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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 13:02:17 +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/t1418562142oal4uv70s8vmqpo.htm/, Retrieved Thu, 16 May 2024 12:10:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267533, Retrieved Thu, 16 May 2024 12:10:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [36c866d94170840abc594fd3e7d5794f]
-    D                [Simple Linear Regression] [] [2014-12-14 13:02:17] [72ee53c6f28232e74174360ca89644de] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86	12.9
70	12.2
71	12.8
108	7.4
64	6.7
119	12.6
97	14.8
129	13.3
153	11.1
78	8.2
80	11.4
99	6.4
68	10.6
147	12
40	6.3
57	11.3
120	11.9
71	9.3
84	9.6
68	10
55	6.4
137	13.8
79	10.8
116	13.8
101	11.7
111	10.9
189	16.1
66	13.4
81	9.9
63	11.5
69	8.3
71	11.7
64	9
143	9.7
85	10.8
86	10.3
55	10.4
69	12.7
120	9.3
96	11.8
60	5.9
95	11.4
100	13
68	10.8
57	12.3
105	11.3
85	11.8
103	7.9
57	12.7
51	12.3
69	11.6
41	6.7
49	10.9
50	12.1
93	13.3
58	10.1
54	5.7
74	14.3
15	8
69	13.3
107	9.3
65	12.5
58	7.6
107	15.9
70	9.2
53	9.1
136	11.1
126	13
95	14.5
69	12.2
136	12.3
58	11.4
59	8.8
118	14.6
82	12.6
102	13
65	12.6
90	13.2
64	9.9
83	7.7
70	10.5
50	13.4
77	10.9
37	4.3
81	10.3
101	11.8
79	11.2
71	11.4
60	8.6
55	13.2
44	12.6
40	5.6
56	9.9
43	8.8
45	7.7
32	9
56	7.3
40	11.4
34	13.6
89	7.9
50	10.7
56	10.3
46	8.3
76	9.6
64	14.2
74	8.5
57	13.5
45	4.9
30	6.4
62	9.6
51	11.6
36	11.1
34	4.35
61	12.7
70	18.1
69	17.85
145	16.6
23	12.6
120	17.1
147	19.1
215	16.1
24	13.35
84	18.4
30	14.7
77	10.6
46	12.6
61	16.2
178	13.6
160	18.9
57	14.1
42	14.5
163	16.15
75	14.75
94	14.8
45	12.45
78	12.65
47	17.35
29	8.6
97	18.4
116	16.1
32	11.6
50	17.75
118	15.25
66	17.65
86	16.35
89	17.65
76	13.6
75	14.35
57	14.75
72	18.25
60	9.9
109	16
76	18.25
65	16.85
40	14.6
58	13.85
123	18.95
71	15.6
102	14.85
80	11.75
97	18.45
46	15.9
93	17.1
19	16.1
140	19.9
78	10.95
98	18.45
40	15.1
80	15
76	11.35
79	15.95
87	18.1
95	14.6
49	15.4
49	15.4
80	17.6
86	13.35
69	19.1
79	15.35
52	7.6
120	13.4
69	13.9
94	19.1
72	15.25
43	12.9
87	16.1
52	17.35
71	13.15
61	12.15
51	12.6
50	10.35
67	15.4
30	9.6
70	18.2
52	13.6
75	14.85
87	14.75
69	14.1
72	14.9
79	16.25
121	19.25
43	13.6
58	13.6
57	15.65
50	12.75
69	14.6
64	9.85
38	12.65
90	19.2
96	16.6
49	11.2
56	15.25
102	11.9
40	13.2
100	16.35
67	12.4
78	15.85
55	18.15
59	11.15
96	15.65
86	17.75
38	7.65
43	12.35
23	15.6
77	19.3
48	15.2
26	17.1
91	15.6
94	18.4
62	19.05
74	18.55
114	19.1
52	13.1
64	12.85
31	9.5
38	4.5
27	11.85
105	13.6
64	11.7
62	12.4
65	13.35
58	11.4
76	14.9
140	19.9
68	11.2
80	14.6
71	17.6
76	14.05
63	16.1
46	13.35
53	11.85
74	11.95
70	14.75
78	15.15
56	13.2
100	16.85
51	7.85
52	7.7
102	12.6
78	7.85
78	10.95
55	12.35
98	9.95
76	14.9
73	16.65
47	13.4
45	13.95
83	15.7
60	16.85
48	10.95
50	15.35
56	12.2
77	15.1
91	17.75
76	15.2
68	14.6
74	16.65
29	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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.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=267533&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]'Sir Ronald Aylmer Fisher' @ fisher.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=267533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267533&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'Sir Ronald Aylmer Fisher' @ fisher.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)37.4546.8395.4760
X2.8160.515.5220
- - -
Residual Std. Err. 28.811 on 276 df
Multiple R-sq. 0.1
Adjusted R-sq. 0.096

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 37.454 & 6.839 & 5.476 & 0 \tabularnewline
X & 2.816 & 0.51 & 5.522 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 28.811  on  276 df \tabularnewline
Multiple R-sq.  & 0.1 \tabularnewline
Adjusted R-sq.  & 0.096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267533&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]37.454[/C][C]6.839[/C][C]5.476[/C][C]0[/C][/ROW]
[C]X[/C][C]2.816[/C][C]0.51[/C][C]5.522[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]28.811  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.1[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267533&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)37.4546.8395.4760
X2.8160.515.5220
- - -
Residual Std. Err. 28.811 on 276 df
Multiple R-sq. 0.1
Adjusted R-sq. 0.096






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOTAL 125315.20825315.20830.4970
Residuals276229101.788830.079 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOTAL
 & 1 & 25315.208 & 25315.208 & 30.497 & 0 \tabularnewline
Residuals & 276 & 229101.788 & 830.079 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267533&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]25315.208[/C][C]25315.208[/C][C]30.497[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]229101.788[/C][C]830.079[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267533&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 125315.20825315.20830.4970
Residuals276229101.788830.079


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()