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

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> y <- c(4.62,4.64,4.57,4.49,4.48,4.5,4.52,4.63,4.75,4.99,5.28,5.33,5.26,5.14,4.99,4.85,4.83,4.83,4.88,4.91,4.93,4.93,4.95,4.95,4.88,4.78,4.61,4.46,4.42,4.43,4.41,4.4,4.36,4.36,4.38,4.4,4.37,4.32,4.18,4.04,4,3.97,3.94,3.93,3.89,3.89,3.88,3.9,3.9,3.95,4.02,4.07,4.17,4.27,4.32,4.38,4.45,4.71,4.96,4.95,4.78,4.78,4.68,4.65,4.64,4.74,4.76,4.61,4.75,4.73,4.68,4.68,4.75,4.79,4.81,4.92,4.99,5.18,5.29,5.48,5.66)
> x <- c(2.97,3.04,3.12,3.21,3.34,3.45,3.74,4.02,4.24,4.87,5.62,6.02,5.98,5.89,5.76,5.58,5.39,5.19,5.16,5.2,5.25,5.26,5.21,5.18,5.13,5.03,5.01,4.87,4.86,4.82,4.69,4.65,4.61,4.47,4.37,4.29,4.2,4.19,4.09,3.88,3.87,3.74,3.61,3.43,3.29,3.18,3.07,3.02,2.97,2.98,3.01,3.06,3.12,3.16,3.19,3.21,3.27,3.36,3.45,3.52,3.58,3.62,3.5,3.43,3.41,3.48,3.63,3.76,3.8,3.72,3.67,3.58,3.47,3.43,3.55,3.65,3.7,3.7,3.93,4.15,4.24)
> #'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] 0.5318634 0.5318403 0.5318171 0.5317938 0.5317704 0.5317469 0.5317233
  [8] 0.5316997 0.5316759 0.5316521 0.5316281 0.5316041 0.5315800 0.5315558
 [15] 0.5315315 0.5315071 0.5314826 0.5314581 0.5314334 0.5314087 0.5313839
 [22] 0.5313590 0.5313340 0.5313089 0.5312837 0.5312584 0.5312331 0.5312077
 [29] 0.5311822 0.5311565 0.5311309 0.5311051 0.5310792 0.5310533 0.5310273
 [36] 0.5310012 0.5309750 0.5309487 0.5309223 0.5308959 0.5308693 0.5308427
 [43] 0.5308160 0.5307893 0.5307624 0.5307355 0.5307084 0.5306813 0.5306541
 [50] 0.5306269 0.5305995 0.5305721 0.5305446 0.5305170 0.5304893 0.5304616
 [57] 0.5304338 0.5304058 0.5303779 0.5303498 0.5303217 0.5302934 0.5302651
 [64] 0.5302368 0.5302083 0.5301798 0.5301512 0.5301225 0.5300937 0.5300649
 [71] 0.5300360 0.5300070 0.5299779 0.5299488 0.5299196 0.5298903 0.5298609
 [78] 0.5298315 0.5298019 0.5297724 0.5297427 0.5297130 0.5296832 0.5296533
 [85] 0.5296233 0.5295933 0.5295632 0.5295330 0.5295028 0.5294725 0.5294421
 [92] 0.5294116 0.5293811 0.5293505 0.5293199 0.5292891 0.5292583 0.5292274
 [99] 0.5291965 0.5291655 0.5291344 0.5291033 0.5290721 0.5290408 0.5290094
[106] 0.5289780 0.5289465 0.5289150 0.5288833 0.5288517 0.5288199 0.5287881
[113] 0.5287562 0.5287243 0.5286922 0.5286602 0.5286280 0.5285958 0.5285635
[120] 0.5285312 0.5284988 0.5284663 0.5284338 0.5284012 0.5283686 0.5283359
[127] 0.5283031 0.5282702 0.5282374 0.5282044 0.5281714 0.5281383 0.5281051
[134] 0.5280719 0.5280387 0.5280054 0.5279720 0.5279385 0.5279050 0.5278715
[141] 0.5278379 0.5278042 0.5277704 0.5277366 0.5277028 0.5276689 0.5276349
[148] 0.5276009 0.5275668 0.5275327 0.5274985 0.5274642 0.5274299 0.5273956
[155] 0.5273612 0.5273267 0.5272922 0.5272576 0.5272230 0.5271883 0.5271535
[162] 0.5271188 0.5270839 0.5270490 0.5270141 0.5269790 0.5269440 0.5269089
[169] 0.5268737 0.5268385 0.5268032 0.5267679 0.5267326 0.5266971 0.5266617
[176] 0.5266262 0.5265906 0.5265550 0.5265193 0.5264836 0.5264478 0.5264120
[183] 0.5263761 0.5263402 0.5263043 0.5262683 0.5262322 0.5261961 0.5261600
[190] 0.5261238 0.5260875 0.5260512 0.5260149 0.5259785 0.5259421 0.5259056
[197] 0.5258691 0.5258325 0.5257959 0.5257592 0.5257225 0.5256858 0.5256490
[204] 0.5256122 0.5255753 0.5255384 0.5255014 0.5254644 0.5254274 0.5253903
[211] 0.5253531 0.5253159 0.5252787 0.5252415 0.5252042 0.5251668 0.5251294
[218] 0.5250920 0.5250545 0.5250170 0.5249795 0.5249419 0.5249043 0.5248666
[225] 0.5248289 0.5247911 0.5247533 0.5247155 0.5246776 0.5246397 0.5246018
[232] 0.5245638 0.5245258 0.5244877 0.5244496 0.5244115 0.5243733 0.5243351
[239] 0.5242969 0.5242586 0.5242203 0.5241819 0.5241435 0.5241051 0.5240666
[246] 0.5240281 0.5239896 0.5239510 0.5239124 0.5238738 0.5238351 0.5237964
[253] 0.5237576 0.5237189 0.5236800 0.5236412 0.5236023 0.5235634 0.5235244
[260] 0.5234855 0.5234464 0.5234074 0.5233683 0.5233292 0.5232900 0.5232509
[267] 0.5232117 0.5231724 0.5231331 0.5230938 0.5230545 0.5230151 0.5229757
[274] 0.5229363 0.5228968 0.5228573 0.5228178 0.5227782 0.5227386 0.5226990
[281] 0.5226593 0.5226197 0.5225799 0.5225402 0.5225004 0.5224606 0.5224208
[288] 0.5223809 0.5223410 0.5223011 0.5222612 0.5222212 0.5221812 0.5221412
[295] 0.5221011 0.5220610 0.5220209 0.5219807 0.5219406 0.5219004 0.5218601
[302] 0.5218199 0.5217796 0.5217393 0.5216989 0.5216585 0.5216181 0.5215777
[309] 0.5215373 0.5214968 0.5214563 0.5214158 0.5213752 0.5213346 0.5212940
[316] 0.5212534 0.5212127 0.5211720 0.5211313 0.5210905 0.5210498 0.5210090
[323] 0.5209682 0.5209273 0.5208864 0.5208455 0.5208046 0.5207637 0.5207227
[330] 0.5206817 0.5206407 0.5205996 0.5205586 0.5205175 0.5204763 0.5204352
[337] 0.5203940 0.5203528 0.5203116 0.5202703 0.5202291 0.5201878 0.5201465
[344] 0.5201051 0.5200637 0.5200223 0.5199809 0.5199395 0.5198980 0.5198565
[351] 0.5198150 0.5197735 0.5197319 0.5196903 0.5196487 0.5196071 0.5195655
[358] 0.5195238 0.5194821 0.5194403 0.5193986 0.5193568 0.5193150 0.5192732
[365] 0.5192314 0.5191895 0.5191476 0.5191057 0.5190638 0.5190218 0.5189798
[372] 0.5189378 0.5188958 0.5188537 0.5188117 0.5187696 0.5187274 0.5186853
[379] 0.5186431 0.5186009 0.5185587 0.5185165 0.5184742 0.5184319 0.5183896
[386] 0.5183473 0.5183050 0.5182626 0.5182202 0.5181778 0.5181353 0.5180928
[393] 0.5180504 0.5180078 0.5179653 0.5179227 0.5178802 0.5178376 0.5177949
[400] 0.5177523 0.5177096
> mx
[1] 0.5318634
> 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/1sulr1258034320.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/2j9fc1258034320.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/3zw9l1258034320.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/4qvrh1258034320.tab") 
> 
> system("convert tmp/1sulr1258034320.ps tmp/1sulr1258034320.png")
> system("convert tmp/2j9fc1258034320.ps tmp/2j9fc1258034320.png")
> system("convert tmp/3zw9l1258034320.ps tmp/3zw9l1258034320.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.241   0.808   1.390