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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software ModuleIan.Hollidayrwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationWed, 28 Apr 2010 07:33:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Apr/28/t1272440394xivdpwjvfmulga6.htm/, Retrieved Tue, 30 Apr 2024 19:01:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74949, Retrieved Tue, 30 Apr 2024 19:01:25 +0000
QR Codes:

Original text written by user:Data from the STARS database http://stars.ac.uk/index.php
IsPrivate?No (this computation is public)
User-defined keywordsTriglyceride, weight loss, linear regression
Estimated Impact296

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] [PY2224 Mock Exam ...] [2010-04-28 07:33:16] [a9208f4f8d3b118336aae915785f2bd9] [Current]
- RMPD    [Correlation] [PY2224 Mock Exam ...] [2010-04-28 07:52:28] [98fd0e87c3eb04e0cc2efde01dbafab6]
-           [Correlation] [PY2224 Mock Exam ...] [2010-04-28 08:03:45] [98fd0e87c3eb04e0cc2efde01dbafab6]
-  M D        [Correlation] [PY2224 May Mock E...] [2010-04-28 12:25:43] [98fd0e87c3eb04e0cc2efde01dbafab6]
-    D          [Correlation] [PY2224 May Mock E...] [2010-04-30 11:35:53] [98fd0e87c3eb04e0cc2efde01dbafab6]
-    D            [Correlation] [] [2010-05-04 13:10:21] [82439cd473f0ddf8a88eb1802dda9b6c]
-    D            [Correlation] [] [2010-05-04 13:07:45] [e8bb49267f0b4e611f4778412d0811f2]
-    D            [Correlation] [Mockexam1] [2010-05-04 13:09:19] [226e457c23f16abdaf22fe48e6e411fd]
-    D            [Correlation] [Correlation of tr...] [2010-05-04 13:12:24] [f0a7b9ce333a507984a56d87311bd9a6]
-    D            [Correlation] [Mock] [2010-05-04 13:15:09] [d85e8cd4dd2ccdf2c3dfa3761837f774]
-    D            [Correlation] [Correlation of Tr...] [2010-05-04 13:14:23] [7756e15f439c0db38d660c862abbb747]
-    D            [Correlation] [Correlation graph...] [2010-05-04 13:15:47] [991f3c16ff1ec6689e9f3866d072593e]
-    D            [Correlation] [correlation] [2010-05-04 13:15:13] [c7d0e78e2fa8da0e0b2bee0011c20ac0]
-    D            [Correlation] [mockexam] [2010-05-04 13:16:50] [66f61a2d5ef80b1eafe31e5651ad0889]
-    D            [Correlation] [triglyceride vs w...] [2010-05-04 13:15:36] [a58114c03403c4a3c11c78968b4ee919]
-    D            [Correlation] [triglyceride leve...] [2010-05-04 13:17:15] [2185b0545466c0a8649e1b1b76e104e0]
-    D            [Correlation] [question 2 1] [2010-05-04 13:14:55] [256a42577f5eb7e9c8a1b74c73a90fa8]
-    D            [Correlation] [] [2010-05-04 13:15:11] [5cae40017fc37cfe76436682b5003098]
-                 [Correlation] [mock correlation] [2010-05-04 13:18:20] [153000c0b3bd367036e4d581452d08df]
-                 [Correlation] [mock correlation] [2010-05-04 13:18:20] [153000c0b3bd367036e4d581452d08df]
-    D            [Correlation] [] [2010-05-04 13:18:55] [609c1e5ad6fe9b179b6d83d13356f854]
-    D            [Correlation] [Stats mock] [2010-05-04 13:20:06] [012a64ac316c94a67eaef3285dac2cf7]
-    D            [Correlation] [mock exam comp1] [2010-05-04 13:17:06] [0dff2a868db4b5bcbf64703b84410784]
-    D            [Correlation] [mock exam 1] [2010-05-04 13:20:20] [74be16979710d4c4e7c6647856088456]
-    D            [Correlation] [] [2010-05-04 13:14:09] [bc03f19b1cbb14de25d671293ac6c773]
-    D            [Correlation] [Mock ii] [2010-05-04 13:21:20] [856c65906cd78e3f7881668c6dfea87f]
-    D            [Correlation] [ii] [2010-05-04 13:13:13] [885328d98a95a442af53d0763bccf325]
-    D            [Correlation] [Basline correlation] [2010-05-04 13:21:45] [74be16979710d4c4e7c6647856088456]
-    D            [Correlation] [Graph 1] [2010-05-04 13:23:28] [c519646407a489a26f129bdc22b2e203]
-   P               [Correlation] [graph 2] [2010-05-04 14:33:27] [c519646407a489a26f129bdc22b2e203]
-    D            [Correlation] [] [2010-05-04 13:23:40] [74be16979710d4c4e7c6647856088456]
-    D            [Correlation] [Correlation betwe...] [2010-05-04 13:23:56] [991f3c16ff1ec6689e9f3866d072593e]
-   PD            [Correlation] [obeisty study] [2010-05-04 13:23:18] [74be16979710d4c4e7c6647856088456]
-                 [Correlation] [A graph to show c...] [2010-05-04 13:10:46] [a04c3705631ba28c4a7ea7999bc2469c]
-   PD            [Correlation] [Weight] [2010-05-04 13:23:12] [31938d087c55cf67127a01ef1e8f38ba]
-    D            [Correlation] [] [2010-05-04 13:20:43] [7ee8584ae92dbbc2a823887b8397aaa8]
-    D            [Correlation] [question 2 2 ] [2010-05-04 13:26:22] [256a42577f5eb7e9c8a1b74c73a90fa8]
-    D            [Correlation] [mock] [2010-05-04 13:15:22] [9071c1a88a977c8c2dd0accff6b1d644]
-    D            [Correlation] [] [2010-05-04 13:25:33] [226e457c23f16abdaf22fe48e6e411fd]
-                 [Correlation] [] [2010-05-04 13:17:25] [0848a45f8a904661abc16c2a3570ded4]
-    D            [Correlation] [correlation of ch...] [2010-05-04 13:21:40] [a2ec18f77143ca7c2255feafca790c81]
-    D            [Correlation] [] [2010-05-04 13:19:53] [869dc8c90da15910a169a569d8b6a5c9]
-    D            [Correlation] [correlation of ch...] [2010-05-04 13:21:40] [a2ec18f77143ca7c2255feafca790c81]
-    D            [Correlation] [Correlation week 8 ] [2010-05-04 13:27:21] [74be16979710d4c4e7c6647856088456]
-    D            [Correlation] [Mock exam ] [2010-05-04 13:27:05] [efb93495a892eea584966de4a02d2ce4]
-    D            [Correlation] [Correlation ] [2010-05-04 13:25:09] [da3db4ee336105e3f28c420d1eeb41bc]
-    D            [Correlation] [correlation] [2010-05-04 13:21:11] [9dc333cea70095e4d9c08ad15f70f6c6]
-    D            [Correlation] [] [2010-05-04 13:25:51] [a120050d9c71216a504f7d26958aa6f2]
-    D            [Correlation] [exam - correlatio...] [2010-05-04 13:25:20] [6754037f2a7547483397efade45eb176]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.6	-41.0
1.8	55.0
5.2	30.0
4.1	0.0
0.4	17.0
2.7	-61.0
2.4	27.0
2.6	1.0
2.4	-67.0
7.2	80.0
3.7	-70.0
8.4	41.0
1.5	-37.0
8.0	0.0
0.0	7.0
7.1	-50.0
2.8	74.0
8.2	79.0
2.3	56.0
5.0	18.0
5.9	4.0
6.2	15.0
3.6	69.0
1.6	-6.0
3.2	32.0
2.6	57.0
1.6	59.0
5.8	68.0
2.8	-39.0
1.2	8.0
-1.5	-349.0
7.8	169.0
2.5	51.0
9.6	43.0
7.4	58.0

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74949&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74949&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-41.79221.464-1.9470.06
X13.5134.4873.0120.005
- - -
Residual Std. Err. 72.241 on 33 df
Multiple R-sq. 0.216
Adjusted R-sq. 0.192

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -41.792 & 21.464 & -1.947 & 0.06 \tabularnewline
X & 13.513 & 4.487 & 3.012 & 0.005 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 72.241  on  33 df \tabularnewline
Multiple R-sq.  & 0.216 \tabularnewline
Adjusted R-sq.  & 0.192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74949&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]-41.792[/C][C]21.464[/C][C]-1.947[/C][C]0.06[/C][/ROW]
[C]X[/C][C]13.513[/C][C]4.487[/C][C]3.012[/C][C]0.005[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]72.241  on  33 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.216[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74949&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)-41.79221.464-1.9470.06
X13.5134.4873.0120.005
- - -
Residual Std. Err. 72.241 on 33 df
Multiple R-sq. 0.216
Adjusted R-sq. 0.192






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
dWt147340.68347340.6839.0710.005
Residuals33172221.4895218.833 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
dWt & 1 & 47340.683 & 47340.683 & 9.071 & 0.005 \tabularnewline
Residuals & 33 & 172221.489 & 5218.833 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74949&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]47340.683[/C][C]47340.683[/C][C]9.071[/C][C]0.005[/C][/ROW]
[ROW][C]Residuals[/C][C]33[/C][C]172221.489[/C][C]5218.833[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74949&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74949&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)
dWt147340.68347340.6839.0710.005
Residuals33172221.4895218.833


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)
}# end cols
a<-table.row.end(a)
} #end rows
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()