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(116.2,111.2,105.8,122.7,99.5,107.9,124.6,115.0,110.3,132.7,99.7,96.5,118.7,112.9,130.5,137.9,115.0,116.8,140.9,120.7,134.2,147.3,112.4,107.1,128.4,137.7,135.0,151.0,137.4,132.4,161.3,139.8,146.0,166.5,143.3,121.0,152.6,154.4,154.6,158.0,142.6,153.4,163.4,167.3,154.8,165.7,144.7,120.9,152.8,160.2,128.3,150.5,117.0,116.0,133.3,116.4,104.0,126.6,92.9,83.6)
> x <- c(121.6,118.8,114.0,111.5,97.2,102.5,113.4,109.8,104.9,126.1,80.0,96.8,117.2,112.3,117.3,111.1,102.2,104.3,122.9,107.6,121.3,131.5,89.0,104.4,128.9,135.9,133.3,121.3,120.5,120.4,137.9,126.1,133.2,151.1,105.0,119.0,140.4,156.6,137.1,122.7,125.8,139.3,134.9,149.2,132.3,149.0,117.2,119.6,152.0,149.4,127.3,114.1,102.1,107.7,104.4,102.1,96.0,109.3,90.0,83.9)
> #'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] 0.8244989 0.8247282 0.8249567 0.8251843 0.8254110 0.8256369 0.8258618
  [8] 0.8260860 0.8263092 0.8265316 0.8267531 0.8269737 0.8271935 0.8274124
 [15] 0.8276304 0.8278475 0.8280638 0.8282792 0.8284937 0.8287073 0.8289200
 [22] 0.8291319 0.8293429 0.8295529 0.8297621 0.8299704 0.8301779 0.8303844
 [29] 0.8305900 0.8307948 0.8309987 0.8312016 0.8314037 0.8316049 0.8318052
 [36] 0.8320046 0.8322031 0.8324006 0.8325973 0.8327931 0.8329880 0.8331820
 [43] 0.8333751 0.8335673 0.8337586 0.8339490 0.8341385 0.8343271 0.8345147
 [50] 0.8347015 0.8348873 0.8350723 0.8352563 0.8354395 0.8356217 0.8358030
 [57] 0.8359834 0.8361629 0.8363414 0.8365191 0.8366958 0.8368717 0.8370466
 [64] 0.8372206 0.8373937 0.8375658 0.8377371 0.8379074 0.8380768 0.8382453
 [71] 0.8384129 0.8385795 0.8387453 0.8389101 0.8390740 0.8392369 0.8393990
 [78] 0.8395601 0.8397203 0.8398796 0.8400379 0.8401954 0.8403519 0.8405074
 [85] 0.8406621 0.8408158 0.8409686 0.8411205 0.8412715 0.8414215 0.8415706
 [92] 0.8417188 0.8418660 0.8420123 0.8421577 0.8423022 0.8424457 0.8425883
 [99] 0.8427300 0.8428707 0.8430105 0.8431494 0.8432874 0.8434244 0.8435605
[106] 0.8436957 0.8438299 0.8439632 0.8440956 0.8442270 0.8443575 0.8444871
[113] 0.8446158 0.8447435 0.8448703 0.8449961 0.8451211 0.8452451 0.8453681
[120] 0.8454903 0.8456115 0.8457317 0.8458511 0.8459695 0.8460870 0.8462035
[127] 0.8463192 0.8464339 0.8465476 0.8466605 0.8467724 0.8468833 0.8469934
[134] 0.8471025 0.8472107 0.8473179 0.8474242 0.8475296 0.8476341 0.8477376
[141] 0.8478403 0.8479419 0.8480427 0.8481425 0.8482414 0.8483394 0.8484364
[148] 0.8485326 0.8486277 0.8487220 0.8488154 0.8489078 0.8489993 0.8490898
[155] 0.8491795 0.8492682 0.8493560 0.8494429 0.8495288 0.8496138 0.8496979
[162] 0.8497811 0.8498634 0.8499447 0.8500251 0.8501046 0.8501832 0.8502609
[169] 0.8503376 0.8504135 0.8504884 0.8505624 0.8506354 0.8507076 0.8507788
[176] 0.8508492 0.8509186 0.8509871 0.8510547 0.8511213 0.8511871 0.8512519
[183] 0.8513159 0.8513789 0.8514410 0.8515022 0.8515625 0.8516219 0.8516804
[190] 0.8517380 0.8517947 0.8518505 0.8519053 0.8519593 0.8520123 0.8520645
[197] 0.8521157 0.8521661 0.8522156 0.8522641 0.8523118 0.8523585 0.8524044
[204] 0.8524493 0.8524934 0.8525366 0.8525789 0.8526202 0.8526607 0.8527003
[211] 0.8527390 0.8527769 0.8528138 0.8528498 0.8528850 0.8529193 0.8529526
[218] 0.8529851 0.8530167 0.8530475 0.8530773 0.8531063 0.8531344 0.8531616
[225] 0.8531879 0.8532133 0.8532379 0.8532616 0.8532844 0.8533064 0.8533275
[232] 0.8533477 0.8533670 0.8533854 0.8534030 0.8534198 0.8534356 0.8534506
[239] 0.8534647 0.8534780 0.8534904 0.8535019 0.8535126 0.8535224 0.8535314
[246] 0.8535395 0.8535467 0.8535531 0.8535586 0.8535633 0.8535671 0.8535701
[253] 0.8535722 0.8535735 0.8535739 0.8535735 0.8535723 0.8535702 0.8535672
[260] 0.8535634 0.8535588 0.8535533 0.8535470 0.8535398 0.8535318 0.8535230
[267] 0.8535134 0.8535029 0.8534916 0.8534794 0.8534664 0.8534526 0.8534380
[274] 0.8534225 0.8534062 0.8533891 0.8533712 0.8533524 0.8533329 0.8533125
[281] 0.8532913 0.8532693 0.8532464 0.8532228 0.8531983 0.8531730 0.8531470
[288] 0.8531201 0.8530924 0.8530639 0.8530346 0.8530045 0.8529736 0.8529419
[295] 0.8529094 0.8528761 0.8528420 0.8528071 0.8527714 0.8527349 0.8526976
[302] 0.8526596 0.8526207 0.8525811 0.8525407 0.8524995 0.8524575 0.8524147
[309] 0.8523712 0.8523269 0.8522818 0.8522359 0.8521893 0.8521418 0.8520937
[316] 0.8520447 0.8519950 0.8519445 0.8518932 0.8518412 0.8517884 0.8517349
[323] 0.8516805 0.8516255 0.8515697 0.8515131 0.8514558 0.8513977 0.8513388
[330] 0.8512793 0.8512189 0.8511578 0.8510960 0.8510335 0.8509701 0.8509061
[337] 0.8508413 0.8507758 0.8507095 0.8506425 0.8505748 0.8505063 0.8504372
[344] 0.8503672 0.8502966 0.8502252 0.8501531 0.8500803 0.8500068 0.8499325
[351] 0.8498575 0.8497818 0.8497054 0.8496283 0.8495505 0.8494719 0.8493927
[358] 0.8493127 0.8492321 0.8491507 0.8490686 0.8489859 0.8489024 0.8488182
[365] 0.8487334 0.8486478 0.8485616 0.8484746 0.8483870 0.8482987 0.8482097
[372] 0.8481200 0.8480296 0.8479385 0.8478468 0.8477544 0.8476613 0.8475675
[379] 0.8474731 0.8473780 0.8472822 0.8471857 0.8470886 0.8469908 0.8468924
[386] 0.8467932 0.8466935 0.8465930 0.8464919 0.8463902 0.8462878 0.8461847
[393] 0.8460810 0.8459766 0.8458716 0.8457660 0.8456597 0.8455527 0.8454451
[400] 0.8453369 0.8452280
> mx
[1] 0.853574
> mxli
[1] 0.54
> 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/1o8251258036061.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/2e4fn1258036061.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/3eury1258036061.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/4cg3d1258036061.tab") 
> 
> system("convert tmp/1o8251258036061.ps tmp/1o8251258036061.png")
> system("convert tmp/2e4fn1258036061.ps tmp/2e4fn1258036061.png")
> system("convert tmp/3eury1258036061.ps tmp/3eury1258036061.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.910   0.780   1.573