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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software ModuleIan.Hollidayrwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationWed, 26 Jan 2011 22:34:44 +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/2011/Jan/26/t12960823438uovkukzyf5bvis.htm/, Retrieved Fri, 01 Nov 2024 01:00:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117812, Retrieved Fri, 01 Nov 2024 01:00:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact257

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] [CARE Regression -...] [2011-01-26 16:56:48] [74be16979710d4c4e7c6647856088456]
-   P   [Simple Linear Regression] [CARE regression -...] [2011-01-26 17:08:26] [74be16979710d4c4e7c6647856088456]
-    D      [Simple Linear Regression] [CARE regression] [2011-01-26 22:34:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R           [Simple Linear Regression] [Test Regression ] [2011-01-26 23:29:36] [74be16979710d4c4e7c6647856088456]
-               [Simple Linear Regression] [Test Regression 2] [2011-01-26 23:39:02] [74be16979710d4c4e7c6647856088456]
-   P           [Simple Linear Regression] [Test Regression 3] [2011-01-26 23:42:26] [74be16979710d4c4e7c6647856088456]
- R P           [Simple Linear Regression] [Test Regression 4] [2011-01-26 23:44:18] [74be16979710d4c4e7c6647856088456]
- RM D            [Kernel Density Estimation] [] [2011-01-27 18:49:44] [b98453cac15ba1066b407e146608df68]
-               [Simple Linear Regression] [test] [2011-01-27 00:08:19] [74be16979710d4c4e7c6647856088456]
- R P           [Simple Linear Regression] [test with intercept] [2011-01-27 00:10:05] [74be16979710d4c4e7c6647856088456]
-               [Simple Linear Regression] [test 1] [2011-01-27 17:11:55] [b98453cac15ba1066b407e146608df68]
- R P           [Simple Linear Regression] [test 2] [2011-01-27 17:12:50] [b98453cac15ba1066b407e146608df68]
- R P           [Simple Linear Regression] [test 3] [2011-01-27 17:15:33] [b98453cac15ba1066b407e146608df68]
- R P           [Simple Linear Regression] [test 4] [2011-01-27 17:16:19] [b98453cac15ba1066b407e146608df68]
-  MP           [Simple Linear Regression] [test 5] [2011-01-27 17:17:23] [b98453cac15ba1066b407e146608df68]
-  MP           [Simple Linear Regression] [test 6] [2011-01-27 17:18:20] [b98453cac15ba1066b407e146608df68]
- R P         [Simple Linear Regression] [CARE regression] [2011-01-26 23:33:10] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
111	45	27	52
102	50	18	55
108	49	19	80
109	55	20	45
118	39	29	60
79	68	46	34
88	69	27	45
102	56	23	68
105	58	29	26
92	48	38	70
131	34	20	85
104	50	37	54
83	76	32	55
84	49	26	40
85	51	40	55
110	53	30	50
121	36	26	71
120	62	23	55
100	46	27	70
94	50	38	55
89	47	25	60
93	50	33	65
128	44	45	66
84	50	34	55
127	29	20	90
106	49	24	55
129	26	26	60
82	79	26	35
106	53	39	55
109	53	27	26
91	72	18	14
111	35	34	45
105	42	25	35
118	37	26	65
103	46	28	35
101	48	21	60
101	46	39	60
95	49	25	60
108	65	29	65
95	52	37	45
98	75	34	20
82	58	30	50
100	43	28	60
100	60	25	48
107	43	27	40
95	51	33	55
97	70	30	54
93	69	26	40
81	65	18	40
89	63	21	34
111	44	39	60
95	61	36	30
106	40	32	75
83	62	23	24
81	59	27	30
115	47	45	80
112	50	24	60
92	50	29	46
85	65	21	35
95	54	28	60
115	44	37	75
91	66	22	54
107	34	31	78
102	74	32	20
86	57	20	45
96	60	33	60
114	36	32	70
105	50	18	35
82	60	44	20
120	45	24	60
88	55	21	20
90	44	29	50
85	57	30	50
106	33	37	75
109	30	33	70
75	64	25	20
91	49	19	45
96	76	16	20
108	40	31	50
86	48	29	55
98	65	37	15
99	50	41	26
95	70	28	25
88	78	19	30
111	44	28	60
103	48	33	40
107	52	32	40
118	40	28	50

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117812&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117812&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Linear Regression Model
Y ~ X - 1
coefficients:
EstimateStd. Errort valuePr(>|t|)
X1.7830.06328.2940
- - -
Residual Std. Err. 31.793 on 87 df
Multiple R-sq. 0.902
Adjusted R-sq. 0.901

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X - 1 \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
X & 1.783 & 0.063 & 28.294 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 31.793  on  87 df \tabularnewline
Multiple R-sq.  & 0.902 \tabularnewline
Adjusted R-sq.  & 0.901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117812&T=1

[TABLE]
[ROW][C]Linear Regression Model[/C][/ROW]
[ROW][C]Y ~ X - 1[/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]X[/C][C]1.783[/C][C]0.063[/C][C]28.294[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]31.793  on  87 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.902[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117812&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 - 1
coefficients:
EstimateStd. Errort valuePr(>|t|)
X1.7830.06328.2940
- - -
Residual Std. Err. 31.793 on 87 df
Multiple R-sq. 0.902
Adjusted R-sq. 0.901






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Add1809207.241809207.241800.560
Residuals8787939.7591010.802 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Add & 1 & 809207.241 & 809207.241 & 800.56 & 0 \tabularnewline
Residuals & 87 & 87939.759 & 1010.802 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117812&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]Add[/C][C]1[/C][C]809207.241[/C][C]809207.241[/C][C]800.56[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]87[/C][C]87939.759[/C][C]1010.802[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117812&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117812&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)
Add1809207.241809207.241800.560
Residuals8787939.7591010.802


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = FALSE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = FALSE ;
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)
}# end cols
a<-table.row.end(a)
} #end rows
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()