R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
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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.
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> y <- c(8,8.1,7.7,7.5,7.6,7.8,7.8,7.8,7.5,7.5,7.1,7.5,7.5,7.6,7.7,7.7,7.9,8.1,8.2,8.2,8.2,7.9,7.3,6.9,6.6,6.7,6.9,7,7.1,7.2,7.1,6.9,7,6.8,6.4,6.7,6.6,6.4,6.3,6.2,6.5,6.8,6.8,6.4,6.1,5.8,6.1,7.2,7.3,6.9,6.1,5.8,6.2,7.1,7.7,7.9,7.7,7.4,7.5,8)
> x <- c(30084,26290,24379,23335,21346,21106,24514,30805,28353,31348,34556,33855,34787,32529,29998,29257,28155,30466,35704,39327,39351,42234,43630,43722,43121,37985,37135,34646,33026,35087,38846,42013,43908,42868,44423,44167,43636,44382,42142,43452,36912,42413,45344,44873,47510,49554,47369,45998,48140,48441,44928,40454,38661,37246,36843,36424,37594,38144,38737,34560)
> #'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] -0.5372491 -0.5377563 -0.5382630 -0.5387693 -0.5392752 -0.5397806
  [7] -0.5402855 -0.5407900 -0.5412940 -0.5417975 -0.5423006 -0.5428032
 [13] -0.5433053 -0.5438069 -0.5443080 -0.5448086 -0.5453087 -0.5458083
 [19] -0.5463074 -0.5468060 -0.5473040 -0.5478015 -0.5482984 -0.5487949
 [25] -0.5492907 -0.5497861 -0.5502808 -0.5507750 -0.5512687 -0.5517618
 [31] -0.5522543 -0.5527462 -0.5532375 -0.5537283 -0.5542184 -0.5547080
 [37] -0.5551969 -0.5556853 -0.5561730 -0.5566601 -0.5571466 -0.5576325
 [43] -0.5581177 -0.5586023 -0.5590862 -0.5595695 -0.5600522 -0.5605342
 [49] -0.5610155 -0.5614962 -0.5619762 -0.5624555 -0.5629342 -0.5634121
 [55] -0.5638894 -0.5643660 -0.5648419 -0.5653171 -0.5657916 -0.5662653
 [61] -0.5667384 -0.5672107 -0.5676823 -0.5681532 -0.5686234 -0.5690928
 [67] -0.5695615 -0.5700294 -0.5704966 -0.5709630 -0.5714286 -0.5718935
 [73] -0.5723577 -0.5728210 -0.5732836 -0.5737454 -0.5742064 -0.5746667
 [79] -0.5751261 -0.5755847 -0.5760426 -0.5764996 -0.5769558 -0.5774112
 [85] -0.5778658 -0.5783196 -0.5787725 -0.5792246 -0.5796759 -0.5801264
 [91] -0.5805760 -0.5810247 -0.5814726 -0.5819197 -0.5823659 -0.5828112
 [97] -0.5832557 -0.5836992 -0.5841420 -0.5845838 -0.5850248 -0.5854649
[103] -0.5859040 -0.5863423 -0.5867797 -0.5872163 -0.5876519 -0.5880865
[109] -0.5885203 -0.5889532 -0.5893852 -0.5898162 -0.5902463 -0.5906755
[115] -0.5911037 -0.5915310 -0.5919574 -0.5923828 -0.5928073 -0.5932309
[121] -0.5936535 -0.5940751 -0.5944958 -0.5949155 -0.5953342 -0.5957520
[127] -0.5961688 -0.5965847 -0.5969995 -0.5974134 -0.5978263 -0.5982382
[133] -0.5986491 -0.5990590 -0.5994679 -0.5998759 -0.6002828 -0.6006887
[139] -0.6010936 -0.6014975 -0.6019004 -0.6023023 -0.6027031 -0.6031029
[145] -0.6035017 -0.6038995 -0.6042963 -0.6046920 -0.6050866 -0.6054803
[151] -0.6058729 -0.6062644 -0.6066549 -0.6070444 -0.6074328 -0.6078201
[157] -0.6082064 -0.6085916 -0.6089758 -0.6093589 -0.6097410 -0.6101219
[163] -0.6105018 -0.6108807 -0.6112584 -0.6116351 -0.6120107 -0.6123852
[169] -0.6127586 -0.6131310 -0.6135022 -0.6138724 -0.6142414 -0.6146094
[175] -0.6149763 -0.6153421 -0.6157067 -0.6160703 -0.6164328 -0.6167941
[181] -0.6171544 -0.6175135 -0.6178716 -0.6182285 -0.6185843 -0.6189390
[187] -0.6192925 -0.6196450 -0.6199963 -0.6203465 -0.6206956 -0.6210435
[193] -0.6213903 -0.6217360 -0.6220805 -0.6224240 -0.6227662 -0.6231074
[199] -0.6234474 -0.6237863 -0.6241240 -0.6244606 -0.6247960 -0.6251303
[205] -0.6254635 -0.6257955 -0.6261263 -0.6264560 -0.6267846 -0.6271120
[211] -0.6274382 -0.6277633 -0.6280873 -0.6284100 -0.6287317 -0.6290521
[217] -0.6293714 -0.6296896 -0.6300066 -0.6303224 -0.6306371 -0.6309506
[223] -0.6312629 -0.6315741 -0.6318841 -0.6321929 -0.6325006 -0.6328071
[229] -0.6331124 -0.6334166 -0.6337196 -0.6340214 -0.6343221 -0.6346215
[235] -0.6349198 -0.6352170 -0.6355129 -0.6358077 -0.6361013 -0.6363938
[241] -0.6366850 -0.6369751 -0.6372640 -0.6375518 -0.6378383 -0.6381237
[247] -0.6384079 -0.6386910 -0.6389728 -0.6392535 -0.6395330 -0.6398113
[253] -0.6400884 -0.6403644 -0.6406392 -0.6409128 -0.6411852 -0.6414565
[259] -0.6417266 -0.6419954 -0.6422632 -0.6425297 -0.6427951 -0.6430593
[265] -0.6433223 -0.6435841 -0.6438447 -0.6441042 -0.6443625 -0.6446196
[271] -0.6448756 -0.6451304 -0.6453840 -0.6456364 -0.6458876 -0.6461377
[277] -0.6463866 -0.6466343 -0.6468809 -0.6471262 -0.6473704 -0.6476135
[283] -0.6478553 -0.6480960 -0.6483356 -0.6485739 -0.6488111 -0.6490471
[289] -0.6492820 -0.6495156 -0.6497481 -0.6499795 -0.6502097 -0.6504387
[295] -0.6506666 -0.6508933 -0.6511188 -0.6513432 -0.6515664 -0.6517884
[301] -0.6520093 -0.6522290 -0.6524476 -0.6526650 -0.6528813 -0.6530964
[307] -0.6533104 -0.6535232 -0.6537348 -0.6539453 -0.6541547 -0.6543629
[313] -0.6545700 -0.6547759 -0.6549807 -0.6551843 -0.6553868 -0.6555881
[319] -0.6557883 -0.6559874 -0.6561853 -0.6563821 -0.6565778 -0.6567723
[325] -0.6569657 -0.6571579 -0.6573490 -0.6575390 -0.6577279 -0.6579156
[331] -0.6581022 -0.6582877 -0.6584721 -0.6586554 -0.6588375 -0.6590185
[337] -0.6591984 -0.6593772 -0.6595548 -0.6597314 -0.6599068 -0.6600811
[343] -0.6602544 -0.6604265 -0.6605975 -0.6607674 -0.6609362 -0.6611039
[349] -0.6612705 -0.6614360 -0.6616004 -0.6617637 -0.6619259 -0.6620871
[355] -0.6622471 -0.6624061 -0.6625639 -0.6627207 -0.6628764 -0.6630310
[361] -0.6631846 -0.6633370 -0.6634884 -0.6636387 -0.6637880 -0.6639361
[367] -0.6640832 -0.6642293 -0.6643742 -0.6645181 -0.6646610 -0.6648028
[373] -0.6649435 -0.6650832 -0.6652218 -0.6653593 -0.6654958 -0.6656313
[379] -0.6657657 -0.6658991 -0.6660314 -0.6661627 -0.6662930 -0.6664222
[385] -0.6665503 -0.6666775 -0.6668036 -0.6669287 -0.6670527 -0.6671757
[391] -0.6672978 -0.6674187 -0.6675387 -0.6676576 -0.6677756 -0.6678925
[397] -0.6680084 -0.6681233 -0.6682372 -0.6683500 -0.6684619
> mx
[1] 0.6684619
> 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/html/freestat/rcomp/tmp/17hxi1257413884.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/freestat/rcomp/tmp/2opkp1257413884.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/freestat/rcomp/tmp/3hlff1257413884.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/4o1q21257413884.tab") 
> 
> system("convert tmp/17hxi1257413884.ps tmp/17hxi1257413884.png")
> system("convert tmp/2opkp1257413884.ps tmp/2opkp1257413884.png")
> system("convert tmp/3hlff1257413884.ps tmp/3hlff1257413884.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.266   0.839   1.446