R version 2.7.0 (2008-04-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(78.4,114.6,113.3,117.0,99.6,99.4,101.9,115.2,108.5,113.8,121.0,92.2,90.2,101.5,126.6,93.9,89.8,93.4,101.5,110.4,105.9,108.4,113.9,86.1,69.4,101.2,100.5,98.0,106.6,90.1,96.9,125.9,112.0,100.0,123.9,79.8,83.4,113.6,112.9,104.0,109.9,99.0,106.3,128.9,111.1,102.9,130.0,87.0,87.5,117.6,103.4,110.8,112.6,102.5,112.4,135.6,105.1,127.7,137.0,91.0,90.5,122.4,123.3,124.3,120.0,118.1,119.0,142.7,123.6,129.6,151.6,110.4,99.2,130.5,136.2,129.7,128.0,121.6,135.8,143.8,147.5,136.2,156.6,123.3,100.4)
> x <- c(97.8,107.4,117.5,105.6,97.4,99.5,98.0,104.3,100.6,101.1,103.9,96.9,95.5,108.4,117.0,103.8,100.8,110.6,104.0,112.6,107.3,98.9,109.8,104.9,102.2,123.9,124.9,112.7,121.9,100.6,104.3,120.4,107.5,102.9,125.6,107.5,108.8,128.4,121.1,119.5,128.7,108.7,105.5,119.8,111.3,110.6,120.1,97.5,107.7,127.3,117.2,119.8,116.2,111.0,112.4,130.6,109.1,118.8,123.9,101.6,112.8,128.0,129.6,125.8,119.5,115.7,113.6,129.7,112.0,116.8,127.0,112.1,114.2,121.1,131.6,125.0,120.4,117.7,117.5,120.6,127.5,112.3,124.5,115.2,105.4)
> #'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] 0.6797271 0.6797685 0.6798099 0.6798511 0.6798922 0.6799331 0.6799739
  [8] 0.6800146 0.6800551 0.6800956 0.6801359 0.6801760 0.6802160 0.6802559
 [15] 0.6802957 0.6803353 0.6803748 0.6804142 0.6804534 0.6804925 0.6805315
 [22] 0.6805703 0.6806090 0.6806476 0.6806861 0.6807244 0.6807625 0.6808006
 [29] 0.6808385 0.6808763 0.6809139 0.6809514 0.6809888 0.6810261 0.6810632
 [36] 0.6811002 0.6811370 0.6811737 0.6812103 0.6812468 0.6812831 0.6813193
 [43] 0.6813553 0.6813912 0.6814270 0.6814627 0.6814982 0.6815336 0.6815688
 [50] 0.6816039 0.6816389 0.6816738 0.6817085 0.6817431 0.6817775 0.6818118
 [57] 0.6818460 0.6818800 0.6819140 0.6819477 0.6819814 0.6820149 0.6820483
 [64] 0.6820815 0.6821146 0.6821476 0.6821804 0.6822131 0.6822457 0.6822781
 [71] 0.6823104 0.6823426 0.6823746 0.6824065 0.6824382 0.6824699 0.6825013
 [78] 0.6825327 0.6825639 0.6825950 0.6826259 0.6826568 0.6826874 0.6827180
 [85] 0.6827484 0.6827786 0.6828088 0.6828388 0.6828686 0.6828984 0.6829280
 [92] 0.6829574 0.6829867 0.6830159 0.6830450 0.6830739 0.6831027 0.6831313
 [99] 0.6831598 0.6831882 0.6832164 0.6832445 0.6832725 0.6833003 0.6833280
[106] 0.6833555 0.6833830 0.6834102 0.6834374 0.6834644 0.6834913 0.6835180
[113] 0.6835446 0.6835711 0.6835974 0.6836236 0.6836496 0.6836756 0.6837013
[120] 0.6837270 0.6837525 0.6837779 0.6838031 0.6838282 0.6838531 0.6838780
[127] 0.6839027 0.6839272 0.6839516 0.6839759 0.6840000 0.6840240 0.6840479
[134] 0.6840716 0.6840952 0.6841187 0.6841420 0.6841652 0.6841882 0.6842111
[141] 0.6842339 0.6842565 0.6842790 0.6843014 0.6843236 0.6843457 0.6843676
[148] 0.6843894 0.6844111 0.6844326 0.6844540 0.6844753 0.6844964 0.6845173
[155] 0.6845382 0.6845589 0.6845795 0.6845999 0.6846202 0.6846403 0.6846604
[162] 0.6846802 0.6847000 0.6847196 0.6847391 0.6847584 0.6847776 0.6847966
[169] 0.6848155 0.6848343 0.6848530 0.6848715 0.6848898 0.6849081 0.6849261
[176] 0.6849441 0.6849619 0.6849796 0.6849971 0.6850145 0.6850318 0.6850489
[183] 0.6850659 0.6850827 0.6850994 0.6851160 0.6851324 0.6851487 0.6851649
[190] 0.6851809 0.6851968 0.6852125 0.6852281 0.6852436 0.6852589 0.6852741
[197] 0.6852892 0.6853041 0.6853189 0.6853335 0.6853480 0.6853624 0.6853766
[204] 0.6853907 0.6854046 0.6854184 0.6854321 0.6854456 0.6854590 0.6854723
[211] 0.6854854 0.6854984 0.6855112 0.6855239 0.6855365 0.6855489 0.6855612
[218] 0.6855733 0.6855854 0.6855972 0.6856090 0.6856206 0.6856320 0.6856433
[225] 0.6856545 0.6856656 0.6856765 0.6856872 0.6856979 0.6857084 0.6857187
[232] 0.6857289 0.6857390 0.6857489 0.6857587 0.6857684 0.6857779 0.6857873
[239] 0.6857966 0.6858057 0.6858146 0.6858235 0.6858322 0.6858407 0.6858492
[246] 0.6858574 0.6858656 0.6858736 0.6858815 0.6858892 0.6858968 0.6859042
[253] 0.6859115 0.6859187 0.6859258 0.6859327 0.6859394 0.6859460 0.6859525
[260] 0.6859589 0.6859651 0.6859712 0.6859771 0.6859829 0.6859886 0.6859941
[267] 0.6859995 0.6860047 0.6860098 0.6860148 0.6860196 0.6860243 0.6860289
[274] 0.6860333 0.6860376 0.6860417 0.6860457 0.6860496 0.6860533 0.6860569
[281] 0.6860604 0.6860637 0.6860669 0.6860699 0.6860728 0.6860756 0.6860782
[288] 0.6860807 0.6860831 0.6860853 0.6860874 0.6860893 0.6860911 0.6860928
[295] 0.6860943 0.6860957 0.6860970 0.6860981 0.6860991 0.6860999 0.6861006
[302] 0.6861012 0.6861016 0.6861019 0.6861021 0.6861021 0.6861020 0.6861017
[309] 0.6861014 0.6861008 0.6861002 0.6860994 0.6860984 0.6860974 0.6860962
[316] 0.6860948 0.6860933 0.6860917 0.6860900 0.6860881 0.6860860 0.6860839
[323] 0.6860816 0.6860791 0.6860766 0.6860738 0.6860710 0.6860680 0.6860649
[330] 0.6860616 0.6860582 0.6860547 0.6860511 0.6860473 0.6860433 0.6860392
[337] 0.6860350 0.6860307 0.6860262 0.6860216 0.6860168 0.6860119 0.6860069
[344] 0.6860018 0.6859965 0.6859910 0.6859855 0.6859798 0.6859739 0.6859680
[351] 0.6859618 0.6859556 0.6859492 0.6859427 0.6859361 0.6859293 0.6859223
[358] 0.6859153 0.6859081 0.6859008 0.6858933 0.6858857 0.6858780 0.6858701
[365] 0.6858621 0.6858540 0.6858457 0.6858373 0.6858288 0.6858201 0.6858113
[372] 0.6858023 0.6857932 0.6857840 0.6857747 0.6857652 0.6857556 0.6857458
[379] 0.6857359 0.6857259 0.6857158 0.6857055 0.6856951 0.6856845 0.6856738
[386] 0.6856630 0.6856520 0.6856410 0.6856297 0.6856184 0.6856069 0.6855952
[393] 0.6855835 0.6855716 0.6855596 0.6855474 0.6855351 0.6855227 0.6855101
[400] 0.6854974 0.6854846
> mx
[1] 0.6861021
> mxli
[1] 1.05
> 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/1odus1226503007.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/2yrut1226503007.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/3rsp31226503007.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/4q3sd1226503007.tab") 
> 
> system("convert tmp/1odus1226503007.ps tmp/1odus1226503007.png")
> system("convert tmp/2yrut1226503007.ps tmp/2yrut1226503007.png")
> system("convert tmp/3rsp31226503007.ps tmp/3rsp31226503007.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.865   0.825   1.992