R version 2.7.2 (2008-08-25)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(10068,10101,10131,10143,10170,10192,10214,10239,10263,10310,10355,10396,10446,10511,10585,10667)
> x <- c(4923,4940,4956,4959,4972,4983,4994,5007,5018,5042,5068,5087,5112,5144,5182,5224)
> #'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!)
> n <- length(x)
> c <- array(NA,dim=c(401))
> l <- array(NA,dim=c(401))
> mx <- 0
> mxli <- -999
> for (i in 1:401)
+ {
+ l[i] <- (i-201)/100
+ if (l[i] != 0)
+ {
+ x1 <- (x^l[i] - 1) / l[i]
+ } else {
+ x1 <- log(x)
+ }
+ c[i] <- cor(x1,y)
+ if (mx < abs(c[i]))
+ {
+ mx <- abs(c[i])
+ mxli <- l[i]
+ }
+ }
> c
  [1] 0.9997579 0.9997593 0.9997607 0.9997622 0.9997636 0.9997650 0.9997664
  [8] 0.9997678 0.9997692 0.9997706 0.9997719 0.9997733 0.9997747 0.9997760
 [15] 0.9997774 0.9997787 0.9997801 0.9997814 0.9997827 0.9997841 0.9997854
 [22] 0.9997867 0.9997880 0.9997893 0.9997906 0.9997918 0.9997931 0.9997944
 [29] 0.9997956 0.9997969 0.9997981 0.9997994 0.9998006 0.9998018 0.9998031
 [36] 0.9998043 0.9998055 0.9998067 0.9998079 0.9998091 0.9998102 0.9998114
 [43] 0.9998126 0.9998138 0.9998149 0.9998161 0.9998172 0.9998183 0.9998195
 [50] 0.9998206 0.9998217 0.9998228 0.9998239 0.9998250 0.9998261 0.9998272
 [57] 0.9998283 0.9998293 0.9998304 0.9998315 0.9998325 0.9998335 0.9998346
 [64] 0.9998356 0.9998366 0.9998377 0.9998387 0.9998397 0.9998407 0.9998417
 [71] 0.9998426 0.9998436 0.9998446 0.9998456 0.9998465 0.9998475 0.9998484
 [78] 0.9998494 0.9998503 0.9998512 0.9998521 0.9998530 0.9998539 0.9998548
 [85] 0.9998557 0.9998566 0.9998575 0.9998584 0.9998592 0.9998601 0.9998610
 [92] 0.9998618 0.9998626 0.9998635 0.9998643 0.9998651 0.9998659 0.9998667
 [99] 0.9998675 0.9998683 0.9998691 0.9998699 0.9998707 0.9998714 0.9998722
[106] 0.9998730 0.9998737 0.9998744 0.9998752 0.9998759 0.9998766 0.9998773
[113] 0.9998781 0.9998788 0.9998795 0.9998801 0.9998808 0.9998815 0.9998822
[120] 0.9998828 0.9998835 0.9998841 0.9998848 0.9998854 0.9998860 0.9998867
[127] 0.9998873 0.9998879 0.9998885 0.9998891 0.9998897 0.9998903 0.9998908
[134] 0.9998914 0.9998920 0.9998925 0.9998931 0.9998936 0.9998941 0.9998947
[141] 0.9998952 0.9998957 0.9998962 0.9998967 0.9998972 0.9998977 0.9998982
[148] 0.9998987 0.9998992 0.9998996 0.9999001 0.9999005 0.9999010 0.9999014
[155] 0.9999018 0.9999023 0.9999027 0.9999031 0.9999035 0.9999039 0.9999043
[162] 0.9999047 0.9999050 0.9999054 0.9999058 0.9999061 0.9999065 0.9999068
[169] 0.9999072 0.9999075 0.9999078 0.9999082 0.9999085 0.9999088 0.9999091
[176] 0.9999094 0.9999096 0.9999099 0.9999102 0.9999105 0.9999107 0.9999110
[183] 0.9999112 0.9999115 0.9999117 0.9999119 0.9999121 0.9999124 0.9999126
[190] 0.9999128 0.9999129 0.9999131 0.9999133 0.9999135 0.9999137 0.9999138
[197] 0.9999140 0.9999141 0.9999143 0.9999144 0.9999145 0.9999146 0.9999147
[204] 0.9999149 0.9999150 0.9999150 0.9999151 0.9999152 0.9999153 0.9999154
[211] 0.9999154 0.9999155 0.9999155 0.9999156 0.9999156 0.9999156 0.9999156
[218] 0.9999157 0.9999157 0.9999157 0.9999157 0.9999156 0.9999156 0.9999156
[225] 0.9999156 0.9999155 0.9999155 0.9999154 0.9999154 0.9999153 0.9999152
[232] 0.9999152 0.9999151 0.9999150 0.9999149 0.9999148 0.9999147 0.9999145
[239] 0.9999144 0.9999143 0.9999142 0.9999140 0.9999139 0.9999137 0.9999135
[246] 0.9999134 0.9999132 0.9999130 0.9999128 0.9999126 0.9999124 0.9999122
[253] 0.9999120 0.9999118 0.9999115 0.9999113 0.9999110 0.9999108 0.9999105
[260] 0.9999103 0.9999100 0.9999097 0.9999094 0.9999091 0.9999088 0.9999085
[267] 0.9999082 0.9999079 0.9999076 0.9999073 0.9999069 0.9999066 0.9999062
[274] 0.9999059 0.9999055 0.9999051 0.9999048 0.9999044 0.9999040 0.9999036
[281] 0.9999032 0.9999028 0.9999024 0.9999019 0.9999015 0.9999011 0.9999006
[288] 0.9999002 0.9998997 0.9998993 0.9998988 0.9998983 0.9998978 0.9998973
[295] 0.9998968 0.9998963 0.9998958 0.9998953 0.9998948 0.9998943 0.9998937
[302] 0.9998932 0.9998926 0.9998921 0.9998915 0.9998909 0.9998904 0.9998898
[309] 0.9998892 0.9998886 0.9998880 0.9998874 0.9998868 0.9998861 0.9998855
[316] 0.9998849 0.9998842 0.9998836 0.9998829 0.9998823 0.9998816 0.9998809
[323] 0.9998802 0.9998795 0.9998788 0.9998781 0.9998774 0.9998767 0.9998760
[330] 0.9998753 0.9998745 0.9998738 0.9998730 0.9998723 0.9998715 0.9998707
[337] 0.9998700 0.9998692 0.9998684 0.9998676 0.9998668 0.9998660 0.9998652
[344] 0.9998643 0.9998635 0.9998627 0.9998618 0.9998610 0.9998601 0.9998593
[351] 0.9998584 0.9998575 0.9998566 0.9998558 0.9998549 0.9998540 0.9998530
[358] 0.9998521 0.9998512 0.9998503 0.9998493 0.9998484 0.9998475 0.9998465
[365] 0.9998455 0.9998446 0.9998436 0.9998426 0.9998416 0.9998406 0.9998396
[372] 0.9998386 0.9998376 0.9998366 0.9998355 0.9998345 0.9998335 0.9998324
[379] 0.9998314 0.9998303 0.9998292 0.9998282 0.9998271 0.9998260 0.9998249
[386] 0.9998238 0.9998227 0.9998216 0.9998204 0.9998193 0.9998182 0.9998170
[393] 0.9998159 0.9998147 0.9998136 0.9998124 0.9998112 0.9998100 0.9998088
[400] 0.9998077 0.9998064
> mx
[1] 0.9999157
> mxli
[1] 0.19
> if (mxli != 0)
+ {
+ x1 <- (x^mxli - 1) / mxli
+ } else {
+ x1 <- log(x)
+ }
> r<-lm(y~x)
> se <- sqrt(var(r$residuals))
> r1 <- lm(y~x1)
> se1 <- sqrt(var(r1$residuals))
> postscript(file="/var/www/html/rcomp/tmp/115a21226416507.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Linearity Plot',xlab='Lambda',ylab='correlation')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/2sq111226416507.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x,y,main='Linear Fit of Original Data',xlab='x',ylab='y')
> abline(r)
> grid()
> mtext(paste('Residual Standard Deviation = ',se))
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/359u21226416507.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(x1,y,main='Linear Fit of Transformed Data',xlab='x',ylab='y')
> abline(r1)
> grid()
> mtext(paste('Residual Standard Deviation = ',se1))
> 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,'Box-Cox Linearity Plot',2,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'# observations x',header=TRUE)
> a<-table.element(a,n)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'maximum correlation',header=TRUE)
> a<-table.element(a,mx)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'optimal lambda(x)',header=TRUE)
> a<-table.element(a,mxli)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Residual SD (orginial)',header=TRUE)
> a<-table.element(a,se)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Residual SD (transformed)',header=TRUE)
> a<-table.element(a,se1)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/4tr9n1226416507.tab") 
> 
> system("convert tmp/115a21226416507.ps tmp/115a21226416507.png")
> system("convert tmp/2sq111226416507.ps tmp/2sq111226416507.png")
> system("convert tmp/359u21226416507.ps tmp/359u21226416507.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.089   0.548   2.003