FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationSun, 16 Dec 2012 15:59:40 -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/16/t13556916054qm0jo8e42man7e.htm/, Retrieved Wed, 24 Apr 2024 23:50:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200591, Retrieved Wed, 24 Apr 2024 23:50:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85

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] [] [2012-12-16 20:59:40] [a5d65c007476aeb95d503c7a121a195d] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
210907	56
120982	56
176508	54
179321	89
123185	40
52746	25
385534	92
33170	18
101645	63
149061	44
165446	33
237213	84
173326	88
133131	55
258873	60
180083	66
324799	154
230964	53
236785	119
135473	41
202925	61
215147	58
344297	75
153935	33
132943	40
174724	92
174415	100
225548	112
223632	73
124817	40
221698	45
210767	60
170266	62
260561	75
84853	31
294424	77
101011	34
215641	46
325107	99
7176	17
167542	66
106408	30
96560	76
265769	146
269651	67
149112	56
175824	107
152871	58
111665	34
116408	61
362301	119
78800	42
183167	66
277965	89
150629	44
168809	66
24188	24
329267	259
65029	17
101097	64
218946	41
244052	68
341570	168
103597	43
233328	132
256462	105
206161	71
311473	112
235800	94
177939	82
207176	70
196553	57
174184	53
143246	103
187559	121
187681	62
119016	52
182192	52
73566	32
194979	62
167488	45
143756	46
275541	63
243199	75
182999	88
135649	46
152299	53
120221	37
346485	90
145790	63
193339	78
80953	25
122774	45
130585	46
112611	41
286468	144
241066	82
148446	91
204713	71
182079	63
140344	53
220516	62
243060	63
162765	32
182613	39
232138	62
265318	117
85574	34
310839	92
225060	93
232317	54
144966	144
43287	14
155754	61
164709	109
201940	38
235454	73
220801	75
99466	50
92661	61
133328	55
61361	77
125930	75
100750	72
224549	50
82316	32
102010	53
101523	42
243511	71
22938	10
41566	35
152474	65
61857	25
99923	66
132487	41
317394	86
21054	16
209641	42
22648	19
31414	19
46698	45
131698	65
91735	35
244749	95
184510	49
79863	37
128423	64
97839	38
38214	34
151101	32
272458	65
172494	52
108043	62
328107	65
250579	83
351067	95
158015	29
98866	18
85439	33
229242	247
351619	139
84207	29
120445	118
324598	110
131069	67
204271	42
165543	65
141722	94
116048	64
250047	81
299775	95
195838	67
173260	63
254488	83
104389	45
136084	30
199476	70
92499	32
224330	83
135781	31
74408	67
81240	66
14688	10
181633	70
271856	103
7199	5
46660	20
17547	5
133368	36
95227	34
152601	48
98146	40
79619	43
59194	31
139942	42
118612	46
72880	33
65475	18
99643	55
71965	35
77272	59
49289	19
135131	66
108446	60
89746	36
44296	25
77648	47
181528	54
134019	53
124064	40
92630	40
121848	39
52915	14
81872	45
58981	36
53515	28
60812	44
56375	30
65490	22
80949	17
76302	31
104011	55
98104	54
67989	21
30989	14
135458	81
73504	35
63123	43
61254	46
74914	30
31774	23
81437	38
87186	54
50090	20
65745	53
56653	45
158399	39
46455	20
73624	24
38395	31
91899	35
139526	151
52164	52
51567	30
70551	31
84856	29
102538	57
86678	40
85709	44
34662	25
150580	77
99611	35
19349	11
99373	63
86230	44
30837	19
31706	13
89806	42
62088	38
40151	29
27634	20
76990	27
37460	20
54157	19
49862	37
84337	26
64175	42
59382	49
119308	30
76702	49
103425	67
70344	28
43410	19
104838	49
62215	27
69304	30
53117	22
19764	12
86680	31
84105	20
77945	20
89113	39
91005	29
40248	16
64187	27
50857	21
56613	19
62792	35
72535	14

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200591&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200591&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)14.2042.7245.2140
X0017.3740
- - -
Residual Std. Err. 23.687 on 287 df
Multiple R-sq. 0.513
Adjusted R-sq. 0.511

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 14.204 & 2.724 & 5.214 & 0 \tabularnewline
X & 0 & 0 & 17.374 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 23.687  on  287 df \tabularnewline
Multiple R-sq.  & 0.513 \tabularnewline
Adjusted R-sq.  & 0.511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200591&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]14.204[/C][C]2.724[/C][C]5.214[/C][C]0[/C][/ROW]
[C]X[/C][C]0[/C][C]0[/C][C]17.374[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]23.687  on  287 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.513[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200591&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)14.2042.7245.2140
X0017.3740
- - -
Residual Std. Err. 23.687 on 287 df
Multiple R-sq. 0.513
Adjusted R-sq. 0.511






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
A1169356.408169356.408301.8440
Residuals287161027.855561.073 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
A & 1 & 169356.408 & 169356.408 & 301.844 & 0 \tabularnewline
Residuals & 287 & 161027.855 & 561.073 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200591&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]A[/C][C]1[/C][C]169356.408[/C][C]169356.408[/C][C]301.844[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]287[/C][C]161027.855[/C][C]561.073[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200591&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)
A1169356.408169356.408301.8440
Residuals287161027.855561.073


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()