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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 12:50:11 +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/t1418561428fxk4dvl6y85jfzb.htm/, Retrieved Thu, 16 May 2024 17:20:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267526, Retrieved Thu, 16 May 2024 17:20:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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] [72ee53c6f28232e74174360ca89644de] [Current]
-    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] [36c866d94170840abc594fd3e7d5794f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96	12,9
70	12,2
88	12,8
114	7,4
69	6,7
176	12,6
114	14,8
121	13,3
110	11,1
158	8,2
116	11,4
181	6,4
77	10,6
141	12
35	6,3
80	11,3
152	11,9
97	9,3
99	9,6
84	10
68	6,4
101	13,8
107	10,8
88	13,8
112	11,7
171	10,9
137	16,1
77	13,4
66	9,9
93	11,5
105	8,3
131	11,7
102	9
161	9,7
120	10,8
127	10,3
77	10,4
108	12,7
85	9,3
168	11,8
48	5,9
152	11,4
75	13
107	10,8
62	12,3
121	11,3
124	11,8
72	7,9
40	12,7
58	12,3
97	11,6
88	6,7
126	10,9
104	12,1
148	13,3
146	10,1
80	5,7
97	14,3
25	8
99	13,3
118	9,3
58	12,5
63	7,6
139	15,9
50	9,2
60	9,1
152	11,1
142	13
94	14,5
66	12,2
127	12,3
67	11,4
90	8,8
75	14,6
128	12,6
146	13
69	12,6
186	13,2
81	9,9
85	7,7
54	10,5
46	13,4
106	10,9
34	4,3
60	10,3
95	11,8
57	11,2
62	11,4
36	8,6
56	13,2
54	12,6
64	5,6
76	9,9
98	8,8
88	7,7
35	9
102	7,3
61	11,4
80	13,6
49	7,9
78	10,7
90	10,3
45	8,3
55	9,6
96	14,2
43	8,5
52	13,5
60	4,9
54	6,4
51	9,6
51	11,6
38	11,1
41	4,35
146	12,7
182	18,1
192	17,85
263	16,6
35	12,6
439	17,1
214	19,1
341	16,1
58	13,35
292	18,4
85	14,7
200	10,6
158	12,6
199	16,2
297	13,6
227	18,9
108	14,1
86	14,5
302	16,15
148	14,75
178	14,8
120	12,45
207	12,65
157	17,35
128	8,6
296	18,4
323	16,1
79	11,6
70	17,75
146	15,25
246	17,65
196	16,35
199	17,65
127	13,6
153	14,35
299	14,75
228	18,25
190	9,9
180	16
212	18,25
269	16,85
130	14,6
179	13,85
243	18,95
190	15,6
299	14,85
121	11,75
137	18,45
305	15,9
157	17,1
96	16,1
183	19,9
52	10,95
238	18,45
40	15,1
226	15
190	11,35
214	15,95
145	18,1
119	14,6
222	15,4
222	15,4
159	17,6
165	13,35
249	19,1
125	15,35
122	7,6
186	13,4
148	13,9
274	19,1
172	15,25
84	12,9
168	16,1
102	17,35
106	13,15
2	12,15
139	12,6
95	10,35
130	15,4
72	9,6
141	18,2
113	13,6
206	14,85
268	14,75
175	14,1
77	14,9
125	16,25
255	19,25
111	13,6
132	13,6
211	15,65
92	12,75
76	14,6
171	9,85
83	12,65
266	19,2
186	16,6
50	11,2
117	15,25
219	11,9
246	13,2
279	16,35
148	12,4
137	15,85
181	18,15
98	11,15
226	15,65
234	17,75
138	7,65
85	12,35
66	15,6
236	19,3
106	15,2
135	17,1
122	15,6
218	18,4
199	19,05
112	18,55
278	19,1
94	13,1
113	12,85
84	9,5
86	4,5
62	11,85
222	13,6
167	11,7
82	12,4
207	13,35
184	11,4
83	14,9
183	19,9
89	11,2
225	14,6
237	17,6
102	14,05
221	16,1
128	13,35
91	11,85
198	11,95
204	14,75
158	15,15
138	13,2
226	16,85
44	7,85
196	7,7
83	12,6
79	7,85
52	10,95
105	12,35
116	9,95
83	14,9
196	16,65
153	13,4
157	13,95
75	15,7
106	16,85
58	10,95
75	15,35
74	12,2
185	15,1
265	17,75
131	15,2
139	14,6
196	16,65
78	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=267526&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=267526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267526&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)-27.36413.472-2.0310.043
X12.3791.00512.3220
- - -
Residual Std. Err. 56.754 on 276 df
Multiple R-sq. 0.355
Adjusted R-sq. 0.353

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -27.364 & 13.472 & -2.031 & 0.043 \tabularnewline
X & 12.379 & 1.005 & 12.322 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 56.754  on  276 df \tabularnewline
Multiple R-sq.  & 0.355 \tabularnewline
Adjusted R-sq.  & 0.353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267526&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]-27.364[/C][C]13.472[/C][C]-2.031[/C][C]0.043[/C][/ROW]
[C]X[/C][C]12.379[/C][C]1.005[/C][C]12.322[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]56.754  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.355[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267526&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)-27.36413.472-2.0310.043
X12.3791.00512.3220
- - -
Residual Std. Err. 56.754 on 276 df
Multiple R-sq. 0.355
Adjusted R-sq. 0.353






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOT 1489033.944489033.944151.8250
Residuals276889007.933221.043 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOT
 & 1 & 489033.944 & 489033.944 & 151.825 & 0 \tabularnewline
Residuals & 276 & 889007.93 & 3221.043 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267526&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]TOT
[/C][C]1[/C][C]489033.944[/C][C]489033.944[/C][C]151.825[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]889007.93[/C][C]3221.043[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267526&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)
TOT 1489033.944489033.944151.8250
Residuals276889007.933221.043


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()