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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> x <- c(8.2,8.0,7.5,6.8,6.5,6.6,7.6,8.0,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7.0,7.1,7.2,7.1,6.9,7.0,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7)
> #'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(qnorm(ppoints(x), mean=0, sd=1),x1)
+ if (mx < c[i])
+ {
+ mx <- c[i]
+ mxli <- l[i]
+ }
+ }
> c
  [1] -0.4577087 -0.4577139 -0.4577190 -0.4577240 -0.4577289 -0.4577337
  [7] -0.4577385 -0.4577432 -0.4577478 -0.4577524 -0.4577568 -0.4577612
 [13] -0.4577655 -0.4577697 -0.4577738 -0.4577779 -0.4577818 -0.4577857
 [19] -0.4577896 -0.4577933 -0.4577969 -0.4578005 -0.4578040 -0.4578074
 [25] -0.4578108 -0.4578140 -0.4578172 -0.4578203 -0.4578233 -0.4578263
 [31] -0.4578291 -0.4578319 -0.4578346 -0.4578372 -0.4578398 -0.4578423
 [37] -0.4578446 -0.4578469 -0.4578492 -0.4578513 -0.4578534 -0.4578554
 [43] -0.4578573 -0.4578591 -0.4578609 -0.4578626 -0.4578642 -0.4578657
 [49] -0.4578671 -0.4578685 -0.4578698 -0.4578710 -0.4578721 -0.4578732
 [55] -0.4578742 -0.4578750 -0.4578759 -0.4578766 -0.4578773 -0.4578778
 [61] -0.4578784 -0.4578788 -0.4578791 -0.4578794 -0.4578796 -0.4578797
 [67] -0.4578797 -0.4578797 -0.4578796 -0.4578794 -0.4578791 -0.4578788
 [73] -0.4578783 -0.4578778 -0.4578773 -0.4578766 -0.4578759 -0.4578751
 [79] -0.4578742 -0.4578732 -0.4578722 -0.4578710 -0.4578698 -0.4578686
 [85] -0.4578672 -0.4578658 -0.4578643 -0.4578627 -0.4578610 -0.4578593
 [91] -0.4578575 -0.4578556 -0.4578536 -0.4578516 -0.4578495 -0.4578473
 [97] -0.4578450 -0.4578427 -0.4578402 -0.4578377 -0.4578352 -0.4578325
[103] -0.4578298 -0.4578270 -0.4578241 -0.4578211 -0.4578181 -0.4578150
[109] -0.4578118 -0.4578086 -0.4578052 -0.4578018 -0.4577984 -0.4577948
[115] -0.4577912 -0.4577875 -0.4577837 -0.4577798 -0.4577759 -0.4577719
[121] -0.4577678 -0.4577636 -0.4577594 -0.4577551 -0.4577507 -0.4577462
[127] -0.4577417 -0.4577371 -0.4577324 -0.4577277 -0.4577228 -0.4577179
[133] -0.4577129 -0.4577079 -0.4577028 -0.4576975 -0.4576923 -0.4576869
[139] -0.4576815 -0.4576760 -0.4576704 -0.4576648 -0.4576591 -0.4576533
[145] -0.4576474 -0.4576415 -0.4576354 -0.4576293 -0.4576232 -0.4576170
[151] -0.4576106 -0.4576043 -0.4575978 -0.4575913 -0.4575847 -0.4575780
[157] -0.4575713 -0.4575644 -0.4575575 -0.4575506 -0.4575435 -0.4575364
[163] -0.4575292 -0.4575220 -0.4575147 -0.4575073 -0.4574998 -0.4574922
[169] -0.4574846 -0.4574769 -0.4574692 -0.4574613 -0.4574534 -0.4574454
[175] -0.4574374 -0.4574293 -0.4574211 -0.4574128 -0.4574045 -0.4573961
[181] -0.4573876 -0.4573790 -0.4573704 -0.4573617 -0.4573529 -0.4573441
[187] -0.4573352 -0.4573262 -0.4573172 -0.4573080 -0.4572989 -0.4572896
[193] -0.4572803 -0.4572709 -0.4572614 -0.4572518 -0.4572422 -0.4572325
[199] -0.4572228 -0.4572129 -0.4572030 -0.4571931 -0.4571830 -0.4571729
[205] -0.4571628 -0.4571525 -0.4571422 -0.4571318 -0.4571213 -0.4571108
[211] -0.4571002 -0.4570895 -0.4570788 -0.4570680 -0.4570571 -0.4570462
[217] -0.4570352 -0.4570241 -0.4570129 -0.4570017 -0.4569904 -0.4569791
[223] -0.4569676 -0.4569561 -0.4569446 -0.4569329 -0.4569212 -0.4569095
[229] -0.4568976 -0.4568857 -0.4568737 -0.4568617 -0.4568496 -0.4568374
[235] -0.4568252 -0.4568128 -0.4568005 -0.4567880 -0.4567755 -0.4567629
[241] -0.4567502 -0.4567375 -0.4567247 -0.4567119 -0.4566989 -0.4566860
[247] -0.4566729 -0.4566598 -0.4566466 -0.4566333 -0.4566200 -0.4566066
[253] -0.4565931 -0.4565796 -0.4565660 -0.4565523 -0.4565386 -0.4565248
[259] -0.4565110 -0.4564970 -0.4564830 -0.4564690 -0.4564549 -0.4564407
[265] -0.4564264 -0.4564121 -0.4563977 -0.4563832 -0.4563687 -0.4563541
[271] -0.4563395 -0.4563248 -0.4563100 -0.4562951 -0.4562802 -0.4562652
[277] -0.4562502 -0.4562351 -0.4562199 -0.4562047 -0.4561894 -0.4561740
[283] -0.4561586 -0.4561431 -0.4561275 -0.4561119 -0.4560962 -0.4560804
[289] -0.4560646 -0.4560487 -0.4560328 -0.4560167 -0.4560007 -0.4559845
[295] -0.4559683 -0.4559521 -0.4559357 -0.4559193 -0.4559029 -0.4558863
[301] -0.4558698 -0.4558531 -0.4558364 -0.4558196 -0.4558028 -0.4557859
[307] -0.4557689 -0.4557519 -0.4557348 -0.4557176 -0.4557004 -0.4556831
[313] -0.4556658 -0.4556484 -0.4556309 -0.4556134 -0.4555958 -0.4555781
[319] -0.4555604 -0.4555427 -0.4555248 -0.4555069 -0.4554889 -0.4554709
[325] -0.4554528 -0.4554347 -0.4554165 -0.4553982 -0.4553799 -0.4553615
[331] -0.4553430 -0.4553245 -0.4553059 -0.4552873 -0.4552686 -0.4552498
[337] -0.4552310 -0.4552121 -0.4551932 -0.4551742 -0.4551551 -0.4551360
[343] -0.4551168 -0.4550976 -0.4550783 -0.4550589 -0.4550395 -0.4550200
[349] -0.4550004 -0.4549808 -0.4549612 -0.4549414 -0.4549217 -0.4549018
[355] -0.4548819 -0.4548619 -0.4548419 -0.4548218 -0.4548017 -0.4547815
[361] -0.4547612 -0.4547409 -0.4547206 -0.4547001 -0.4546796 -0.4546591
[367] -0.4546385 -0.4546178 -0.4545971 -0.4545763 -0.4545554 -0.4545345
[373] -0.4545136 -0.4544926 -0.4544715 -0.4544503 -0.4544292 -0.4544079
[379] -0.4543866 -0.4543652 -0.4543438 -0.4543223 -0.4543008 -0.4542792
[385] -0.4542575 -0.4542358 -0.4542141 -0.4541922 -0.4541704 -0.4541484
[391] -0.4541264 -0.4541044 -0.4540823 -0.4540601 -0.4540379 -0.4540156
[397] -0.4539933 -0.4539709 -0.4539485 -0.4539260 -0.4539034
> mx
[1] 0
> mxli
[1] -999
> if (mxli != 0)
+ {
+ x1 <- (x^mxli - 1) / mxli
+ } else {
+ x1 <- log(x)
+ }
> postscript(file="/var/www/html/rcomp/tmp/18y141257891938.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Normality Plot',xlab='Lambda',ylab='correlation')
> mtext(paste('Optimal Lambda =',mxli))
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/23afg1257891938.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3coeq1257891938.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x1,main='Histogram of Transformed Data',xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/4mzpu1257891938.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(x)
> qqline(x)
> grid()
> mtext('Original Data')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/5iug91257891938.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(x1)
> qqline(x1)
> grid()
> mtext('Transformed Data')
> 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 Normality 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',header=TRUE)
> a<-table.element(a,mxli)
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/651yt1257891938.tab") 
> 
> system("convert tmp/18y141257891938.ps tmp/18y141257891938.png")
> system("convert tmp/23afg1257891938.ps tmp/23afg1257891938.png")
> system("convert tmp/3coeq1257891938.ps tmp/3coeq1257891938.png")
> system("convert tmp/4mzpu1257891938.ps tmp/4mzpu1257891938.png")
> system("convert tmp/5iug91257891938.ps tmp/5iug91257891938.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.075   0.797   3.730