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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 computationFri, 30 Apr 2010 11:37:32 +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/30/t127262749403sse9hnjhkfflo.htm/, Retrieved Sat, 20 Apr 2024 09:29:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=75064, Retrieved Sat, 20 Apr 2024 09:29:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLinear Regression Model
Estimated Impact463

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] [98fd0e87c3eb04e0cc2efde01dbafab6]
-    D  [Simple Linear Regression] [PY2224 May Mock E...] [2010-04-30 11:33:27] [98fd0e87c3eb04e0cc2efde01dbafab6]
-           [Simple Linear Regression] [PY2224 May Mock E...] [2010-04-30 11:37:32] [a9208f4f8d3b118336aae915785f2bd9] [Current]
-             [Simple Linear Regression] [Ian test answer] [2010-05-04 12:39:34] [74be16979710d4c4e7c6647856088456]
-    D        [Simple Linear Regression] [Regression] [2010-05-04 13:12:47] [f92b1014b0eca5452e0c3ed42064454c]
-    D        [Simple Linear Regression] [] [2010-05-04 13:20:38] [74be16979710d4c4e7c6647856088456]
-    D        [Simple Linear Regression] [] [2010-05-04 13:22:27] [e8bb49267f0b4e611f4778412d0811f2]
-    D        [Simple Linear Regression] [regression of wei...] [2010-05-04 13:23:17] [f0a7b9ce333a507984a56d87311bd9a6]
-    D        [Simple Linear Regression] [] [2010-05-04 13:21:36] [5767bd6424518d00d47b9a54e25f82fa]
-    D        [Simple Linear Regression] [regression solution] [2010-05-04 13:15:33] [e4bd24891566c9218b3fb717799b8eeb]
-    D        [Simple Linear Regression] [] [2010-05-04 13:24:39] [b556ad7677148e2149f669ccc7efda70]
-    D        [Simple Linear Regression] [] [2010-05-04 13:24:39] [b556ad7677148e2149f669ccc7efda70]
-    D        [Simple Linear Regression] [mock exam 2] [2010-05-04 13:27:49] [74be16979710d4c4e7c6647856088456]
-    D        [Simple Linear Regression] [iii] [2010-05-04 13:28:02] [885328d98a95a442af53d0763bccf325]
-    D        [Simple Linear Regression] [regression line o...] [2010-05-04 13:29:19] [2185b0545466c0a8649e1b1b76e104e0]
-             [Simple Linear Regression] [] [2010-05-04 13:30:01] [74be16979710d4c4e7c6647856088456]
-             [Simple Linear Regression] [] [2010-05-04 13:30:01] [74be16979710d4c4e7c6647856088456]
-    D        [Simple Linear Regression] [Mock Exam] [2010-05-04 13:30:45] [98f7bb06c1449e4a4374f6ae31ec1a81]
-    D        [Simple Linear Regression] [regression] [2010-05-04 13:31:33] [c7d0e78e2fa8da0e0b2bee0011c20ac0]
-    D        [Simple Linear Regression] [Regression] [2010-05-04 13:31:25] [7756e15f439c0db38d660c862abbb747]
-             [Simple Linear Regression] [part 1] [2010-05-04 13:33:21] [98c63a60e57a9ebbf84cf062cbeaf5fe]
-    D        [Simple Linear Regression] [Triglyceride vs w...] [2010-05-04 13:34:22] [7b5e237c5dc223226d9c139a76db490f]
-             [Simple Linear Regression] [blog 2] [2010-05-04 13:32:01] [5cae40017fc37cfe76436682b5003098]
-    D        [Simple Linear Regression] [] [2010-05-04 13:35:26] [82439cd473f0ddf8a88eb1802dda9b6c]
-    D        [Simple Linear Regression] [] [2010-05-04 13:34:30] [869dc8c90da15910a169a569d8b6a5c9]
-    D        [Simple Linear Regression] [] [2010-05-04 13:36:10] [7ee8584ae92dbbc2a823887b8397aaa8]
-    D        [Simple Linear Regression] [question 2 3] [2010-05-04 13:36:47] [256a42577f5eb7e9c8a1b74c73a90fa8]
-    D        [Simple Linear Regression] [Linear Regression] [2010-05-04 13:37:08] [991f3c16ff1ec6689e9f3866d072593e]
-    D        [Simple Linear Regression] [correlation betwe...] [2010-05-04 13:36:56] [0d9a06d5a3b5d935641c7444d1321f71]
-    D        [Simple Linear Regression] [Mock Exam: Linear] [2010-05-04 13:35:34] [226e457c23f16abdaf22fe48e6e411fd]
-    D        [Simple Linear Regression] [] [2010-05-04 13:39:06] [36cf82ea4074b55afa05ece289b9dfca]
-    D        [Simple Linear Regression] [blog 1] [2010-05-04 13:40:29] [bcdd3a0c82f5258468053a42cfd4486b]
-   PD        [Simple Linear Regression] [Linear Regression] [2010-05-04 13:39:46] [31938d087c55cf67127a01ef1e8f38ba]
-    D        [Simple Linear Regression] [linear regression ] [2010-05-04 13:33:42] [9dc333cea70095e4d9c08ad15f70f6c6]
-    D        [Simple Linear Regression] [calculation] [2010-05-04 13:42:10] [e4bd24891566c9218b3fb717799b8eeb]
-             [Simple Linear Regression] [mock] [2010-05-04 13:25:16] [9071c1a88a977c8c2dd0accff6b1d644]
-    D        [Simple Linear Regression] [the change in tri...] [2010-05-04 13:43:19] [2138d0a3887167bab056950bbcdaeb16]
-    D        [Simple Linear Regression] [Regression] [2010-05-04 13:44:50] [6754037f2a7547483397efade45eb176]
-    D        [Simple Linear Regression] [linear regression...] [2010-05-04 13:31:02] [a58114c03403c4a3c11c78968b4ee919]
-    D        [Simple Linear Regression] [regression model] [2010-05-04 13:28:12] [eeb9f4fe90b65b794b6bda3d89777ecb]
-    D        [Simple Linear Regression] [mock exam regression] [2010-05-04 13:45:43] [981ccd4f0082ace49a11aa7a2b792a9c]
-             [Simple Linear Regression] [Linear regression ] [2010-05-04 13:46:37] [a04c3705631ba28c4a7ea7999bc2469c]
-    D        [Simple Linear Regression] [part 3] [2010-05-04 13:45:26] [e50002609a86c8cc3f92b69a15f3a57a]
-             [Simple Linear Regression] [Linear regression ] [2010-05-04 13:46:37] [a04c3705631ba28c4a7ea7999bc2469c]
-    D        [Simple Linear Regression] [regression] [2010-05-04 13:40:53] [a2ec18f77143ca7c2255feafca790c81]
-             [Simple Linear Regression] [Regression] [2010-05-04 13:31:37] [c0fd4f9a7f3faddc4844dbb572f0833e]
- R  D        [Simple Linear Regression] [mock iii] [2010-05-04 13:48:34] [856c65906cd78e3f7881668c6dfea87f]
-             [Simple Linear Regression] [blog 2] [2010-05-04 13:48:38] [bcdd3a0c82f5258468053a42cfd4486b]
-    D        [Simple Linear Regression] [] [2010-05-04 13:48:56] [d74adfedd89cf791550428da9b28a192]
-    D        [Simple Linear Regression] [weight loss and T...] [2010-05-04 13:49:08] [74be16979710d4c4e7c6647856088456]
-    D        [Simple Linear Regression] [stats mock] [2010-05-04 13:49:27] [012a64ac316c94a67eaef3285dac2cf7]

[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

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75064&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75064&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75064&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'George Udny Yule' @ 72.249.76.132






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)-0.5134.329-0.0150.989
X1.6811.4560.1470.889
- - -
Residual Std. Err. 45.16 on 5 df
Multiple R-sq. 0.004
Adjusted R-sq. -0.195

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & -0.51 & 34.329 & -0.015 & 0.989 \tabularnewline
X & 1.68 & 11.456 & 0.147 & 0.889 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 45.16  on  5 df \tabularnewline
Multiple R-sq.  & 0.004 \tabularnewline
Adjusted R-sq.  & -0.195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75064&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]-0.51[/C][C]34.329[/C][C]-0.015[/C][C]0.989[/C][/ROW]
[C]X[/C][C]1.68[/C][C]11.456[/C][C]0.147[/C][C]0.889[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]45.16  on  5 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.004[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75064&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75064&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)-0.5134.329-0.0150.989
X1.6811.4560.1470.889
- - -
Residual Std. Err. 45.16 on 5 df
Multiple R-sq. 0.004
Adjusted R-sq. -0.195






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
X143.83643.8360.0210.889
Residuals510197.0212039.404 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
X & 1 & 43.836 & 43.836 & 0.021 & 0.889 \tabularnewline
Residuals & 5 & 10197.021 & 2039.404 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=75064&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]X[/C][C]1[/C][C]43.836[/C][C]43.836[/C][C]0.021[/C][C]0.889[/C][/ROW]
[ROW][C]Residuals[/C][C]5[/C][C]10197.021[/C][C]2039.404[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=75064&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=75064&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)
X143.83643.8360.0210.889
Residuals510197.0212039.404


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()