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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 12:39:34 +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/t141856079395wymh078z8481o.htm/, Retrieved Thu, 16 May 2024 17:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267516, Retrieved Thu, 16 May 2024 17:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

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 12:39:34] [72ee53c6f28232e74174360ca89644de] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149	12.9
139	12.2
148	12.8
158	7.4
128	6.7
224	12.6
159	14.8
105	13.3
159	11.1
167	8.2
165	11.4
159	6.4
119	10.6
176	12
54	6.3
91	11.3
163	11.9
124	9.3
137	9.6
121	10
153	6.4
148	13.8
221	10.8
188	13.8
149	11.7
244	10.9
148	16.1
92	13.4
150	9.9
153	11.5
94	8.3
156	11.7
132	9
161	9.7
105	10.8
97	10.3
151	10.4
131	12.7
166	9.3
157	11.8
111	5.9
145	11.4
162	13
163	10.8
59	12.3
187	11.3
109	11.8
90	7.9
105	12.7
83	12.3
116	11.6
42	6.7
148	10.9
155	12.1
125	13.3
116	10.1
128	5.7
138	14.3
49	8
96	13.3
164	9.3
162	12.5
99	7.6
202	15.9
186	9.2
66	9.1
183	11.1
214	13
188	14.5
104	12.2
177	12.3
126	11.4
76	8.8
99	14.6
139	12.6
162	13
108	12.6
159	13.2
74	9.9
110	7.7
96	10.5
116	13.4
87	10.9
97	4.3
127	10.3
106	11.8
80	11.2
74	11.4
91	8.6
133	13.2
74	12.6
114	5.6
140	9.9
95	8.8
98	7.7
121	9
126	7.3
98	11.4
95	13.6
110	7.9
70	10.7
102	10.3
86	8.3
130	9.6
96	14.2
102	8.5
100	13.5
94	4.9
52	6.4
98	9.6
118	11.6
99	11.1
48	4.35
50	12.7
150	18.1
154	17.85
109	16.6
68	12.6
194	17.1
158	19.1
159	16.1
67	13.35
147	18.4
39	14.7
100	10.6
111	12.6
138	16.2
101	13.6
131	18.9
101	14.1
114	14.5
165	16.15
114	14.75
111	14.8
75	12.45
82	12.65
121	17.35
32	8.6
150	18.4
117	16.1
71	11.6
165	17.75
154	15.25
126	17.65
149	16.35
145	17.65
120	13.6
109	14.35
132	14.75
172	18.25
169	9.9
114	16
156	18.25
172	16.85
68	14.6
89	13.85
167	18.95
113	15.6
115	14.85
78	11.75
118	18.45
87	15.9
173	17.1
2	16.1
162	19.9
49	10.95
122	18.45
96	15.1
100	15
82	11.35
100	15.95
115	18.1
141	14.6
165	15.4
165	15.4
110	17.6
118	13.35
158	19.1
146	15.35
49	7.6
90	13.4
121	13.9
155	19.1
104	15.25
147	12.9
110	16.1
108	17.35
113	13.15
115	12.15
61	12.6
60	10.35
109	15.4
68	9.6
111	18.2
77	13.6
73	14.85
151	14.75
89	14.1
78	14.9
110	16.25
220	19.25
65	13.6
141	13.6
117	15.65
122	12.75
63	14.6
44	9.85
52	12.65
131	19.2
101	16.6
42	11.2
152	15.25
107	11.9
77	13.2
154	16.35
103	12.4
96	15.85
175	18.15
57	11.15
112	15.65
143	17.75
49	7.65
110	12.35
131	15.6
167	19.3
56	15.2
137	17.1
86	15.6
121	18.4
149	19.05
168	18.55
140	19.1
88	13.1
168	12.85
94	9.5
51	4.5
48	11.85
145	13.6
66	11.7
85	12.4
109	13.35
63	11.4
102	14.9
162	19.9
86	11.2
114	14.6
164	17.6
119	14.05
126	16.1
132	13.35
142	11.85
83	11.95
94	14.75
81	15.15
166	13.2
110	16.85
64	7.85
93	7.7
104	12.6
105	7.85
49	10.95
88	12.35
95	9.95
102	14.9
99	16.65
63	13.4
76	13.95
109	15.7
117	16.85
57	10.95
120	15.35
73	12.2
91	15.1
108	17.75
105	15.2
117	14.6
119	16.65
31	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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267516&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267516&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






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)70.3169.0287.7880
X3.5520.6735.2760
- - -
Residual Std. Err. 38.035 on 276 df
Multiple R-sq. 0.092
Adjusted R-sq. 0.088

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 70.316 & 9.028 & 7.788 & 0 \tabularnewline
X & 3.552 & 0.673 & 5.276 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 38.035  on  276 df \tabularnewline
Multiple R-sq.  & 0.092 \tabularnewline
Adjusted R-sq.  & 0.088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267516&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]70.316[/C][C]9.028[/C][C]7.788[/C][C]0[/C][/ROW]
[C]X[/C][C]3.552[/C][C]0.673[/C][C]5.276[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]38.035  on  276 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.092[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267516&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)70.3169.0287.7880
X3.5520.6735.2760
- - -
Residual Std. Err. 38.035 on 276 df
Multiple R-sq. 0.092
Adjusted R-sq. 0.088






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
TOTAL140265.75140265.75127.8340
Residuals276399271.1261446.635 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
TOTAL & 1 & 40265.751 & 40265.751 & 27.834 & 0 \tabularnewline
Residuals & 276 & 399271.126 & 1446.635 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267516&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]40265.751[/C][C]40265.751[/C][C]27.834[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]276[/C][C]399271.126[/C][C]1446.635[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267516&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)
TOTAL140265.75140265.75127.8340
Residuals276399271.1261446.635


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()