R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> y <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132)
> x <- c(1.262,1.743,1.964,3.258,4.966,4.944,5.907,5.561,5.321,3.582,1.757,1.894,1.442,2.238,2.179,3.218,5.139,4.990,4.914,6.084,5.672,3.548,1.793,2.086,1.376,2.202,2.683,3.303,5.202,5.231,4.880,7.998,4.977,3.531,2.025,2.205,1.504,2.090,2.702,2.939,4.500,6.208,6.415,5.657,5.964,3.163,1.997,2.422,1.507,1.992,2.487,3.490,4.647,5.594,5.611,5.788,6.204,3.013,1.931,2.549,1.580,2.111,2.192,3.601,4.665,4.876,5.813,5.589,5.331,3.075,2.002,2.306,1.594,2.467,2.222,3.607,4.685,4.962,5.770,5.480,5.000,3.228,1.993,2.288,1.351,2.218,2.461,3.028,4.784,4.975,4.607,6.249,4.809,3.157,1.910,2.228,1.169,2.154,2.249,2.687,4.359,5.382,4.459,6.398,4.596,3.024,1.887,2.070,1.511,2.059,2.635,2.867,4.403,5.720,4.502,5.749,5.627,2.846,1.762,2.429,1.579,2.146,2.462,3.695,4.831,5.134,6.250,5.760,6.249,2.917,1.741,2.359)
> #'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]  4.747123e-02  4.733538e-02  4.719884e-02  4.706161e-02  4.692370e-02
  [6]  4.678511e-02  4.664585e-02  4.650591e-02  4.636531e-02  4.622404e-02
 [11]  4.608211e-02  4.593952e-02  4.579628e-02  4.565238e-02  4.550784e-02
 [16]  4.536265e-02  4.521682e-02  4.507035e-02  4.492325e-02  4.477552e-02
 [21]  4.462717e-02  4.447819e-02  4.432860e-02  4.417839e-02  4.402758e-02
 [26]  4.387616e-02  4.372413e-02  4.357151e-02  4.341830e-02  4.326449e-02
 [31]  4.311011e-02  4.295514e-02  4.279959e-02  4.264348e-02  4.248679e-02
 [36]  4.232955e-02  4.217175e-02  4.201339e-02  4.185448e-02  4.169503e-02
 [41]  4.153504e-02  4.137452e-02  4.121346e-02  4.105188e-02  4.088978e-02
 [46]  4.072717e-02  4.056404e-02  4.040041e-02  4.023627e-02  4.007164e-02
 [51]  3.990652e-02  3.974091e-02  3.957483e-02  3.940826e-02  3.924123e-02
 [56]  3.907373e-02  3.890577e-02  3.873736e-02  3.856849e-02  3.839918e-02
 [61]  3.822944e-02  3.805926e-02  3.788865e-02  3.771761e-02  3.754617e-02
 [66]  3.737430e-02  3.720204e-02  3.702937e-02  3.685630e-02  3.668285e-02
 [71]  3.650901e-02  3.633479e-02  3.616020e-02  3.598524e-02  3.580992e-02
 [76]  3.563424e-02  3.545821e-02  3.528184e-02  3.510513e-02  3.492808e-02
 [81]  3.475071e-02  3.457301e-02  3.439500e-02  3.421668e-02  3.403805e-02
 [86]  3.385912e-02  3.367990e-02  3.350040e-02  3.332061e-02  3.314055e-02
 [91]  3.296022e-02  3.277962e-02  3.259877e-02  3.241766e-02  3.223631e-02
 [96]  3.205471e-02  3.187289e-02  3.169083e-02  3.150856e-02  3.132606e-02
[101]  3.114336e-02  3.096045e-02  3.077734e-02  3.059404e-02  3.041055e-02
[106]  3.022688e-02  3.004303e-02  2.985902e-02  2.967484e-02  2.949050e-02
[111]  2.930602e-02  2.912138e-02  2.893661e-02  2.875171e-02  2.856667e-02
[116]  2.838151e-02  2.819624e-02  2.801086e-02  2.782537e-02  2.763978e-02
[121]  2.745410e-02  2.726833e-02  2.708248e-02  2.689656e-02  2.671056e-02
[126]  2.652450e-02  2.633838e-02  2.615221e-02  2.596600e-02  2.577974e-02
[131]  2.559344e-02  2.540712e-02  2.522077e-02  2.503440e-02  2.484802e-02
[136]  2.466163e-02  2.447524e-02  2.428885e-02  2.410247e-02  2.391610e-02
[141]  2.372976e-02  2.354344e-02  2.335715e-02  2.317090e-02  2.298468e-02
[146]  2.279852e-02  2.261241e-02  2.242635e-02  2.224036e-02  2.205443e-02
[151]  2.186858e-02  2.168281e-02  2.149712e-02  2.131152e-02  2.112601e-02
[156]  2.094060e-02  2.075529e-02  2.057010e-02  2.038501e-02  2.020005e-02
[161]  2.001521e-02  1.983050e-02  1.964592e-02  1.946147e-02  1.927717e-02
[166]  1.909302e-02  1.890902e-02  1.872518e-02  1.854150e-02  1.835798e-02
[171]  1.817464e-02  1.799147e-02  1.780848e-02  1.762568e-02  1.744306e-02
[176]  1.726063e-02  1.707841e-02  1.689638e-02  1.671456e-02  1.653295e-02
[181]  1.635155e-02  1.617038e-02  1.598942e-02  1.580869e-02  1.562819e-02
[186]  1.544793e-02  1.526790e-02  1.508812e-02  1.490858e-02  1.472929e-02
[191]  1.455026e-02  1.437148e-02  1.419296e-02  1.401471e-02  1.383673e-02
[196]  1.365902e-02  1.348158e-02  1.330443e-02  1.312755e-02  1.295096e-02
[201]  1.277466e-02  1.259866e-02  1.242295e-02  1.224753e-02  1.207242e-02
[206]  1.189762e-02  1.172312e-02  1.154893e-02  1.137506e-02  1.120151e-02
[211]  1.102828e-02  1.085537e-02  1.068278e-02  1.051053e-02  1.033860e-02
[216]  1.016701e-02  9.995759e-03  9.824846e-03  9.654275e-03  9.484048e-03
[221]  9.314169e-03  9.144639e-03  8.975461e-03  8.806637e-03  8.638170e-03
[226]  8.470062e-03  8.302315e-03  8.134932e-03  7.967914e-03  7.801263e-03
[231]  7.634983e-03  7.469074e-03  7.303538e-03  7.138378e-03  6.973596e-03
[236]  6.809193e-03  6.645171e-03  6.481532e-03  6.318277e-03  6.155409e-03
[241]  5.992929e-03  5.830838e-03  5.669139e-03  5.507832e-03  5.346919e-03
[246]  5.186401e-03  5.026281e-03  4.866558e-03  4.707236e-03  4.548314e-03
[251]  4.389794e-03  4.231677e-03  4.073965e-03  3.916659e-03  3.759759e-03
[256]  3.603266e-03  3.447183e-03  3.291508e-03  3.136245e-03  2.981393e-03
[261]  2.826953e-03  2.672926e-03  2.519313e-03  2.366114e-03  2.213331e-03
[266]  2.060963e-03  1.909012e-03  1.757478e-03  1.606362e-03  1.455664e-03
[271]  1.305385e-03  1.155525e-03  1.006084e-03  8.570629e-04  7.084622e-04
[276]  5.602820e-04  4.125226e-04  2.651842e-04  1.182670e-04 -2.822878e-05
[281] -1.743031e-04 -3.199557e-04 -4.651867e-04 -6.099959e-04 -7.543834e-04
[286] -8.983492e-04 -1.041893e-03 -1.185016e-03 -1.327717e-03 -1.469997e-03
[291] -1.611855e-03 -1.753293e-03 -1.894310e-03 -2.034907e-03 -2.175083e-03
[296] -2.314840e-03 -2.454177e-03 -2.593095e-03 -2.731595e-03 -2.869676e-03
[301] -3.007339e-03 -3.144586e-03 -3.281415e-03 -3.417829e-03 -3.553826e-03
[306] -3.689409e-03 -3.824577e-03 -3.959332e-03 -4.093673e-03 -4.227602e-03
[311] -4.361120e-03 -4.494226e-03 -4.626922e-03 -4.759209e-03 -4.891087e-03
[316] -5.022558e-03 -5.153622e-03 -5.284280e-03 -5.414532e-03 -5.544381e-03
[321] -5.673826e-03 -5.802869e-03 -5.931511e-03 -6.059753e-03 -6.187596e-03
[326] -6.315040e-03 -6.442087e-03 -6.568739e-03 -6.694995e-03 -6.820858e-03
[331] -6.946328e-03 -7.071407e-03 -7.196095e-03 -7.320394e-03 -7.444306e-03
[336] -7.567831e-03 -7.690971e-03 -7.813726e-03 -7.936099e-03 -8.058090e-03
[341] -8.179701e-03 -8.300933e-03 -8.421788e-03 -8.542266e-03 -8.662370e-03
[346] -8.782101e-03 -8.901459e-03 -9.020447e-03 -9.139065e-03 -9.257316e-03
[351] -9.375201e-03 -9.492721e-03 -9.609878e-03 -9.726673e-03 -9.843107e-03
[356] -9.959183e-03 -1.007490e-02 -1.019026e-02 -1.030527e-02 -1.041993e-02
[361] -1.053423e-02 -1.064819e-02 -1.076180e-02 -1.087506e-02 -1.098798e-02
[366] -1.110055e-02 -1.121278e-02 -1.132468e-02 -1.143623e-02 -1.154745e-02
[371] -1.165833e-02 -1.176888e-02 -1.187910e-02 -1.198899e-02 -1.209855e-02
[376] -1.220778e-02 -1.231669e-02 -1.242528e-02 -1.253355e-02 -1.264149e-02
[381] -1.274912e-02 -1.285643e-02 -1.296343e-02 -1.307011e-02 -1.317649e-02
[386] -1.328255e-02 -1.338831e-02 -1.349376e-02 -1.359891e-02 -1.370375e-02
[391] -1.380830e-02 -1.391255e-02 -1.401650e-02 -1.412015e-02 -1.422351e-02
[396] -1.432658e-02 -1.442936e-02 -1.453185e-02 -1.463406e-02 -1.473598e-02
[401] -1.483762e-02
> mx
[1] 0.04747123
> 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/rcomp/tmp/1e9wf1323898971.ps",horizontal=F,onefile=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/rcomp/tmp/28iu11323898971.ps",horizontal=F,onefile=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/rcomp/tmp/3xf881323898971.ps",horizontal=F,onefile=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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/4x0sl1323898971.tab") 
> 
> try(system("convert tmp/1e9wf1323898971.ps tmp/1e9wf1323898971.png",intern=TRUE))
character(0)
> try(system("convert tmp/28iu11323898971.ps tmp/28iu11323898971.png",intern=TRUE))
character(0)
> try(system("convert tmp/3xf881323898971.ps tmp/3xf881323898971.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.750   0.120   1.852