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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 computationFri, 01 Jun 2012 06:03:58 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jun/01/t13385450539mdm4a0yh6m5iid.htm/, Retrieved Thu, 02 May 2024 07:02:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168543, Retrieved Thu, 02 May 2024 07:02:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

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] [Triglyceridge Reg...] [2011-07-07 15:11:49] [74be16979710d4c4e7c6647856088456]
- R     [Simple Linear Regression] [Triglyceride] [2012-05-04 19:33:41] [98fd0e87c3eb04e0cc2efde01dbafab6]
- R PD      [Simple Linear Regression] [] [2012-06-01 10:03:58] [9728ea23609e5fa30c768da48682d7e6] [Current]
-    D        [Simple Linear Regression] [] [2012-06-01 10:12:13] [9fd651d676601517bf05777b8cc41305]
-    D          [Simple Linear Regression] [] [2012-06-01 10:13:59] [9fd651d676601517bf05777b8cc41305]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
50	47
50	55
52	51
47	45
39	41
52	52
45	45
59	59
52	51
44	44
55	55
59	59
53	50
50	49
53	54
51	52
54	55
75	75
63	64
56	53
59	55
53	52
51	51
58	51
63	59
56	57
52	57
58	60
54	53
60	59
57	59
57	56
56	57
47	47
45	45
53	51
53	53
52	53
47	47
48	44
51	50
54	54
63	59
56	56
52	52
64	62
50	50
56	56
62	61
57	56
56	57
64	63
55	54
61	60
60	55
55	55
59	55
62	62
55	55
62	61
53	55
57	55
64	64
65	66
62	62
50	50
71	71
56	54
53	53
50	50
64	64
76	77
55	55
57	58
57	56
66	66
59	59
58	54
54	59
63	61
64	62
63	62
60	55
78	75
68	68
61	61
68	63
56	56
70	67
61	61
62	61
55	57
64	66
59	58
54	56
62	63
53	52
68	68
54	55
56	58
76	76
76	77
68	69
75	76
69	73
54	58
76	75
66	67
62	64
75	70
65	64
66	70
74	73
57	58
71	71
55	56
70	68
61	61
69	69
79	79
65	64
65	66
79	76
68	68
70	70
89	86
70	75
69	68
68	70
71	71
75	73
64	65
88	86
85	82
71	76
80	76
66	66
62	66
63	63
78	77
83	84
66	68
81	82
80	78
74	71
119	124
80	80
65	66
71	68
90	91
79	81
67	67
77	77
69	73
101	100
78	80
73	74
69	70
69	71
76	75
83	80
83	83
103	101
82	85
69	70
59	61
84	86
84	90
96	94
88	86
92	101
102	107
97	98
88	87
87	89
90	91
65	67
85	83
96	95
88	93
76	75

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'AstonUniversity' @ aston.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 & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168543&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168543&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'AstonUniversity' @ aston.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-1.0830.857-1.2630.208
X1.0160.01379.4720
- - -
Residual Std. Err. 2.303 on 179 df
Multiple R-sq. 0.972
Adjusted R-sq. 0.972

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -1.083 & 0.857 & -1.263 & 0.208 \tabularnewline
X & 1.016 & 0.013 & 79.472 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.303  on  179 df \tabularnewline
Multiple R-sq.  & 0.972 \tabularnewline
Adjusted R-sq.  & 0.972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168543&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]-1.083[/C][C]0.857[/C][C]-1.263[/C][C]0.208[/C][/ROW]
[C]X[/C][C]1.016[/C][C]0.013[/C][C]79.472[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.303  on  179 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.972[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168543&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)-1.0830.857-1.2630.208
X1.0160.01379.4720
- - -
Residual Std. Err. 2.303 on 179 df
Multiple R-sq. 0.972
Adjusted R-sq. 0.972






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
W133499.9633499.966315.7230
Residuals179949.4555.304 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
W & 1 & 33499.96 & 33499.96 & 6315.723 & 0 \tabularnewline
Residuals & 179 & 949.455 & 5.304 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168543&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]W[/C][C]1[/C][C]33499.96[/C][C]33499.96[/C][C]6315.723[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]179[/C][C]949.455[/C][C]5.304[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168543&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)
W133499.9633499.966315.7230
Residuals179949.4555.304


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = greater ; par2 = 1 ; par3 = 2 ; par4 = T-Test ; par5 = paired ; par6 = 0.0 ; par7 = 0.95 ; par8 = TRUE ;
Parameters (R input):
par1 = 2 ; par2 = 1 ; 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()