R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(8,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7,7.1,7.2,7.1,6.9,7,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5,8,8.1)
> x <- c(11.1,10.9,10,9.2,9.2,9.5,9.6,9.5,9.1,8.9,9,10.1,10.3,10.2,9.6,9.2,9.3,9.4,9.4,9.2,9,9,9,9.8,10,9.8,9.3,9,9,9.1,9.1,9.1,9.2,8.8,8.3,8.4,8.1,7.7,7.9,7.9,8,7.9,7.6,7.1,6.8,6.5,6.9,8.2,8.7,8.3,7.9,7.5,7.8,8.3,8.4,8.2,7.7,7.2,7.3,8.1,8.5)
> #'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] 0.6128751 0.6128593 0.6128432 0.6128267 0.6128099 0.6127927 0.6127753
  [8] 0.6127575 0.6127394 0.6127209 0.6127021 0.6126830 0.6126635 0.6126438
 [15] 0.6126236 0.6126032 0.6125824 0.6125613 0.6125399 0.6125181 0.6124960
 [22] 0.6124736 0.6124508 0.6124277 0.6124043 0.6123805 0.6123564 0.6123320
 [29] 0.6123072 0.6122821 0.6122567 0.6122310 0.6122049 0.6121785 0.6121517
 [36] 0.6121246 0.6120972 0.6120695 0.6120414 0.6120130 0.6119842 0.6119551
 [43] 0.6119257 0.6118960 0.6118659 0.6118355 0.6118047 0.6117736 0.6117422
 [50] 0.6117105 0.6116784 0.6116460 0.6116132 0.6115801 0.6115467 0.6115130
 [57] 0.6114789 0.6114444 0.6114097 0.6113746 0.6113392 0.6113034 0.6112673
 [64] 0.6112309 0.6111942 0.6111571 0.6111197 0.6110819 0.6110438 0.6110054
 [71] 0.6109666 0.6109275 0.6108881 0.6108483 0.6108082 0.6107678 0.6107270
 [78] 0.6106859 0.6106445 0.6106027 0.6105606 0.6105182 0.6104754 0.6104323
 [85] 0.6103889 0.6103451 0.6103010 0.6102566 0.6102118 0.6101667 0.6101213
 [92] 0.6100755 0.6100294 0.6099829 0.6099362 0.6098890 0.6098416 0.6097938
 [99] 0.6097457 0.6096973 0.6096485 0.6095994 0.6095499 0.6095001 0.6094500
[106] 0.6093996 0.6093488 0.6092977 0.6092462 0.6091944 0.6091423 0.6090899
[113] 0.6090371 0.6089840 0.6089305 0.6088767 0.6088226 0.6087682 0.6087134
[120] 0.6086583 0.6086028 0.6085470 0.6084909 0.6084345 0.6083777 0.6083206
[127] 0.6082631 0.6082054 0.6081472 0.6080888 0.6080300 0.6079709 0.6079115
[134] 0.6078517 0.6077916 0.6077312 0.6076704 0.6076093 0.6075479 0.6074861
[141] 0.6074240 0.6073616 0.6072988 0.6072357 0.6071723 0.6071086 0.6070445
[148] 0.6069801 0.6069153 0.6068502 0.6067848 0.6067191 0.6066530 0.6065866
[155] 0.6065199 0.6064529 0.6063855 0.6063178 0.6062497 0.6061813 0.6061126
[162] 0.6060436 0.6059742 0.6059045 0.6058345 0.6057641 0.6056935 0.6056224
[169] 0.6055511 0.6054794 0.6054074 0.6053351 0.6052625 0.6051895 0.6051162
[176] 0.6050425 0.6049686 0.6048943 0.6048196 0.6047447 0.6046694 0.6045938
[183] 0.6045179 0.6044416 0.6043651 0.6042881 0.6042109 0.6041333 0.6040555
[190] 0.6039772 0.6038987 0.6038198 0.6037407 0.6036611 0.6035813 0.6035011
[197] 0.6034206 0.6033398 0.6032587 0.6031772 0.6030954 0.6030133 0.6029309
[204] 0.6028481 0.6027650 0.6026816 0.6025979 0.6025139 0.6024295 0.6023448
[211] 0.6022598 0.6021744 0.6020888 0.6020028 0.6019165 0.6018298 0.6017429
[218] 0.6016556 0.6015680 0.6014801 0.6013919 0.6013033 0.6012144 0.6011252
[225] 0.6010357 0.6009459 0.6008557 0.6007652 0.6006745 0.6005833 0.6004919
[232] 0.6004002 0.6003081 0.6002157 0.6001230 0.6000300 0.5999366 0.5998430
[239] 0.5997490 0.5996547 0.5995601 0.5994652 0.5993700 0.5992744 0.5991785
[246] 0.5990824 0.5989859 0.5988890 0.5987919 0.5986945 0.5985967 0.5984986
[253] 0.5984002 0.5983015 0.5982025 0.5981032 0.5980036 0.5979036 0.5978033
[260] 0.5977028 0.5976019 0.5975007 0.5973991 0.5972973 0.5971952 0.5970927
[267] 0.5969900 0.5968869 0.5967835 0.5966798 0.5965759 0.5964715 0.5963669
[274] 0.5962620 0.5961568 0.5960512 0.5959454 0.5958392 0.5957328 0.5956260
[281] 0.5955189 0.5954115 0.5953038 0.5951958 0.5950875 0.5949789 0.5948700
[288] 0.5947608 0.5946513 0.5945414 0.5944313 0.5943209 0.5942101 0.5940991
[295] 0.5939877 0.5938761 0.5937641 0.5936519 0.5935393 0.5934265 0.5933133
[302] 0.5931999 0.5930861 0.5929720 0.5928577 0.5927430 0.5926280 0.5925128
[309] 0.5923972 0.5922814 0.5921652 0.5920488 0.5919320 0.5918150 0.5916976
[316] 0.5915800 0.5914620 0.5913438 0.5912253 0.5911064 0.5909873 0.5908679
[323] 0.5907482 0.5906282 0.5905079 0.5903873 0.5902664 0.5901452 0.5900237
[330] 0.5899019 0.5897799 0.5896575 0.5895349 0.5894120 0.5892887 0.5891652
[337] 0.5890414 0.5889173 0.5887929 0.5886682 0.5885433 0.5884180 0.5882925
[344] 0.5881667 0.5880405 0.5879141 0.5877875 0.5876605 0.5875332 0.5874057
[351] 0.5872778 0.5871497 0.5870213 0.5868926 0.5867637 0.5866344 0.5865049
[358] 0.5863750 0.5862449 0.5861145 0.5859839 0.5858529 0.5857217 0.5855902
[365] 0.5854584 0.5853263 0.5851940 0.5850613 0.5849284 0.5847952 0.5846618
[372] 0.5845280 0.5843940 0.5842597 0.5841251 0.5839903 0.5838551 0.5837197
[379] 0.5835841 0.5834481 0.5833119 0.5831754 0.5830386 0.5829015 0.5827642
[386] 0.5826266 0.5824888 0.5823506 0.5822122 0.5820735 0.5819346 0.5817953
[393] 0.5816558 0.5815161 0.5813761 0.5812358 0.5810952 0.5809543 0.5808132
[400] 0.5806719 0.5805302
> mx
[1] 0.6128751
> 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/19axy1258116299.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/2kg9r1258116299.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/3zuyy1258116299.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/491wv1258116299.tab") 
> 
> system("convert tmp/19axy1258116299.ps tmp/19axy1258116299.png")
> system("convert tmp/2kg9r1258116299.ps tmp/2kg9r1258116299.png")
> system("convert tmp/3zuyy1258116299.ps tmp/3zuyy1258116299.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.795   0.517   1.669