
27	12.6
37	16.2
58	13.6
66	18.9
21	14.1
19	14.5
78	16.15
35	14.75
48	14.8
27	12.45
43	12.65
30	17.35
25	8.6
69	18.4
72	16.1
23	11.6
13	17.75
61	15.25
43	17.65
51	16.35
67	17.65
36	13.6
44	14.35
45	14.75
34	18.25
36	9.9
72	16
39	18.25
43	16.85
25	14.6
56	13.85
80	18.95
40	15.6
73	14.85
34	11.75
72	18.45
42	15.9
61	17.1
23	16.1
74	19.9
16	10.95
66	18.45
9	15.1
41	15
57	11.35
48	15.95
51	18.1
53	14.6
29	15.4
29	15.4
55	17.6
54	13.35
43	19.1
51	15.35
20	7.6
79	13.4
39	13.9
61	19.1
55	15.25
30	12.9
55	16.1
22	17.35
37	13.15
2	12.15
38	12.6
27	10.35
56	15.4
25	9.6
39	18.2
33	13.6
43	14.85
57	14.75
43	14.1
23	14.9
44	16.25
54	19.25
28	13.6
36	13.6
39	15.65
16	12.75
23	14.6
40	9.85
24	12.65
78	19.2
57	16.6
37	11.2
27	15.25
61	11.9
27	13.2
69	16.35
34	12.4
44	15.85
34	18.15
39	11.15
51	15.65
34	17.75
31	7.65
13	12.35
12	15.6
51	19.3
24	15.2
19	17.1
30	15.6
81	18.4
42	19.05
22	18.55
85	19.1
27	13.1
25	12.85
22	9.5
19	4.5
14	11.85
45	13.6
45	11.7
28	12.4
51	13.35
41	11.4
31	14.9
74	19.9
19	11.2
51	14.6
73	17.6
24	14.05
61	16.1
23	13.35
14	11.85
54	11.95
51	14.75
62	15.15
36	13.2
59	16.85
24	7.85
26	7.7
54	12.6
39	7.85
16	10.95
36	12.35
31	9.95
31	14.9
42	16.65
39	13.4
25	13.95
31	15.7
38	16.85
31	10.95
17	15.35
22	12.2
55	15.1
62	17.75
51	15.2
30	14.6
49	16.65
16	8.1

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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267531&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]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267531&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
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)14.7814.223.5020.001
X2.0540.3156.5270
- - -
Residual Std. Err. 17.779 on 276 df
Multiple R-sq. 0.134
Adjusted R-sq. 0.131

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 14.781 & 4.22 & 3.502 & 0.001 \tabularnewline
X & 2.054 & 0.315 & 6.527 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 17.779  on  276 df \tabularnewline
Multiple R-sq.  & 0.134 \tabularnewline
Adjusted R-sq.  & 0.131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267531&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]14.781[/C][C]4.22[/C][C]3.502[/C][C]0.001[/C][/ROW]
[C]X[/C][C]2.054[/C][C]0.315[/C][C]6.527[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]17.779  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.134[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267531&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)14.7814.223.5020.001
X2.0540.3156.5270
- - -
Residual Std. Err. 17.779 on 276 df
Multiple R-sq. 0.134
Adjusted R-sq. 0.131






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOTAL 113464.89713464.89742.5980
Residuals27687241.304316.092 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOTAL
 & 1 & 13464.897 & 13464.897 & 42.598 & 0 \tabularnewline
Residuals & 276 & 87241.304 & 316.092 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267531&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]TOTAL
[/C][C]1[/C][C]13464.897[/C][C]13464.897[/C][C]42.598[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]87241.304[/C][C]316.092[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267531&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267531&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)
TOTAL 113464.89713464.89742.5980
Residuals27687241.304316.092


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()