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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 computationThu, 20 Dec 2012 10:59:01 -0500
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/Dec/20/t1356019172rburjrr7fz8zp69.htm/, Retrieved Thu, 25 Apr 2024 12:58:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202818, Retrieved Thu, 25 Apr 2024 12:58:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

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] [simple regression] [2012-12-20 15:59:01] [09a8c52255f1f9505addc8ea27636e79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41	38	13	12	14	12	53
39	32	16	11	18	11	86
30	35	19	15	11	14	66
31	33	15	6	12	12	67
34	37	14	13	16	21	76
35	29	13	10	18	12	78
39	31	19	12	14	22	53
34	36	15	14	14	11	80
36	35	14	12	15	10	74
37	38	15	6	15	13	76
38	31	16	10	17	10	79
36	34	16	12	19	8	54
38	35	16	12	10	15	67
39	38	16	11	16	14	54
33	37	17	15	18	10	87
32	33	15	12	14	14	58
36	32	15	10	14	14	75
38	38	20	12	17	11	88
39	38	18	11	14	10	64
32	32	16	12	16	13	57
32	33	16	11	18	7	66
31	31	16	12	11	14	68
39	38	19	13	14	12	54
37	39	16	11	12	14	56
39	32	17	9	17	11	86
41	32	17	13	9	9	80
36	35	16	10	16	11	76
33	37	15	14	14	15	69
33	33	16	12	15	14	78
34	33	14	10	11	13	67
31	28	15	12	16	9	80
27	32	12	8	13	15	54
37	31	14	10	17	10	71
34	37	16	12	15	11	84
34	30	14	12	14	13	74
32	33	7	7	16	8	71
29	31	10	6	9	20	63
36	33	14	12	15	12	71
29	31	16	10	17	10	76
35	33	16	10	13	10	69
37	32	16	10	15	9	74
34	33	14	12	16	14	75
38	32	20	15	16	8	54
35	33	14	10	12	14	52
38	28	14	10	12	11	69
37	35	11	12	11	13	68
38	39	14	13	15	9	65
33	34	15	11	15	11	75
36	38	16	11	17	15	74
38	32	14	12	13	11	75
32	38	16	14	16	10	72
32	30	14	10	14	14	67
32	33	12	12	11	18	63
34	38	16	13	12	14	62
32	32	9	5	12	11	63
37	32	14	6	15	12	76
39	34	16	12	16	13	74
29	34	16	12	15	9	67
37	36	15	11	12	10	73
35	34	16	10	12	15	70
30	28	12	7	8	20	53
38	34	16	12	13	12	77
34	35	16	14	11	12	77
31	35	14	11	14	14	52
34	31	16	12	15	13	54
35	37	17	13	10	11	80
36	35	18	14	11	17	66
30	27	18	11	12	12	73
39	40	12	12	15	13	63
35	37	16	12	15	14	69
38	36	10	8	14	13	67
31	38	14	11	16	15	54
34	39	18	14	15	13	81
38	41	18	14	15	10	69
34	27	16	12	13	11	84
39	30	17	9	12	19	80
37	37	16	13	17	13	70
34	31	16	11	13	17	69
28	31	13	12	15	13	77
37	27	16	12	13	9	54
33	36	16	12	15	11	79
37	38	20	12	16	10	30
35	37	16	12	15	9	71
37	33	15	12	16	12	73
32	34	15	11	15	12	72
33	31	16	10	14	13	77
38	39	14	9	15	13	75
33	34	16	12	14	12	69
29	32	16	12	13	15	54
33	33	15	12	7	22	70
31	36	12	9	17	13	73
36	32	17	15	13	15	54
35	41	16	12	15	13	77
32	28	15	12	14	15	82
29	30	13	12	13	10	80
39	36	16	10	16	11	80
37	35	16	13	12	16	69
35	31	16	9	14	11	78
37	34	16	12	17	11	81
32	36	14	10	15	10	76
38	36	16	14	17	10	76
37	35	16	11	12	16	73
36	37	20	15	16	12	85
32	28	15	11	11	11	66
33	39	16	11	15	16	79
40	32	13	12	9	19	68
38	35	17	12	16	11	76
41	39	16	12	15	16	71
36	35	16	11	10	15	54
43	42	12	7	10	24	46
30	34	16	12	15	14	82
31	33	16	14	11	15	74
32	41	17	11	13	11	88
32	33	13	11	14	15	38
37	34	12	10	18	12	76
37	32	18	13	16	10	86
33	40	14	13	14	14	54
34	40	14	8	14	13	70
33	35	13	11	14	9	69
38	36	16	12	14	15	90
33	37	13	11	12	15	54
31	27	16	13	14	14	76
38	39	13	12	15	11	89
37	38	16	14	15	8	76
33	31	15	13	15	11	73
31	33	16	15	13	11	79
39	32	15	10	17	8	90
44	39	17	11	17	10	74
33	36	15	9	19	11	81
35	33	12	11	15	13	72
32	33	16	10	13	11	71
28	32	10	11	9	20	66
40	37	16	8	15	10	77
27	30	12	11	15	15	65
37	38	14	12	15	12	74
32	29	15	12	16	14	82
28	22	13	9	11	23	54
34	35	15	11	14	14	63
30	35	11	10	11	16	54
35	34	12	8	15	11	64
31	35	8	9	13	12	69
32	34	16	8	15	10	54
30	34	15	9	16	14	84
30	35	17	15	14	12	86
31	23	16	11	15	12	77
40	31	10	8	16	11	89
32	27	18	13	16	12	76
36	36	13	12	11	13	60
32	31	16	12	12	11	75
35	32	13	9	9	19	73
38	39	10	7	16	12	85
42	37	15	13	13	17	79
34	38	16	9	16	9	71
35	39	16	6	12	12	72
35	34	14	8	9	19	69
33	31	10	8	13	18	78
36	32	17	15	13	15	54
32	37	13	6	14	14	69
33	36	15	9	19	11	81
34	32	16	11	13	9	84
32	35	12	8	12	18	84
34	36	13	8	13	16	69

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202818&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202818&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)22.6982.3949.4820
X0.350.075.0090
- - -
Residual Std. Err. 3.148 on 160 df
Multiple R-sq. 0.136
Adjusted R-sq. 0.13

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 22.698 & 2.394 & 9.482 & 0 \tabularnewline
X & 0.35 & 0.07 & 5.009 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 3.148  on  160 df \tabularnewline
Multiple R-sq.  & 0.136 \tabularnewline
Adjusted R-sq.  & 0.13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202818&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]22.698[/C][C]2.394[/C][C]9.482[/C][C]0[/C][/ROW]
[C]X[/C][C]0.35[/C][C]0.07[/C][C]5.009[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]3.148  on  160 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.136[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202818&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)22.6982.3949.4820
X0.350.075.0090
- - -
Residual Std. Err. 3.148 on 160 df
Multiple R-sq. 0.136
Adjusted R-sq. 0.13






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
separate1248.581248.58125.0860
Residuals1601585.4499.909 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
separate & 1 & 248.581 & 248.581 & 25.086 & 0 \tabularnewline
Residuals & 160 & 1585.449 & 9.909 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202818&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]separate[/C][C]1[/C][C]248.581[/C][C]248.581[/C][C]25.086[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]160[/C][C]1585.449[/C][C]9.909[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202818&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)
separate1248.581248.58125.0860
Residuals1601585.4499.909


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()