R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(26,20,19,19,20,25,25,22,26,22,17,22,19,24,26,21,13,26,20,22,14,21,7,23,17,25,25,19,20,23,22,22,21,15,20,22,18,20,28,22,18,23,20,25,26,15,17,23,21,13,18,19,22,16,24,18,20,24,14,22,24,18,21,23,17,22,24,21,22,16,21,23,22,24,24,16,16,21,26,15,25,18,23,20,17,25,24,17,19,20,15,27,22,23,16,19,25,19,19,26,21,20,24,22,20,18,18,24,24,22,23,22,20,18,25,18,16,20,19,15,19,19,16,17,28,23,25,20,17,23,16,23,11,18,24,23,21,16,24,23,18,20,9,24,25,20,21,25,22,21,21,22,27,24,24,21,18,16,22,20,18,20)
> #'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]  1.123140e-02  1.102219e-02  1.081273e-02  1.060304e-02  1.039312e-02
  [6]  1.018297e-02  9.972594e-03  9.762004e-03  9.551203e-03  9.340195e-03
 [11]  9.128987e-03  8.917583e-03  8.705989e-03  8.494212e-03  8.282255e-03
 [16]  8.070125e-03  7.857827e-03  7.645368e-03  7.432751e-03  7.219984e-03
 [21]  7.007072e-03  6.794021e-03  6.580836e-03  6.367523e-03  6.154088e-03
 [26]  5.940537e-03  5.726876e-03  5.513110e-03  5.299246e-03  5.085289e-03
 [31]  4.871245e-03  4.657121e-03  4.442922e-03  4.228654e-03  4.014323e-03
 [36]  3.799936e-03  3.585498e-03  3.371015e-03  3.156494e-03  2.941940e-03
 [41]  2.727359e-03  2.512759e-03  2.298144e-03  2.083521e-03  1.868896e-03
 [46]  1.654275e-03  1.439664e-03  1.225069e-03  1.010497e-03  7.959529e-04
 [51]  5.814438e-04  3.669755e-04  1.525540e-04 -6.181449e-05 -2.761239e-04
 [56] -4.903682e-04 -7.045411e-04 -9.186367e-04 -1.132649e-03 -1.346572e-03
 [61] -1.560399e-03 -1.774124e-03 -1.987742e-03 -2.201247e-03 -2.414631e-03
 [66] -2.627890e-03 -2.841018e-03 -3.054008e-03 -3.266855e-03 -3.479552e-03
 [71] -3.692094e-03 -3.904475e-03 -4.116688e-03 -4.328730e-03 -4.540592e-03
 [76] -4.752270e-03 -4.963759e-03 -5.175051e-03 -5.386142e-03 -5.597026e-03
 [81] -5.807697e-03 -6.018150e-03 -6.228379e-03 -6.438378e-03 -6.648143e-03
 [86] -6.857667e-03 -7.066945e-03 -7.275973e-03 -7.484743e-03 -7.693252e-03
 [91] -7.901494e-03 -8.109463e-03 -8.317155e-03 -8.524564e-03 -8.731685e-03
 [96] -8.938514e-03 -9.145044e-03 -9.351271e-03 -9.557191e-03 -9.762798e-03
[101] -9.968087e-03 -1.017305e-02 -1.037769e-02 -1.058200e-02 -1.078597e-02
[106] -1.098960e-02 -1.119289e-02 -1.139582e-02 -1.159840e-02 -1.180062e-02
[111] -1.200248e-02 -1.220397e-02 -1.240508e-02 -1.260582e-02 -1.280618e-02
[116] -1.300616e-02 -1.320574e-02 -1.340494e-02 -1.360373e-02 -1.380213e-02
[121] -1.400012e-02 -1.419771e-02 -1.439488e-02 -1.459163e-02 -1.478797e-02
[126] -1.498389e-02 -1.517937e-02 -1.537443e-02 -1.556906e-02 -1.576324e-02
[131] -1.595699e-02 -1.615030e-02 -1.634316e-02 -1.653557e-02 -1.672752e-02
[136] -1.691902e-02 -1.711007e-02 -1.730065e-02 -1.749077e-02 -1.768042e-02
[141] -1.786960e-02 -1.805830e-02 -1.824654e-02 -1.843429e-02 -1.862157e-02
[146] -1.880836e-02 -1.899467e-02 -1.918049e-02 -1.936582e-02 -1.955066e-02
[151] -1.973500e-02 -1.991885e-02 -2.010220e-02 -2.028505e-02 -2.046740e-02
[156] -2.064924e-02 -2.083058e-02 -2.101141e-02 -2.119173e-02 -2.137154e-02
[161] -2.155083e-02 -2.172962e-02 -2.190788e-02 -2.208563e-02 -2.226286e-02
[166] -2.243957e-02 -2.261576e-02 -2.279142e-02 -2.296656e-02 -2.314118e-02
[171] -2.331527e-02 -2.348883e-02 -2.366186e-02 -2.383436e-02 -2.400634e-02
[176] -2.417778e-02 -2.434869e-02 -2.451906e-02 -2.468891e-02 -2.485821e-02
[181] -2.502699e-02 -2.519522e-02 -2.536293e-02 -2.553009e-02 -2.569672e-02
[186] -2.586281e-02 -2.602836e-02 -2.619337e-02 -2.635785e-02 -2.652179e-02
[191] -2.668518e-02 -2.684804e-02 -2.701036e-02 -2.717214e-02 -2.733338e-02
[196] -2.749408e-02 -2.765424e-02 -2.781386e-02 -2.797294e-02 -2.813148e-02
[201] -2.828948e-02 -2.844695e-02 -2.860387e-02 -2.876026e-02 -2.891611e-02
[206] -2.907142e-02 -2.922619e-02 -2.938043e-02 -2.953413e-02 -2.968729e-02
[211] -2.983992e-02 -2.999201e-02 -3.014357e-02 -3.029460e-02 -3.044509e-02
[216] -3.059505e-02 -3.074448e-02 -3.089337e-02 -3.104174e-02 -3.118958e-02
[221] -3.133688e-02 -3.148366e-02 -3.162992e-02 -3.177564e-02 -3.192084e-02
[226] -3.206552e-02 -3.220967e-02 -3.235330e-02 -3.249641e-02 -3.263900e-02
[231] -3.278107e-02 -3.292262e-02 -3.306366e-02 -3.320417e-02 -3.334418e-02
[236] -3.348366e-02 -3.362264e-02 -3.376110e-02 -3.389906e-02 -3.403650e-02
[241] -3.417344e-02 -3.430987e-02 -3.444579e-02 -3.458122e-02 -3.471613e-02
[246] -3.485055e-02 -3.498447e-02 -3.511788e-02 -3.525080e-02 -3.538323e-02
[251] -3.551516e-02 -3.564659e-02 -3.577754e-02 -3.590799e-02 -3.603796e-02
[256] -3.616744e-02 -3.629643e-02 -3.642493e-02 -3.655296e-02 -3.668050e-02
[261] -3.680756e-02 -3.693415e-02 -3.706026e-02 -3.718589e-02 -3.731105e-02
[266] -3.743573e-02 -3.755995e-02 -3.768369e-02 -3.780697e-02 -3.792978e-02
[271] -3.805213e-02 -3.817402e-02 -3.829544e-02 -3.841640e-02 -3.853691e-02
[276] -3.865696e-02 -3.877656e-02 -3.889570e-02 -3.901439e-02 -3.913263e-02
[281] -3.925042e-02 -3.936777e-02 -3.948467e-02 -3.960113e-02 -3.971715e-02
[286] -3.983273e-02 -3.994787e-02 -4.006257e-02 -4.017684e-02 -4.029067e-02
[291] -4.040407e-02 -4.051705e-02 -4.062959e-02 -4.074171e-02 -4.085341e-02
[296] -4.096468e-02 -4.107553e-02 -4.118596e-02 -4.129597e-02 -4.140557e-02
[301] -4.151475e-02 -4.162352e-02 -4.173187e-02 -4.183982e-02 -4.194736e-02
[306] -4.205449e-02 -4.216122e-02 -4.226755e-02 -4.237347e-02 -4.247899e-02
[311] -4.258412e-02 -4.268885e-02 -4.279319e-02 -4.289713e-02 -4.300068e-02
[316] -4.310385e-02 -4.320662e-02 -4.330901e-02 -4.341101e-02 -4.351263e-02
[321] -4.361387e-02 -4.371473e-02 -4.381521e-02 -4.391531e-02 -4.401504e-02
[326] -4.411440e-02 -4.421339e-02 -4.431200e-02 -4.441025e-02 -4.450813e-02
[331] -4.460564e-02 -4.470279e-02 -4.479958e-02 -4.489601e-02 -4.499208e-02
[336] -4.508779e-02 -4.518315e-02 -4.527815e-02 -4.537280e-02 -4.546710e-02
[341] -4.556105e-02 -4.565465e-02 -4.574791e-02 -4.584082e-02 -4.593338e-02
[346] -4.602561e-02 -4.611749e-02 -4.620904e-02 -4.630025e-02 -4.639112e-02
[351] -4.648166e-02 -4.657186e-02 -4.666174e-02 -4.675128e-02 -4.684050e-02
[356] -4.692939e-02 -4.701795e-02 -4.710619e-02 -4.719411e-02 -4.728170e-02
[361] -4.736898e-02 -4.745594e-02 -4.754258e-02 -4.762890e-02 -4.771491e-02
[366] -4.780061e-02 -4.788600e-02 -4.797108e-02 -4.805585e-02 -4.814031e-02
[371] -4.822446e-02 -4.830832e-02 -4.839186e-02 -4.847511e-02 -4.855806e-02
[376] -4.864070e-02 -4.872305e-02 -4.880511e-02 -4.888686e-02 -4.896833e-02
[381] -4.904950e-02 -4.913038e-02 -4.921097e-02 -4.929127e-02 -4.937129e-02
[386] -4.945101e-02 -4.953046e-02 -4.960962e-02 -4.968849e-02 -4.976709e-02
[391] -4.984540e-02 -4.992344e-02 -5.000120e-02 -5.007868e-02 -5.015589e-02
[396] -5.023283e-02 -5.030949e-02 -5.038588e-02 -5.046200e-02 -5.053785e-02
[401] -5.061343e-02
> mx
[1] 0.0112314
> mxli
[1] -2
> if (mxli != 0)
+ {
+ x1 <- (x^mxli - 1) / mxli
+ } else {
+ x1 <- log(x)
+ }
> postscript(file="/var/wessaorg/rcomp/tmp/1n7bk1321807888.ps",horizontal=F,onefile=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/wessaorg/rcomp/tmp/2kan41321807888.ps",horizontal=F,onefile=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/wessaorg/rcomp/tmp/3kecr1321807888.ps",horizontal=F,onefile=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/wessaorg/rcomp/tmp/4jads1321807888.ps",horizontal=F,onefile=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/wessaorg/rcomp/tmp/5uorf1321807888.ps",horizontal=F,onefile=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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/6w76x1321807888.tab") 
> 
> try(system("convert tmp/1n7bk1321807888.ps tmp/1n7bk1321807888.png",intern=TRUE))
character(0)
> try(system("convert tmp/2kan41321807888.ps tmp/2kan41321807888.png",intern=TRUE))
character(0)
> try(system("convert tmp/3kecr1321807888.ps tmp/3kecr1321807888.png",intern=TRUE))
character(0)
> try(system("convert tmp/4jads1321807888.ps tmp/4jads1321807888.png",intern=TRUE))
character(0)
> try(system("convert tmp/5uorf1321807888.ps tmp/5uorf1321807888.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.468   0.235   1.756