R version 2.8.1 (2008-12-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(8.2,8.0,7.5,6.8,6.5,6.6,7.6,8.0,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7.0,7.1,7.2,7.1,6.9,7.0,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7)
> x <- c(9.9,9.8,9.3,8.3,8.0,8.5,10.4,11.1,10.9,10.0,9.2,9.2,9.5,9.6,9.5,9.1,8.9,9.0,10.1,10.3,10.2,9.6,9.2,9.3,9.4,9.4,9.2,9.0,9.0,9.0,9.8,10.0,9.8,9.3,9.0,9.0,9.1,9.1,9.1,9.2,8.8,8.3,8.4,8.1,7.7,7.9,7.9,8.0,7.9,7.6,7.1,6.8,6.5,6.9,8.2,8.7,8.3,7.9,7.5,7.8,8.3,8.4,8.2,7.7)
> #'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] 0.7224427 0.7224688 0.7224945 0.7225197 0.7225444 0.7225686 0.7225924
  [8] 0.7226156 0.7226384 0.7226607 0.7226825 0.7227038 0.7227246 0.7227449
 [15] 0.7227647 0.7227841 0.7228029 0.7228213 0.7228392 0.7228566 0.7228735
 [22] 0.7228899 0.7229059 0.7229213 0.7229363 0.7229507 0.7229647 0.7229782
 [29] 0.7229912 0.7230037 0.7230157 0.7230273 0.7230383 0.7230489 0.7230589
 [36] 0.7230685 0.7230776 0.7230862 0.7230943 0.7231019 0.7231091 0.7231157
 [43] 0.7231219 0.7231275 0.7231327 0.7231374 0.7231416 0.7231453 0.7231485
 [50] 0.7231512 0.7231535 0.7231552 0.7231565 0.7231573 0.7231576 0.7231573
 [57] 0.7231567 0.7231555 0.7231538 0.7231516 0.7231490 0.7231458 0.7231422
 [64] 0.7231381 0.7231335 0.7231284 0.7231228 0.7231167 0.7231102 0.7231031
 [71] 0.7230956 0.7230876 0.7230791 0.7230701 0.7230606 0.7230506 0.7230401
 [78] 0.7230292 0.7230177 0.7230058 0.7229934 0.7229805 0.7229671 0.7229532
 [85] 0.7229388 0.7229239 0.7229086 0.7228928 0.7228765 0.7228596 0.7228424
 [92] 0.7228246 0.7228063 0.7227876 0.7227683 0.7227486 0.7227284 0.7227077
 [99] 0.7226865 0.7226648 0.7226427 0.7226200 0.7225969 0.7225733 0.7225492
[106] 0.7225246 0.7224996 0.7224740 0.7224480 0.7224215 0.7223945 0.7223670
[113] 0.7223390 0.7223106 0.7222816 0.7222522 0.7222223 0.7221919 0.7221610
[120] 0.7221297 0.7220978 0.7220655 0.7220327 0.7219994 0.7219657 0.7219314
[127] 0.7218967 0.7218615 0.7218258 0.7217896 0.7217530 0.7217159 0.7216783
[134] 0.7216402 0.7216016 0.7215625 0.7215230 0.7214830 0.7214425 0.7214016
[141] 0.7213601 0.7213182 0.7212758 0.7212329 0.7211896 0.7211457 0.7211014
[148] 0.7210566 0.7210114 0.7209656 0.7209194 0.7208727 0.7208256 0.7207779
[155] 0.7207298 0.7206812 0.7206321 0.7205826 0.7205326 0.7204821 0.7204311
[162] 0.7203797 0.7203278 0.7202754 0.7202226 0.7201692 0.7201154 0.7200612
[169] 0.7200064 0.7199512 0.7198955 0.7198394 0.7197828 0.7197257 0.7196681
[176] 0.7196101 0.7195516 0.7194926 0.7194332 0.7193733 0.7193129 0.7192521
[183] 0.7191908 0.7191290 0.7190667 0.7190040 0.7189409 0.7188772 0.7188131
[190] 0.7187486 0.7186835 0.7186180 0.7185521 0.7184857 0.7184188 0.7183514
[197] 0.7182836 0.7182153 0.7181466 0.7180774 0.7180078 0.7179376 0.7178671
[204] 0.7177960 0.7177245 0.7176526 0.7175801 0.7175073 0.7174339 0.7173602
[211] 0.7172859 0.7172112 0.7171360 0.7170604 0.7169843 0.7169078 0.7168308
[218] 0.7167534 0.7166755 0.7165971 0.7165183 0.7164391 0.7163594 0.7162792
[225] 0.7161986 0.7161175 0.7160360 0.7159540 0.7158716 0.7157888 0.7157054
[232] 0.7156217 0.7155375 0.7154528 0.7153677 0.7152821 0.7151961 0.7151097
[239] 0.7150228 0.7149354 0.7148476 0.7147594 0.7146707 0.7145816 0.7144920
[246] 0.7144020 0.7143115 0.7142206 0.7141293 0.7140375 0.7139453 0.7138526
[253] 0.7137595 0.7136659 0.7135719 0.7134775 0.7133827 0.7132873 0.7131916
[260] 0.7130954 0.7129988 0.7129018 0.7128043 0.7127063 0.7126080 0.7125092
[267] 0.7124100 0.7123103 0.7122102 0.7121097 0.7120087 0.7119073 0.7118055
[274] 0.7117033 0.7116006 0.7114975 0.7113939 0.7112899 0.7111855 0.7110807
[281] 0.7109754 0.7108698 0.7107637 0.7106571 0.7105502 0.7104428 0.7103350
[288] 0.7102267 0.7101181 0.7100090 0.7098995 0.7097895 0.7096792 0.7095684
[295] 0.7094572 0.7093456 0.7092336 0.7091211 0.7090083 0.7088950 0.7087813
[302] 0.7086672 0.7085526 0.7084377 0.7083223 0.7082065 0.7080903 0.7079737
[309] 0.7078567 0.7077392 0.7076214 0.7075031 0.7073844 0.7072653 0.7071458
[316] 0.7070259 0.7069056 0.7067849 0.7066638 0.7065422 0.7064203 0.7062979
[323] 0.7061752 0.7060520 0.7059284 0.7058044 0.7056801 0.7055553 0.7054301
[330] 0.7053045 0.7051785 0.7050521 0.7049253 0.7047981 0.7046705 0.7045425
[337] 0.7044142 0.7042854 0.7041562 0.7040266 0.7038966 0.7037663 0.7036355
[344] 0.7035043 0.7033728 0.7032408 0.7031085 0.7029757 0.7028426 0.7027091
[351] 0.7025752 0.7024409 0.7023062 0.7021711 0.7020357 0.7018998 0.7017636
[358] 0.7016269 0.7014899 0.7013525 0.7012147 0.7010766 0.7009380 0.7007991
[365] 0.7006598 0.7005201 0.7003800 0.7002395 0.7000987 0.6999575 0.6998159
[372] 0.6996739 0.6995315 0.6993888 0.6992457 0.6991022 0.6989584 0.6988141
[379] 0.6986695 0.6985245 0.6983792 0.6982334 0.6980873 0.6979409 0.6977940
[386] 0.6976468 0.6974992 0.6973513 0.6972030 0.6970543 0.6969052 0.6967558
[393] 0.6966060 0.6964559 0.6963053 0.6961545 0.6960032 0.6958516 0.6956996
[400] 0.6955473 0.6953946
> mx
[1] 0.7231576
> mxli
[1] -1.46
> 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/rcomp/tmp/1ymt41257883298.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/rcomp/tmp/2y0qr1257883298.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/rcomp/tmp/3ll2z1257883298.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/4hkap1257883298.tab") 
> 
> system("convert tmp/1ymt41257883298.ps tmp/1ymt41257883298.png")
> system("convert tmp/2y0qr1257883298.ps tmp/2y0qr1257883298.png")
> system("convert tmp/3ll2z1257883298.ps tmp/3ll2z1257883298.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.950   0.860   1.591