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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> x <- c(2490,3266,3475,3127,2955,3870,2852,3142,3029,3180,2560,2733,2452,2553,2777,2520,2318,2873,2311,2395,2099,2268,2316,2181,2175,2627,2578,3090,2634,3225,2938,3174,3350,2588,2061,2691,2061,2918,2223,2651,2379,3146,2883,2768,3258,2839,2470,5072,1463,1600,2203,2013,2169,2640,2411,2528,2292,1988,1774,2279)
> #'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] -0.4232274 -0.4233402 -0.4234510 -0.4235599 -0.4236669 -0.4237720
  [7] -0.4238751 -0.4239763 -0.4240755 -0.4241728 -0.4242682 -0.4243615
 [13] -0.4244529 -0.4245423 -0.4246297 -0.4247151 -0.4247985 -0.4248799
 [19] -0.4249592 -0.4250366 -0.4251119 -0.4251851 -0.4252563 -0.4253255
 [25] -0.4253926 -0.4254576 -0.4255205 -0.4255814 -0.4256401 -0.4256968
 [31] -0.4257514 -0.4258038 -0.4258541 -0.4259023 -0.4259484 -0.4259923
 [37] -0.4260341 -0.4260737 -0.4261112 -0.4261465 -0.4261796 -0.4262106
 [43] -0.4262393 -0.4262659 -0.4262903 -0.4263124 -0.4263324 -0.4263501
 [49] -0.4263656 -0.4263789 -0.4263899 -0.4263987 -0.4264052 -0.4264095
 [55] -0.4264115 -0.4264113 -0.4264087 -0.4264039 -0.4263968 -0.4263874
 [61] -0.4263757 -0.4263617 -0.4263453 -0.4263267 -0.4263057 -0.4262824
 [67] -0.4262567 -0.4262287 -0.4261984 -0.4261657 -0.4261306 -0.4260932
 [73] -0.4260534 -0.4260112 -0.4259666 -0.4259197 -0.4258703 -0.4258186
 [79] -0.4257644 -0.4257078 -0.4256488 -0.4255874 -0.4255235 -0.4254572
 [85] -0.4253885 -0.4253173 -0.4252437 -0.4251676 -0.4250890 -0.4250080
 [91] -0.4249245 -0.4248385 -0.4247501 -0.4246591 -0.4245657 -0.4244697
 [97] -0.4243713 -0.4242703 -0.4241669 -0.4240609 -0.4239523 -0.4238413
[103] -0.4237277 -0.4236116 -0.4234929 -0.4233717 -0.4232480 -0.4231216
[109] -0.4229927 -0.4228613 -0.4227273 -0.4225907 -0.4224515 -0.4223097
[115] -0.4221654 -0.4220184 -0.4218689 -0.4217167 -0.4215620 -0.4214046
[121] -0.4212446 -0.4210820 -0.4209168 -0.4207489 -0.4205784 -0.4204053
[127] -0.4202295 -0.4200511 -0.4198701 -0.4196864 -0.4195000 -0.4193110
[133] -0.4191193 -0.4189250 -0.4187280 -0.4185283 -0.4183259 -0.4181209
[139] -0.4179131 -0.4177027 -0.4174896 -0.4172738 -0.4170553 -0.4168341
[145] -0.4166102 -0.4163836 -0.4161543 -0.4159223 -0.4156876 -0.4154501
[151] -0.4152099 -0.4149670 -0.4147214 -0.4144730 -0.4142220 -0.4139681
[157] -0.4137116 -0.4134523 -0.4131902 -0.4129254 -0.4126579 -0.4123876
[163] -0.4121146 -0.4118388 -0.4115603 -0.4112790 -0.4109949 -0.4107081
[169] -0.4104185 -0.4101261 -0.4098310 -0.4095331 -0.4092325 -0.4089291
[175] -0.4086228 -0.4083139 -0.4080021 -0.4076876 -0.4073702 -0.4070501
[181] -0.4067273 -0.4064016 -0.4060731 -0.4057419 -0.4054079 -0.4050711
[187] -0.4047315 -0.4043891 -0.4040439 -0.4036959 -0.4033452 -0.4029916
[193] -0.4026353 -0.4022761 -0.4019142 -0.4015494 -0.4011819 -0.4008116
[199] -0.4004385 -0.4000626 -0.3996839 -0.3993024 -0.3989181 -0.3985310
[205] -0.3981411 -0.3977484 -0.3973530 -0.3969547 -0.3965536 -0.3961498
[211] -0.3957432 -0.3953337 -0.3949215 -0.3945065 -0.3940887 -0.3936681
[217] -0.3932448 -0.3928186 -0.3923897 -0.3919580 -0.3915235 -0.3910862
[223] -0.3906462 -0.3902033 -0.3897578 -0.3893094 -0.3888583 -0.3884043
[229] -0.3879477 -0.3874882 -0.3870261 -0.3865611 -0.3860934 -0.3856229
[235] -0.3851497 -0.3846738 -0.3841950 -0.3837136 -0.3832294 -0.3827425
[241] -0.3822528 -0.3817604 -0.3812653 -0.3807675 -0.3802669 -0.3797636
[247] -0.3792576 -0.3787489 -0.3782375 -0.3777234 -0.3772066 -0.3766870
[253] -0.3761648 -0.3756400 -0.3751124 -0.3745821 -0.3740492 -0.3735136
[259] -0.3729754 -0.3724345 -0.3718909 -0.3713447 -0.3707958 -0.3702443
[265] -0.3696902 -0.3691334 -0.3685740 -0.3680120 -0.3674474 -0.3668802
[271] -0.3663104 -0.3657380 -0.3651630 -0.3645854 -0.3640052 -0.3634225
[277] -0.3628372 -0.3622493 -0.3616589 -0.3610660 -0.3604705 -0.3598725
[283] -0.3592719 -0.3586689 -0.3580633 -0.3574552 -0.3568447 -0.3562316
[289] -0.3556161 -0.3549981 -0.3543776 -0.3537547 -0.3531293 -0.3525015
[295] -0.3518712 -0.3512386 -0.3506035 -0.3499660 -0.3493261 -0.3486838
[301] -0.3480392 -0.3473921 -0.3467427 -0.3460910 -0.3454369 -0.3447805
[307] -0.3441217 -0.3434606 -0.3427972 -0.3421316 -0.3414636 -0.3407933
[313] -0.3401208 -0.3394461 -0.3387690 -0.3380898 -0.3374083 -0.3367246
[319] -0.3360387 -0.3353506 -0.3346603 -0.3339678 -0.3332732 -0.3325764
[325] -0.3318775 -0.3311764 -0.3304733 -0.3297680 -0.3290606 -0.3283512
[331] -0.3276396 -0.3269260 -0.3262104 -0.3254927 -0.3247730 -0.3240513
[337] -0.3233276 -0.3226019 -0.3218742 -0.3211446 -0.3204130 -0.3196795
[343] -0.3189441 -0.3182067 -0.3174674 -0.3167263 -0.3159833 -0.3152384
[349] -0.3144917 -0.3137431 -0.3129928 -0.3122406 -0.3114866 -0.3107309
[355] -0.3099734 -0.3092141 -0.3084531 -0.3076904 -0.3069260 -0.3061599
[361] -0.3053921 -0.3046226 -0.3038515 -0.3030788 -0.3023044 -0.3015285
[367] -0.3007509 -0.2999718 -0.2991911 -0.2984088 -0.2976250 -0.2968397
[373] -0.2960530 -0.2952647 -0.2944749 -0.2936837 -0.2928911 -0.2920970
[379] -0.2913015 -0.2905047 -0.2897064 -0.2889068 -0.2881058 -0.2873036
[385] -0.2865000 -0.2856951 -0.2848889 -0.2840814 -0.2832728 -0.2824628
[391] -0.2816517 -0.2808393 -0.2800258 -0.2792111 -0.2783953 -0.2775783
[397] -0.2767602 -0.2759410 -0.2751207 -0.2742993 -0.2734769
> 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/1af471229872815.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/2rau01229872815.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/3bggu1229872815.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/4q50g1229872815.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/55sy41229872815.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/6c3s31229872815.tab") 
> 
> system("convert tmp/1af471229872815.ps tmp/1af471229872815.png")
> system("convert tmp/2rau01229872815.ps tmp/2rau01229872815.png")
> system("convert tmp/3bggu1229872815.ps tmp/3bggu1229872815.png")
> system("convert tmp/4q50g1229872815.ps tmp/4q50g1229872815.png")
> system("convert tmp/55sy41229872815.ps tmp/55sy41229872815.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.090   0.776   1.425