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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 06:07:45 -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/t13385453240syjianodmlkrzf.htm/, Retrieved Thu, 02 May 2024 10:50:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168569, Retrieved Thu, 02 May 2024 10:50:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75

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  D      [Simple Linear Regression] [Weight loss self ...] [2012-06-01 10:07:45] [1b699be450c74ee6d21e019aa867b4f4] [Current]
- RMP         [T-Tests] [Weight loss self ...] [2012-06-01 10:12:27] [1bd8d3e7b11d3e986b30388f410fa8ef]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
77	77
58	51
53	54
68	70
59	59
76	76
76	77
69	73
71	71
65	64
70	75
166	56
51	52
64	64
52	57
65	66
92	101
62	62
76	75
61	61
119	124
61	61
65	66
66	70
54	59
50	50
63	61
58	60
39	41
101	100
71	71
75	73
79	76
52	52
68	63
64	65
56	54
69	69
88	86
65	67
54	53
80	80
63	59
78	80
85	82
54	55
73	65
49	65
54	56
75	75
82	85
56	57
74	73
102	107
64	65
65	64
66	65
73	74
75	70
57	58
68	69
71	71
71	76
78	75
97	98
60	59
64	63
64	62
52	51
80	76
62	61
66	66
55	54
56	57
50	50
50	65
50	55
63	64
69	70
69	70
61	60
55	56
53	52
60	55
56	56
59	61
62	66
53	53
57	59
57	56
70	68
56	56
84	86
69	71
88	87
56	57
103	101
50	50
52	52
55	65
55	55
63	63
47	47
45	45
62	63
53	51
52	51
57	55
64	64
59	55
84	90
79	79
55	57
67	67
76	77
62	62
83	83
96	94
75	76
65	66
78	77
69	73
68	68
55	55
67	65
52	56
47	65
45	45
68	68
44	44
62	61
87	89
56	53
50	47
83	84
53	53
64	62
62	65
90	91
85	83
66	68
52	53
53	55
54	55
64	66
55	55
55	55
59	55
70	67
88	86
57	58
47	47
47	45
55	65
48	44
54	58
69	68
59	65
58	65
57	56
51	50
54	54
53	52
59	58
56	58
59	59
63	62
66	66
96	95
53	50
76	75
54	65
61	61
82	65
62	64
71	68
60	65
66	67
81	82
68	68
80	78
43	65
82	65
63	59
70	70
56	56
60	55
58	54
76	75
50	49
88	93
89	86
59	59
51	51
62	61
74	71
83	80
81	65
90	91
79	81

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168569&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168569&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'Gwilym Jenkins' @ jenkins.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)18.992.457.7520
X0.7080.03619.5040
- - -
Residual Std. Err. 7.728 on 198 df
Multiple R-sq. 0.658
Adjusted R-sq. 0.656

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 18.99 & 2.45 & 7.752 & 0 \tabularnewline
X & 0.708 & 0.036 & 19.504 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 7.728  on  198 df \tabularnewline
Multiple R-sq.  & 0.658 \tabularnewline
Adjusted R-sq.  & 0.656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168569&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]18.99[/C][C]2.45[/C][C]7.752[/C][C]0[/C][/ROW]
[C]X[/C][C]0.708[/C][C]0.036[/C][C]19.504[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]7.728  on  198 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.658[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168569&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)18.992.457.7520
X0.7080.03619.5040
- - -
Residual Std. Err. 7.728 on 198 df
Multiple R-sq. 0.658
Adjusted R-sq. 0.656






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
dWt122722.58622722.586380.4250
Residuals19811826.43459.729 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
dWt & 1 & 22722.586 & 22722.586 & 380.425 & 0 \tabularnewline
Residuals & 198 & 11826.434 & 59.729 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168569&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]dWt[/C][C]1[/C][C]22722.586[/C][C]22722.586[/C][C]380.425[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]198[/C][C]11826.434[/C][C]59.729[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168569&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168569&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)
dWt122722.58622722.586380.4250
Residuals19811826.43459.729


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 1 ; par3 = 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()