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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_linear_regression.wasp
Title produced by softwareLinear Regression Graphical Model Validation
Date of computationWed, 21 Dec 2011 18:57:45 -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/2011/Dec/21/t1324511889u8rk4uathgz2uye.htm/, Retrieved Sun, 11 May 2025 11:41:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159147, Retrieved Sun, 11 May 2025 11:41:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [] [2011-11-25 14:57:13] [493236dcc414c5f9e1823f06b33a5ad6]
-    D    [Univariate Data Series] [] [2011-12-21 21:39:24] [493236dcc414c5f9e1823f06b33a5ad6]
-   PD      [Univariate Data Series] [] [2011-12-21 23:36:19] [493236dcc414c5f9e1823f06b33a5ad6]
-    D        [Univariate Data Series] [] [2011-12-21 23:40:13] [493236dcc414c5f9e1823f06b33a5ad6]
- RM D            [Linear Regression Graphical Model Validation] [] [2011-12-21 23:57:45] [75a32e1bc492240bc1028714aca23077] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
Dataseries Y:
Download CSV
Histogram 
2,1
2,4
2,5
2,1
1,8
1,9
1,9
2,1
2,2
2
2,2
2
1,9
1,6
1,7
2
2,5
2,4
2,3
2,3
2,1
2,4
2,2
2,4
1,9
2,1
2,1
2,1
2
2,1
2,2
2,2
2,6
2,5
2,3
2,2
2,4
2,3
2,2
2,5
2,5
2,5
2,4
2,3
1,7
1,6
1,9
1,9
1,8
1,8
1,9
1,9
1,9
1,9
1,8
1,7
2,1
2,6
3,1
3,1

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=159147&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=159147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159147&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






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term1.778604525249020.5788647615702023.072573497865810.0032302849526793
slope0.2986743162199190.4622768218417910.6460940763370930.52076673032595

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 1.77860452524902 & 0.578864761570202 & 3.07257349786581 & 0.0032302849526793 \tabularnewline
slope & 0.298674316219919 & 0.462276821841791 & 0.646094076337093 & 0.52076673032595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159147&T=1

[TABLE]
[ROW][C]Simple Linear Regression[/C][/ROW]
[ROW][C]Statistics[/C][C]Estimate[/C][C]S.D.[/C][C]T-STAT (H0: coeff=0)[/C][C]P-value (two-sided)[/C][/ROW]
[ROW][C]constant term[/C][C]1.77860452524902[/C][C]0.578864761570202[/C][C]3.07257349786581[/C][C]0.0032302849526793[/C][/ROW]
[ROW][C]slope[/C][C]0.298674316219919[/C][C]0.462276821841791[/C][C]0.646094076337093[/C][C]0.52076673032595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159147&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:

Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term1.778604525249020.5788647615702023.072573497865810.0032302849526793
slope0.2986743162199190.4622768218417910.6460940763370930.52076673032595


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Input Parameters & R Code

Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
library(lattice)
z <- as.data.frame(cbind(x,y))
m <- lm(y~x)
summary(m)
bitmap(file='test1.png')
plot(z,main='Scatterplot, lowess, and regression line')
lines(lowess(z),col='red')
abline(m)
grid()
dev.off()
bitmap(file='test2.png')
m2 <- lm(m$fitted.values ~ x)
summary(m2)
z2 <- as.data.frame(cbind(x,m$fitted.values))
names(z2) <- list('x','Fitted')
plot(z2,main='Scatterplot, lowess, and regression line')
lines(lowess(z2),col='red')
abline(m2)
grid()
dev.off()
bitmap(file='test3.png')
m3 <- lm(m$residuals ~ x)
summary(m3)
z3 <- as.data.frame(cbind(x,m$residuals))
names(z3) <- list('x','Residuals')
plot(z3,main='Scatterplot, lowess, and regression line')
lines(lowess(z3),col='red')
abline(m3)
grid()
dev.off()
bitmap(file='test4.png')
m4 <- lm(m$fitted.values ~ m$residuals)
summary(m4)
z4 <- as.data.frame(cbind(m$residuals,m$fitted.values))
names(z4) <- list('Residuals','Fitted')
plot(z4,main='Scatterplot, lowess, and regression line')
lines(lowess(z4),col='red')
abline(m4)
grid()
dev.off()
bitmap(file='test5.png')
myr <- as.ts(m$residuals)
z5 <- as.data.frame(cbind(lag(myr,1),myr))
names(z5) <- list('Lagged Residuals','Residuals')
plot(z5,main='Lag plot')
m5 <- lm(z5)
summary(m5)
abline(m5)
grid()
dev.off()
bitmap(file='test6.png')
hist(m$residuals,main='Residual Histogram',xlab='Residuals')
dev.off()
bitmap(file='test7.png')
if (par1 > 0)
{
densityplot(~m$residuals,col='black',main=paste('Density Plot   bw = ',par1),bw=par1)
} else {
densityplot(~m$residuals,col='black',main='Density Plot')
}
dev.off()
bitmap(file='test8.png')
acf(m$residuals,main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test9.png')
qqnorm(x)
qqline(x)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Simple Linear Regression',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistics',1,TRUE)
a<-table.element(a,'Estimate',1,TRUE)
a<-table.element(a,'S.D.',1,TRUE)
a<-table.element(a,'T-STAT (H0: coeff=0)',1,TRUE)
a<-table.element(a,'P-value (two-sided)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'constant term',header=TRUE)
a<-table.element(a,m$coefficients[[1]])
sd <- sqrt(vcov(m)[1,1])
a<-table.element(a,sd)
tstat <- m$coefficients[[1]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'slope',header=TRUE)
a<-table.element(a,m$coefficients[[2]])
sd <- sqrt(vcov(m)[2,2])
a<-table.element(a,sd)
tstat <- m$coefficients[[2]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')