R version 2.9.0 (2009-04-17)
Copyright (C) 2009 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(326011,328282,317480,317539,313737,312276,309391,302950,300316,304035,333476,337698,335932,323931,313927,314485,313218,309664,302963,298989,298423,301631,329765,335083,327616,309119,295916,291413,291542,284678,276475,272566,264981,263290,296806,303598,286994,276427,266424,267153,268381,262522,255542,253158,243803,250741,280445,285257,270976,261076,255603,260376,263903,264291,263276,262572,256167,264221,293860,300713)
> x <- c(286602,283042,276687,277915,277128,277103,275037,270150,267140,264993,287259,291186,292300,288186,281477,282656,280190,280408,276836,275216,274352,271311,289802,290726,292300,278506,269826,265861,269034,264176,255198,253353,246057,235372,258556,260993,254663,250643,243422,247105,248541,245039,237080,237085,225554,226839,247934,248333,246969,245098,246263,255765,264319,268347,273046,273963,267430,271993,292710,295881)
> #'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] 0.8175693 0.8176322 0.8176959 0.8177556 0.8178202 0.8178833 0.8179462
  [8] 0.8180078 0.8180705 0.8181323 0.8181959 0.8182574 0.8183192 0.8183806
 [15] 0.8184426 0.8185030 0.8185650 0.8186259 0.8186867 0.8187475 0.8188087
 [22] 0.8188695 0.8189300 0.8189904 0.8190508 0.8191112 0.8191715 0.8192317
 [29] 0.8192914 0.8193514 0.8194110 0.8194706 0.8195301 0.8195895 0.8196487
 [36] 0.8197079 0.8197669 0.8198257 0.8198846 0.8199433 0.8200019 0.8200603
 [43] 0.8201187 0.8201769 0.8202350 0.8202930 0.8203508 0.8204086 0.8204663
 [50] 0.8205238 0.8205813 0.8206386 0.8206958 0.8207528 0.8208098 0.8208667
 [57] 0.8209234 0.8209800 0.8210366 0.8210930 0.8211492 0.8212054 0.8212615
 [64] 0.8213174 0.8213732 0.8214289 0.8214845 0.8215400 0.8215954 0.8216506
 [71] 0.8217058 0.8217608 0.8218157 0.8218705 0.8219252 0.8219797 0.8220342
 [78] 0.8220885 0.8221427 0.8221969 0.8222508 0.8223047 0.8223585 0.8224121
 [85] 0.8224657 0.8225191 0.8225724 0.8226256 0.8226787 0.8227316 0.8227845
 [92] 0.8228372 0.8228898 0.8229423 0.8229947 0.8230470 0.8230992 0.8231512
 [99] 0.8232031 0.8232550 0.8233067 0.8233583 0.8234097 0.8234611 0.8235123
[106] 0.8235635 0.8236145 0.8236654 0.8237162 0.8237668 0.8238174 0.8238678
[113] 0.8239182 0.8239684 0.8240185 0.8240685 0.8241183 0.8241681 0.8242177
[120] 0.8242673 0.8243167 0.8243660 0.8244152 0.8244642 0.8245132 0.8245620
[127] 0.8246108 0.8246594 0.8247079 0.8247563 0.8248045 0.8248527 0.8249007
[134] 0.8249486 0.8249964 0.8250441 0.8250917 0.8251392 0.8251865 0.8252338
[141] 0.8252809 0.8253279 0.8253748 0.8254216 0.8254683 0.8255148 0.8255613
[148] 0.8256076 0.8256538 0.8256999 0.8257459 0.8257917 0.8258375 0.8258831
[155] 0.8259286 0.8259740 0.8260193 0.8260645 0.8261096 0.8261545 0.8261994
[162] 0.8262441 0.8262887 0.8263332 0.8263776 0.8264219 0.8264660 0.8265100
[169] 0.8265540 0.8265978 0.8266415 0.8266851 0.8267285 0.8267719 0.8268151
[176] 0.8268582 0.8269012 0.8269441 0.8269869 0.8270296 0.8270721 0.8271146
[183] 0.8271569 0.8271991 0.8272412 0.8272832 0.8273251 0.8273668 0.8274085
[190] 0.8274500 0.8274914 0.8275327 0.8275739 0.8276150 0.8276559 0.8276968
[197] 0.8277375 0.8277781 0.8278186 0.8278590 0.8278993 0.8279395 0.8279795
[204] 0.8280194 0.8280593 0.8280990 0.8281386 0.8281780 0.8282174 0.8282566
[211] 0.8282958 0.8283348 0.8283737 0.8284125 0.8284512 0.8284898 0.8285282
[218] 0.8285666 0.8286048 0.8286429 0.8286809 0.8287188 0.8287566 0.8287942
[225] 0.8288318 0.8288692 0.8289065 0.8289437 0.8289808 0.8290178 0.8290547
[232] 0.8290914 0.8291281 0.8291646 0.8292010 0.8292373 0.8292735 0.8293095
[239] 0.8293455 0.8293814 0.8294171 0.8294527 0.8294882 0.8295236 0.8295589
[246] 0.8295940 0.8296291 0.8296640 0.8296989 0.8297336 0.8297682 0.8298027
[253] 0.8298370 0.8298713 0.8299055 0.8299395 0.8299734 0.8300072 0.8300409
[260] 0.8300745 0.8301080 0.8301413 0.8301746 0.8302077 0.8302407 0.8302736
[267] 0.8303064 0.8303391 0.8303717 0.8304041 0.8304365 0.8304687 0.8305008
[274] 0.8305328 0.8305647 0.8305965 0.8306282 0.8306597 0.8306912 0.8307225
[281] 0.8307537 0.8307848 0.8308158 0.8308467 0.8308775 0.8309081 0.8309386
[288] 0.8309691 0.8309994 0.8310296 0.8310597 0.8310897 0.8311195 0.8311493
[295] 0.8311789 0.8312085 0.8312379 0.8312672 0.8312964 0.8313255 0.8313545
[302] 0.8313833 0.8314121 0.8314407 0.8314692 0.8314976 0.8315259 0.8315541
[309] 0.8315822 0.8316102 0.8316380 0.8316658 0.8316934 0.8317209 0.8317483
[316] 0.8317756 0.8318028 0.8318299 0.8318568 0.8318837 0.8319104 0.8319370
[323] 0.8319635 0.8319899 0.8320162 0.8320424 0.8320685 0.8320944 0.8321203
[330] 0.8321460 0.8321716 0.8321971 0.8322225 0.8322478 0.8322730 0.8322981
[337] 0.8323230 0.8323479 0.8323726 0.8323972 0.8324217 0.8324461 0.8324704
[344] 0.8324946 0.8325187 0.8325426 0.8325665 0.8325902 0.8326138 0.8326373
[351] 0.8326607 0.8326840 0.8327072 0.8327303 0.8327532 0.8327761 0.8327988
[358] 0.8328215 0.8328440 0.8328664 0.8328887 0.8329109 0.8329329 0.8329549
[365] 0.8329768 0.8329985 0.8330201 0.8330417 0.8330631 0.8330844 0.8331056
[372] 0.8331267 0.8331476 0.8331685 0.8331892 0.8332099 0.8332304 0.8332508
[379] 0.8332711 0.8332914 0.8333114 0.8333314 0.8333513 0.8333711 0.8333907
[386] 0.8334103 0.8334297 0.8334490 0.8334682 0.8334873 0.8335063 0.8335252
[393] 0.8335440 0.8335627 0.8335812 0.8335997 0.8336180 0.8336362 0.8336544
[400] 0.8336724 0.8336903
> mx
[1] 0.8336903
> 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/rcomp/tmp/15xjh1258559297.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/2jmjr1258559297.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/3m7yg1258559297.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/4yxd21258559297.tab") 
> 
> system("convert tmp/15xjh1258559297.ps tmp/15xjh1258559297.png")
> system("convert tmp/2jmjr1258559297.ps tmp/2jmjr1258559297.png")
> system("convert tmp/3m7yg1258559297.ps tmp/3m7yg1258559297.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.773   0.506   0.912