R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(4.640826863,4.640923356,4.641116313,4.642176912,4.643236387,4.64352514,4.64352514,4.643621372,4.644871553,4.646599996,4.647271362,4.647367235,4.647367235,4.647654798,4.649665426,4.650621449,4.65138561,4.651576559,4.651576559,4.65167202,4.653388758,4.656718448,4.657572865,4.658047226,4.658047226,4.657952371,4.658900508,4.660510281,4.66079409,4.660983251,4.660983251,4.660983251,4.662967285,4.665041583,4.666641508,4.666923582,4.666923582,4.666829566,4.667581446,4.666171208,4.665606555,4.665606555,4.665606555,4.665606555,4.666641508,4.667581446,4.667581446,4.667957174,4.668144985,4.668802046,4.667205577,4.666923582,4.665794808,4.665418266,4.665418266,4.665700686,4.665229942,4.664193526,4.664664758,4.66428779)
> x <- c(4.608165695,4.590056548,4.55492897,4.533674184,4.523960131,4.48863637,4.458987676,4.436751534,4.415219602,4.391976966,4.404277244,4.404277244,4.417635062,4.428433007,4.456670178,4.455509411,4.456670178,4.48638665,4.49535532,4.475061501,4.480740108,4.484131858,4.510859507,4.516338972,4.558078578,4.592084946,4.604169686,4.591071262,4.608165695,4.607168189,4.609162207,4.619073091,4.634728988,4.692264893,4.713127327,4.737075257,4.802380355,4.848900371,4.866764924,4.852030264,4.816241156,4.820281566,4.847331743,4.848900371,4.855150391,4.878246106,4.906015245,4.8978398,4.973279508,4.992471323,5.016617366,5.001930853,4.951592753,4.93375425,4.94021283,4.980863136,4.99653637,5.000584958,5.017941869,5.059425458)
> par1 = '0'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> par1 <- as.numeric(par1)
> library(lattice)
> z <- as.data.frame(cbind(x,y))
> m <- lm(y~x)
> summary(m)

Call:
lm(formula = y ~ x)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0144838 -0.0024751  0.0009261  0.0033440  0.0075917 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.49115    0.01534  292.86  < 2e-16 ***
x            0.03562    0.00327   10.90 1.17e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.005315 on 58 degrees of freedom
Multiple R-squared: 0.6718,	Adjusted R-squared: 0.6661 
F-statistic: 118.7 on 1 and 58 DF,  p-value: 1.173e-15 

> postscript(file="/var/www/html/rcomp/tmp/1sl921256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(z,main='Scatterplot, lowess, and regression line')
> lines(lowess(z),col='red')
> abline(m)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2tuf81256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> m2 <- lm(m$fitted.values ~ x)
> summary(m2)

Call:
lm(formula = m$fitted.values ~ x)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.191e-14  1.500e-16  3.081e-16  5.820e-16  9.329e-16 

Coefficients:
             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 4.491e+00  8.414e-15 5.338e+14   <2e-16 ***
x           3.562e-02  1.794e-15 1.986e+13   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.916e-15 on 58 degrees of freedom
Multiple R-squared:     1,	Adjusted R-squared:     1 
F-statistic: 3.944e+26 on 1 and 58 DF,  p-value: < 2.2e-16 

> z2 <- as.data.frame(cbind(x,m$fitted.values))
> names(z2) <- list('x','Fitted')
> plot(z2,main='Scatterplot, lowess, and regression line')
> lines(lowess(z2),col='red')
> abline(m2)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3kos61256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> m3 <- lm(m$residuals ~ x)
> summary(m3)

Call:
lm(formula = m$residuals ~ x)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0144838 -0.0024751  0.0009261  0.0033440  0.0075917 

Coefficients:
              Estimate Std. Error   t value Pr(>|t|)
(Intercept) -4.045e-17  1.534e-02 -2.64e-15        1
x            8.536e-18  3.270e-03  2.61e-15        1

Residual standard error: 0.005315 on 58 degrees of freedom
Multiple R-squared: 1.746e-31,	Adjusted R-squared: -0.01724 
F-statistic: 1.013e-29 on 1 and 58 DF,  p-value: 1 

> z3 <- as.data.frame(cbind(x,m$residuals))
> names(z3) <- list('x','Residuals')
> plot(z3,main='Scatterplot, lowess, and regression line')
> lines(lowess(z3),col='red')
> abline(m3)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/45dsk1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> m4 <- lm(m$fitted.values ~ m$residuals)
> summary(m4)

Call:
lm(formula = m$fitted.values ~ m$residuals)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.010466 -0.007043 -0.002747  0.006550  0.013311 

Coefficients:
             Estimate Std. Error  t value Pr(>|t|)    
(Intercept) 4.658e+00  9.818e-04     4744   <2e-16 ***
m$residuals 1.866e-13  1.879e-01 9.93e-13        1    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.007605 on 58 degrees of freedom
Multiple R-squared: 7.573e-26,	Adjusted R-squared: -0.01724 
F-statistic: 4.392e-24 on 1 and 58 DF,  p-value: 1 

> 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()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/5svqr1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> 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)

Call:
lm(formula = z5)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.607e-03 -6.697e-04  2.054e-05  6.537e-04  3.277e-03 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.0001345  0.0001487   0.905    0.369    
Residuals   0.9225521  0.0286525  32.198   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.001142 on 57 degrees of freedom
  (2 observations deleted due to missingness)
Multiple R-squared: 0.9479,	Adjusted R-squared: 0.947 
F-statistic:  1037 on 1 and 57 DF,  p-value: < 2.2e-16 

> abline(m5)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/6mabz1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(m$residuals,main='Residual Histogram',xlab='Residuals')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/7e8fc1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> if (par1 > 0)
+ {
+ densityplot(~m$residuals,col='black',main=paste('Density Plot   bw = ',par1),bw=par1)
+ } else {
+ densityplot(~m$residuals,col='black',main='Density Plot')
+ }
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/8wl5c1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> acf(m$residuals,main='Residual Autocorrelation Function')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/992fm1256316459.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(x)
> qqline(x)
> grid()
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/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="/var/www/html/rcomp/tmp/10fspq1256316459.tab") 
> 
> system("convert tmp/1sl921256316459.ps tmp/1sl921256316459.png")
> system("convert tmp/2tuf81256316459.ps tmp/2tuf81256316459.png")
> system("convert tmp/3kos61256316459.ps tmp/3kos61256316459.png")
> system("convert tmp/45dsk1256316459.ps tmp/45dsk1256316459.png")
> system("convert tmp/5svqr1256316459.ps tmp/5svqr1256316459.png")
> system("convert tmp/6mabz1256316459.ps tmp/6mabz1256316459.png")
> system("convert tmp/7e8fc1256316459.ps tmp/7e8fc1256316459.png")
> system("convert tmp/8wl5c1256316459.ps tmp/8wl5c1256316459.png")
> system("convert tmp/992fm1256316459.ps tmp/992fm1256316459.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.844   1.362   3.318