R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> y <- c(276427,266424,267153,268381,262522,255542,253158,243803,250741,280445,285257,270976,261076)
> x <- c(250643,243422,247105,248541,245039,237080,237085,225554,226839,247934,248333,246969,245098)
> #'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] 0.8613971 0.8614353 0.8614699 0.8615049 0.8615380 0.8615684 0.8616027
  [8] 0.8616386 0.8616683 0.8617014 0.8617347 0.8617697 0.8618072 0.8618405
 [15] 0.8618745 0.8619059 0.8619416 0.8619727 0.8620062 0.8620393 0.8620725
 [22] 0.8621069 0.8621390 0.8621731 0.8622074 0.8622396 0.8622736 0.8623074
 [29] 0.8623399 0.8623740 0.8624071 0.8624405 0.8624737 0.8625070 0.8625402
 [36] 0.8625733 0.8626065 0.8626399 0.8626732 0.8627065 0.8627396 0.8627727
 [43] 0.8628060 0.8628391 0.8628722 0.8629055 0.8629385 0.8629717 0.8630047
 [50] 0.8630379 0.8630710 0.8631040 0.8631371 0.8631701 0.8632032 0.8632362
 [57] 0.8632692 0.8633022 0.8633352 0.8633682 0.8634011 0.8634341 0.8634670
 [64] 0.8635000 0.8635329 0.8635658 0.8635987 0.8636316 0.8636644 0.8636973
 [71] 0.8637301 0.8637629 0.8637958 0.8638286 0.8638614 0.8638942 0.8639269
 [78] 0.8639597 0.8639924 0.8640252 0.8640579 0.8640906 0.8641233 0.8641560
 [85] 0.8641887 0.8642213 0.8642540 0.8642866 0.8643192 0.8643518 0.8643844
 [92] 0.8644170 0.8644496 0.8644822 0.8645147 0.8645473 0.8645798 0.8646123
 [99] 0.8646448 0.8646773 0.8647098 0.8647422 0.8647747 0.8648071 0.8648396
[106] 0.8648720 0.8649044 0.8649368 0.8649692 0.8650015 0.8650339 0.8650662
[113] 0.8650985 0.8651309 0.8651632 0.8651955 0.8652277 0.8652600 0.8652923
[120] 0.8653245 0.8653567 0.8653890 0.8654212 0.8654533 0.8654855 0.8655177
[127] 0.8655499 0.8655820 0.8656141 0.8656462 0.8656784 0.8657104 0.8657425
[134] 0.8657746 0.8658066 0.8658387 0.8658707 0.8659027 0.8659347 0.8659667
[141] 0.8659987 0.8660307 0.8660626 0.8660946 0.8661265 0.8661584 0.8661903
[148] 0.8662222 0.8662541 0.8662860 0.8663178 0.8663497 0.8663815 0.8664133
[155] 0.8664451 0.8664769 0.8665087 0.8665405 0.8665722 0.8666039 0.8666357
[162] 0.8666674 0.8666991 0.8667308 0.8667625 0.8667941 0.8668258 0.8668574
[169] 0.8668890 0.8669206 0.8669522 0.8669838 0.8670154 0.8670470 0.8670785
[176] 0.8671101 0.8671416 0.8671731 0.8672046 0.8672361 0.8672675 0.8672990
[183] 0.8673304 0.8673619 0.8673933 0.8674247 0.8674561 0.8674875 0.8675189
[190] 0.8675502 0.8675816 0.8676129 0.8676442 0.8676755 0.8677068 0.8677381
[197] 0.8677693 0.8678006 0.8678318 0.8678631 0.8678943 0.8679255 0.8679567
[204] 0.8679878 0.8680190 0.8680501 0.8680813 0.8681124 0.8681435 0.8681746
[211] 0.8682057 0.8682368 0.8682678 0.8682989 0.8683299 0.8683609 0.8683919
[218] 0.8684229 0.8684539 0.8684849 0.8685158 0.8685468 0.8685777 0.8686086
[225] 0.8686395 0.8686704 0.8687013 0.8687321 0.8687630 0.8687938 0.8688246
[232] 0.8688554 0.8688862 0.8689170 0.8689478 0.8689785 0.8690093 0.8690400
[239] 0.8690707 0.8691014 0.8691321 0.8691628 0.8691935 0.8692241 0.8692548
[246] 0.8692854 0.8693160 0.8693466 0.8693772 0.8694078 0.8694383 0.8694689
[253] 0.8694994 0.8695299 0.8695604 0.8695909 0.8696214 0.8696518 0.8696823
[260] 0.8697127 0.8697432 0.8697736 0.8698040 0.8698344 0.8698647 0.8698951
[267] 0.8699254 0.8699558 0.8699861 0.8700164 0.8700467 0.8700770 0.8701072
[274] 0.8701375 0.8701677 0.8701979 0.8702281 0.8702583 0.8702885 0.8703187
[281] 0.8703488 0.8703790 0.8704091 0.8704392 0.8704693 0.8704994 0.8705295
[288] 0.8705596 0.8705896 0.8706197 0.8706497 0.8706797 0.8707097 0.8707397
[295] 0.8707696 0.8707996 0.8708295 0.8708595 0.8708894 0.8709193 0.8709492
[302] 0.8709790 0.8710089 0.8710387 0.8710686 0.8710984 0.8711282 0.8711580
[309] 0.8711878 0.8712175 0.8712473 0.8712770 0.8713067 0.8713364 0.8713661
[316] 0.8713958 0.8714255 0.8714552 0.8714848 0.8715144 0.8715440 0.8715736
[323] 0.8716032 0.8716328 0.8716624 0.8716919 0.8717214 0.8717510 0.8717805
[330] 0.8718100 0.8718394 0.8718689 0.8718983 0.8719278 0.8719572 0.8719866
[337] 0.8720160 0.8720454 0.8720748 0.8721041 0.8721334 0.8721628 0.8721921
[344] 0.8722214 0.8722507 0.8722799 0.8723092 0.8723384 0.8723677 0.8723969
[351] 0.8724261 0.8724553 0.8724844 0.8725136 0.8725427 0.8725719 0.8726010
[358] 0.8726301 0.8726592 0.8726883 0.8727173 0.8727464 0.8727754 0.8728044
[365] 0.8728334 0.8728624 0.8728914 0.8729204 0.8729493 0.8729783 0.8730072
[372] 0.8730361 0.8730650 0.8730939 0.8731227 0.8731516 0.8731804 0.8732093
[379] 0.8732381 0.8732669 0.8732957 0.8733244 0.8733532 0.8733819 0.8734106
[386] 0.8734394 0.8734681 0.8734967 0.8735254 0.8735541 0.8735827 0.8736113
[393] 0.8736400 0.8736686 0.8736971 0.8737257 0.8737543 0.8737828 0.8738114
[400] 0.8738399 0.8738684
> mx
[1] 0.8738684
> mxli
[1] 2
> 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/freestat/rcomp/tmp/1656l1226482634.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/freestat/rcomp/tmp/2hd1q1226482634.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/freestat/rcomp/tmp/31boe1226482634.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/4ocwi1226482634.tab") 
> 
> system("convert tmp/1656l1226482634.ps tmp/1656l1226482634.png")
> system("convert tmp/2hd1q1226482634.ps tmp/2hd1q1226482634.png")
> system("convert tmp/31boe1226482634.ps tmp/31boe1226482634.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.206   0.793   1.414