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(7.3,7.6,7.5,7.6,7.9,7.9,8.1,8.2,8,7.5,6.8,6.5,6.6,7.6,8,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7,7.1,7.2,7.1,6.9,7,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5)
> x <- c(7.9,9.1,9.4,9.4,9.1,9,9.3,9.9,9.8,9.3,8.3,8,8.5,10.4,11.1,10.9,10,9.2,9.2,9.5,9.6,9.5,9.1,8.9,9,10.1,10.3,10.2,9.6,9.2,9.3,9.4,9.4,9.2,9,9,9,9.8,10,9.8,9.3,9,9,9.1,9.1,9.1,9.2,8.8,8.3,8.4,8.1,7.7,7.9,7.9,8,7.9,7.6,7.1,6.8,6.5,6.9,8.2,8.7,8.3,7.9,7.5,7.8,8.3,8.4,8.2,7.7,7.2,7.3)
> #'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] 0.6624645 0.6624861 0.6625073 0.6625281 0.6625486 0.6625687 0.6625884
  [8] 0.6626077 0.6626266 0.6626452 0.6626633 0.6626811 0.6626985 0.6627155
 [15] 0.6627322 0.6627484 0.6627643 0.6627798 0.6627949 0.6628097 0.6628240
 [22] 0.6628380 0.6628515 0.6628647 0.6628776 0.6628900 0.6629020 0.6629137
 [29] 0.6629250 0.6629359 0.6629464 0.6629565 0.6629662 0.6629756 0.6629845
 [36] 0.6629931 0.6630013 0.6630091 0.6630165 0.6630236 0.6630302 0.6630365
 [43] 0.6630424 0.6630479 0.6630530 0.6630577 0.6630620 0.6630660 0.6630695
 [50] 0.6630727 0.6630755 0.6630778 0.6630799 0.6630815 0.6630827 0.6630835
 [57] 0.6630840 0.6630841 0.6630837 0.6630830 0.6630819 0.6630804 0.6630785
 [64] 0.6630763 0.6630736 0.6630706 0.6630671 0.6630633 0.6630591 0.6630545
 [71] 0.6630495 0.6630441 0.6630383 0.6630321 0.6630256 0.6630186 0.6630113
 [78] 0.6630035 0.6629954 0.6629869 0.6629780 0.6629687 0.6629590 0.6629490
 [85] 0.6629385 0.6629276 0.6629164 0.6629047 0.6628927 0.6628803 0.6628675
 [92] 0.6628543 0.6628407 0.6628267 0.6628123 0.6627975 0.6627823 0.6627668
 [99] 0.6627508 0.6627345 0.6627178 0.6627006 0.6626831 0.6626652 0.6626469
[106] 0.6626282 0.6626091 0.6625896 0.6625698 0.6625495 0.6625288 0.6625078
[113] 0.6624863 0.6624645 0.6624423 0.6624196 0.6623966 0.6623732 0.6623494
[120] 0.6623252 0.6623006 0.6622757 0.6622503 0.6622245 0.6621984 0.6621718
[127] 0.6621449 0.6621175 0.6620898 0.6620617 0.6620331 0.6620042 0.6619749
[134] 0.6619452 0.6619151 0.6618847 0.6618538 0.6618225 0.6617909 0.6617588
[141] 0.6617263 0.6616935 0.6616603 0.6616266 0.6615926 0.6615582 0.6615234
[148] 0.6614882 0.6614526 0.6614166 0.6613802 0.6613435 0.6613063 0.6612687
[155] 0.6612308 0.6611924 0.6611537 0.6611146 0.6610751 0.6610351 0.6609948
[162] 0.6609541 0.6609130 0.6608716 0.6608297 0.6607874 0.6607448 0.6607017
[169] 0.6606583 0.6606144 0.6605702 0.6605256 0.6604805 0.6604351 0.6603893
[176] 0.6603431 0.6602966 0.6602496 0.6602022 0.6601545 0.6601063 0.6600578
[183] 0.6600088 0.6599595 0.6599098 0.6598597 0.6598092 0.6597583 0.6597070
[190] 0.6596553 0.6596033 0.6595508 0.6594980 0.6594448 0.6593911 0.6593371
[197] 0.6592827 0.6592279 0.6591727 0.6591172 0.6590612 0.6590048 0.6589481
[204] 0.6588909 0.6588334 0.6587755 0.6587172 0.6586585 0.6585994 0.6585400
[211] 0.6584801 0.6584199 0.6583592 0.6582982 0.6582368 0.6581750 0.6581128
[218] 0.6580502 0.6579872 0.6579239 0.6578601 0.6577960 0.6577315 0.6576666
[225] 0.6576013 0.6575356 0.6574695 0.6574031 0.6573363 0.6572690 0.6572014
[232] 0.6571334 0.6570650 0.6569963 0.6569271 0.6568576 0.6567876 0.6567173
[239] 0.6566466 0.6565755 0.6565041 0.6564322 0.6563600 0.6562873 0.6562143
[246] 0.6561410 0.6560672 0.6559930 0.6559185 0.6558435 0.6557682 0.6556925
[253] 0.6556165 0.6555400 0.6554632 0.6553859 0.6553083 0.6552304 0.6551520
[260] 0.6550732 0.6549941 0.6549146 0.6548347 0.6547544 0.6546738 0.6545927
[267] 0.6545113 0.6544295 0.6543473 0.6542648 0.6541818 0.6540985 0.6540148
[274] 0.6539307 0.6538463 0.6537615 0.6536762 0.6535907 0.6535047 0.6534183
[281] 0.6533316 0.6532445 0.6531570 0.6530692 0.6529809 0.6528923 0.6528034
[288] 0.6527140 0.6526243 0.6525341 0.6524437 0.6523528 0.6522616 0.6521699
[295] 0.6520780 0.6519856 0.6518929 0.6517998 0.6517063 0.6516124 0.6515182
[302] 0.6514236 0.6513286 0.6512333 0.6511375 0.6510414 0.6509450 0.6508481
[309] 0.6507509 0.6506534 0.6505554 0.6504571 0.6503584 0.6502594 0.6501599
[316] 0.6500601 0.6499600 0.6498594 0.6497585 0.6496573 0.6495556 0.6494536
[323] 0.6493512 0.6492485 0.6491454 0.6490419 0.6489381 0.6488339 0.6487293
[330] 0.6486243 0.6485190 0.6484134 0.6483073 0.6482009 0.6480942 0.6479870
[337] 0.6478795 0.6477717 0.6476635 0.6475549 0.6474459 0.6473366 0.6472270
[344] 0.6471169 0.6470065 0.6468958 0.6467847 0.6466732 0.6465614 0.6464492
[351] 0.6463366 0.6462237 0.6461104 0.6459968 0.6458828 0.6457685 0.6456538
[358] 0.6455387 0.6454233 0.6453075 0.6451914 0.6450749 0.6449581 0.6448409
[365] 0.6447233 0.6446054 0.6444871 0.6443685 0.6442495 0.6441302 0.6440105
[372] 0.6438905 0.6437701 0.6436494 0.6435283 0.6434069 0.6432851 0.6431629
[379] 0.6430404 0.6429176 0.6427944 0.6426709 0.6425470 0.6424227 0.6422982
[386] 0.6421732 0.6420479 0.6419223 0.6417963 0.6416700 0.6415433 0.6414163
[393] 0.6412890 0.6411612 0.6410332 0.6409048 0.6407761 0.6406470 0.6405175
[400] 0.6403878 0.6402577
> mx
[1] 0.663084
> mxli
[1] -1.43
> 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/1b2wd1257422039.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/211rp1257422039.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/39awn1257422039.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/41v501257422039.tab") 
> 
> system("convert tmp/1b2wd1257422039.ps tmp/1b2wd1257422039.png")
> system("convert tmp/211rp1257422039.ps tmp/211rp1257422039.png")
> system("convert tmp/39awn1257422039.ps tmp/39awn1257422039.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.752   0.483   0.881