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)
> 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)
> #'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] 0.6245425 0.6245409 0.6245389 0.6245367 0.6245341 0.6245311 0.6245279
  [8] 0.6245243 0.6245204 0.6245161 0.6245116 0.6245067 0.6245014 0.6244959
 [15] 0.6244900 0.6244837 0.6244772 0.6244703 0.6244631 0.6244556 0.6244477
 [22] 0.6244395 0.6244310 0.6244221 0.6244129 0.6244034 0.6243935 0.6243833
 [29] 0.6243728 0.6243620 0.6243508 0.6243393 0.6243274 0.6243152 0.6243027
 [36] 0.6242899 0.6242767 0.6242632 0.6242494 0.6242352 0.6242207 0.6242059
 [43] 0.6241907 0.6241752 0.6241594 0.6241432 0.6241267 0.6241099 0.6240927
 [50] 0.6240752 0.6240573 0.6240392 0.6240207 0.6240018 0.6239827 0.6239632
 [57] 0.6239433 0.6239231 0.6239026 0.6238818 0.6238606 0.6238391 0.6238173
 [64] 0.6237951 0.6237726 0.6237497 0.6237265 0.6237030 0.6236792 0.6236550
 [71] 0.6236304 0.6236056 0.6235804 0.6235549 0.6235290 0.6235028 0.6234762
 [78] 0.6234494 0.6234222 0.6233946 0.6233667 0.6233385 0.6233100 0.6232811
 [85] 0.6232519 0.6232223 0.6231924 0.6231622 0.6231316 0.6231007 0.6230694
 [92] 0.6230379 0.6230060 0.6229737 0.6229411 0.6229082 0.6228749 0.6228413
 [99] 0.6228074 0.6227731 0.6227385 0.6227036 0.6226683 0.6226327 0.6225968
[106] 0.6225605 0.6225238 0.6224869 0.6224496 0.6224119 0.6223740 0.6223357
[113] 0.6222970 0.6222580 0.6222187 0.6221791 0.6221391 0.6220987 0.6220581
[120] 0.6220171 0.6219757 0.6219341 0.6218921 0.6218497 0.6218070 0.6217640
[127] 0.6217206 0.6216769 0.6216329 0.6215885 0.6215438 0.6214988 0.6214534
[134] 0.6214077 0.6213616 0.6213152 0.6212685 0.6212215 0.6211741 0.6211263
[141] 0.6210783 0.6210298 0.6209811 0.6209320 0.6208826 0.6208328 0.6207828
[148] 0.6207323 0.6206816 0.6206305 0.6205790 0.6205273 0.6204752 0.6204227
[155] 0.6203699 0.6203168 0.6202634 0.6202096 0.6201555 0.6201010 0.6200462
[162] 0.6199911 0.6199356 0.6198798 0.6198237 0.6197672 0.6197104 0.6196533
[169] 0.6195958 0.6195380 0.6194798 0.6194214 0.6193625 0.6193034 0.6192439
[176] 0.6191841 0.6191239 0.6190634 0.6190026 0.6189415 0.6188800 0.6188181
[183] 0.6187560 0.6186935 0.6186307 0.6185675 0.6185040 0.6184402 0.6183760
[190] 0.6183115 0.6182467 0.6181815 0.6181160 0.6180502 0.6179840 0.6179175
[197] 0.6178507 0.6177836 0.6177161 0.6176482 0.6175801 0.6175116 0.6174428
[204] 0.6173736 0.6173041 0.6172343 0.6171642 0.6170937 0.6170229 0.6169517
[211] 0.6168802 0.6168084 0.6167363 0.6166638 0.6165910 0.6165179 0.6164444
[218] 0.6163706 0.6162965 0.6162221 0.6161473 0.6160722 0.6159967 0.6159210
[225] 0.6158449 0.6157684 0.6156917 0.6156146 0.6155372 0.6154594 0.6153814
[232] 0.6153030 0.6152242 0.6151452 0.6150658 0.6149861 0.6149060 0.6148257
[239] 0.6147450 0.6146640 0.6145826 0.6145009 0.6144189 0.6143366 0.6142539
[246] 0.6141710 0.6140877 0.6140040 0.6139201 0.6138358 0.6137512 0.6136662
[253] 0.6135810 0.6134954 0.6134095 0.6133232 0.6132367 0.6131498 0.6130626
[260] 0.6129751 0.6128872 0.6127990 0.6127105 0.6126217 0.6125326 0.6124431
[267] 0.6123533 0.6122632 0.6121728 0.6120820 0.6119909 0.6118995 0.6118078
[274] 0.6117158 0.6116234 0.6115307 0.6114377 0.6113444 0.6112508 0.6111568
[281] 0.6110625 0.6109679 0.6108730 0.6107777 0.6106822 0.6105863 0.6104901
[288] 0.6103936 0.6102968 0.6101996 0.6101022 0.6100044 0.6099063 0.6098079
[295] 0.6097091 0.6096101 0.6095107 0.6094110 0.6093110 0.6092107 0.6091101
[302] 0.6090091 0.6089079 0.6088063 0.6087044 0.6086022 0.6084997 0.6083969
[309] 0.6082938 0.6081903 0.6080865 0.6079825 0.6078781 0.6077734 0.6076684
[316] 0.6075630 0.6074574 0.6073515 0.6072452 0.6071386 0.6070318 0.6069246
[323] 0.6068171 0.6067093 0.6066012 0.6064927 0.6063840 0.6062750 0.6061656
[330] 0.6060560 0.6059460 0.6058357 0.6057252 0.6056143 0.6055031 0.6053916
[337] 0.6052798 0.6051677 0.6050553 0.6049426 0.6048295 0.6047162 0.6046026
[344] 0.6044886 0.6043744 0.6042599 0.6041450 0.6040299 0.6039144 0.6037987
[351] 0.6036826 0.6035663 0.6034496 0.6033327 0.6032154 0.6030979 0.6029800
[358] 0.6028619 0.6027434 0.6026247 0.6025056 0.6023863 0.6022666 0.6021467
[365] 0.6020264 0.6019059 0.6017851 0.6016639 0.6015425 0.6014208 0.6012988
[372] 0.6011764 0.6010538 0.6009309 0.6008077 0.6006842 0.6005605 0.6004364
[379] 0.6003120 0.6001873 0.6000624 0.5999371 0.5998116 0.5996858 0.5995597
[386] 0.5994332 0.5993065 0.5991795 0.5990523 0.5989247 0.5987968 0.5986687
[393] 0.5985403 0.5984115 0.5982825 0.5981532 0.5980236 0.5978938 0.5977636
[400] 0.5976332 0.5975025
> mx
[1] 0.6245425
> 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/1aa0f1257259144.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/2d1bk1257259144.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/3xbu51257259144.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/4xv3z1257259144.tab") 
> 
> system("convert tmp/1aa0f1257259144.ps tmp/1aa0f1257259144.png")
> system("convert tmp/2d1bk1257259144.ps tmp/2d1bk1257259144.png")
> system("convert tmp/3xbu51257259144.ps tmp/3xbu51257259144.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.775   0.487   0.941