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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 10:23:10 -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/t1356017108shnkilh2zlxv1ut.htm/, Retrieved Mon, 29 Apr 2024 01:11:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202760, Retrieved Mon, 29 Apr 2024 01:11:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100

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 15:23:10] [09a8c52255f1f9505addc8ea27636e79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41	38	13	12	14	12	53	32
39	32	16	11	18	11	86	51
30	35	19	15	11	14	66	42
31	33	15	6	12	12	67	41
34	37	14	13	16	21	76	46
35	29	13	10	18	12	78	47
39	31	19	12	14	22	53	37
34	36	15	14	14	11	80	49
36	35	14	12	15	10	74	45
37	38	15	6	15	13	76	47
38	31	16	10	17	10	79	49
36	34	16	12	19	8	54	33
38	35	16	12	10	15	67	42
39	38	16	11	16	14	54	33
33	37	17	15	18	10	87	53
32	33	15	12	14	14	58	36
36	32	15	10	14	14	75	45
38	38	20	12	17	11	88	54
39	38	18	11	14	10	64	41
32	32	16	12	16	13	57	36
32	33	16	11	18	7	66	41
31	31	16	12	11	14	68	44
39	38	19	13	14	12	54	33
37	39	16	11	12	14	56	37
39	32	17	9	17	11	86	52
41	32	17	13	9	9	80	47
36	35	16	10	16	11	76	43
33	37	15	14	14	15	69	44
33	33	16	12	15	14	78	45
34	33	14	10	11	13	67	44
31	28	15	12	16	9	80	49
27	32	12	8	13	15	54	33
37	31	14	10	17	10	71	43
34	37	16	12	15	11	84	54
34	30	14	12	14	13	74	42
32	33	7	7	16	8	71	44
29	31	10	6	9	20	63	37
36	33	14	12	15	12	71	43
29	31	16	10	17	10	76	46
35	33	16	10	13	10	69	42
37	32	16	10	15	9	74	45
34	33	14	12	16	14	75	44
38	32	20	15	16	8	54	33
35	33	14	10	12	14	52	31
38	28	14	10	12	11	69	42
37	35	11	12	11	13	68	40
38	39	14	13	15	9	65	43
33	34	15	11	15	11	75	46
36	38	16	11	17	15	74	42
38	32	14	12	13	11	75	45
32	38	16	14	16	10	72	44
32	30	14	10	14	14	67	40
32	33	12	12	11	18	63	37
34	38	16	13	12	14	62	46
32	32	9	5	12	11	63	36
37	32	14	6	15	12	76	47
39	34	16	12	16	13	74	45
29	34	16	12	15	9	67	42
37	36	15	11	12	10	73	43
35	34	16	10	12	15	70	43
30	28	12	7	8	20	53	32
38	34	16	12	13	12	77	45
34	35	16	14	11	12	77	45
31	35	14	11	14	14	52	31
34	31	16	12	15	13	54	33
35	37	17	13	10	11	80	49
36	35	18	14	11	17	66	42
30	27	18	11	12	12	73	41
39	40	12	12	15	13	63	38
35	37	16	12	15	14	69	42
38	36	10	8	14	13	67	44
31	38	14	11	16	15	54	33
34	39	18	14	15	13	81	48
38	41	18	14	15	10	69	40
34	27	16	12	13	11	84	50
39	30	17	9	12	19	80	49
37	37	16	13	17	13	70	43
34	31	16	11	13	17	69	44
28	31	13	12	15	13	77	47
37	27	16	12	13	9	54	33
33	36	16	12	15	11	79	46
37	38	20	12	16	10	30	0
35	37	16	12	15	9	71	45
37	33	15	12	16	12	73	43
32	34	15	11	15	12	72	44
33	31	16	10	14	13	77	47
38	39	14	9	15	13	75	45
33	34	16	12	14	12	69	42
29	32	16	12	13	15	54	33
33	33	15	12	7	22	70	43
31	36	12	9	17	13	73	46
36	32	17	15	13	15	54	33
35	41	16	12	15	13	77	46
32	28	15	12	14	15	82	48
29	30	13	12	13	10	80	47
39	36	16	10	16	11	80	47
37	35	16	13	12	16	69	43
35	31	16	9	14	11	78	46
37	34	16	12	17	11	81	48
32	36	14	10	15	10	76	46
38	36	16	14	17	10	76	45
37	35	16	11	12	16	73	45
36	37	20	15	16	12	85	52
32	28	15	11	11	11	66	42
33	39	16	11	15	16	79	47
40	32	13	12	9	19	68	41
38	35	17	12	16	11	76	47
41	39	16	12	15	16	71	43
36	35	16	11	10	15	54	33
43	42	12	7	10	24	46	30
30	34	16	12	15	14	82	49
31	33	16	14	11	15	74	44
32	41	17	11	13	11	88	55
32	33	13	11	14	15	38	11
37	34	12	10	18	12	76	47
37	32	18	13	16	10	86	53
33	40	14	13	14	14	54	33
34	40	14	8	14	13	70	44
33	35	13	11	14	9	69	42
38	36	16	12	14	15	90	55
33	37	13	11	12	15	54	33
31	27	16	13	14	14	76	46
38	39	13	12	15	11	89	54
37	38	16	14	15	8	76	47
33	31	15	13	15	11	73	45
31	33	16	15	13	11	79	47
39	32	15	10	17	8	90	55
44	39	17	11	17	10	74	44
33	36	15	9	19	11	81	53
35	33	12	11	15	13	72	44
32	33	16	10	13	11	71	42
28	32	10	11	9	20	66	40
40	37	16	8	15	10	77	46
27	30	12	11	15	15	65	40
37	38	14	12	15	12	74	46
32	29	15	12	16	14	82	53
28	22	13	9	11	23	54	33
34	35	15	11	14	14	63	42
30	35	11	10	11	16	54	35
35	34	12	8	15	11	64	40
31	35	8	9	13	12	69	41
32	34	16	8	15	10	54	33
30	34	15	9	16	14	84	51
30	35	17	15	14	12	86	53
31	23	16	11	15	12	77	46
40	31	10	8	16	11	89	55
32	27	18	13	16	12	76	47
36	36	13	12	11	13	60	38
32	31	16	12	12	11	75	46
35	32	13	9	9	19	73	46
38	39	10	7	16	12	85	53
42	37	15	13	13	17	79	47
34	38	16	9	16	9	71	41
35	39	16	6	12	12	72	44
35	34	14	8	9	19	69	43
33	31	10	8	13	18	78	51
36	32	17	15	13	15	54	33
32	37	13	6	14	14	69	43
33	36	15	9	19	11	81	53
34	32	16	11	13	9	84	51
32	35	12	8	12	18	84	50
34	36	13	8	13	16	69	46

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202760&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202760&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202760&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'Gertrude Mary Cox' @ cox.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=202760&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=202760&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202760&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)
seperated1248.581248.58125.0860
Residuals1601585.4499.909 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
seperated & 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=202760&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]seperated[/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=202760&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202760&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)
seperated1248.581248.58125.0860
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()