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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> y <- c(93.5,98.8,106.2,98.3,102.1,117.1,101.5,80.5,105.9,109.5,97.2,114.5,93.5,100.9,121.1,116.5,109.3,118.1,108.3,105.4,116.2,111.2,105.8,122.7,99.5,107.9,124.6,115,110.3,132.7,99.7,96.5,118.7,112.9,130.5,137.9,115,116.8,140.9,120.7,134.2,147.3,112.4,107.1,128.4,137.7,135,151,137.4,132.4,161.3,139.8,146,166.5,143.3,121,152.6,154.4,154.6,158)
> x <- c(103.3,101.2,107.7,110.4,101.9,115.9,89.9,88.6,117.2,123.9,100,103.6,94.1,98.7,119.5,112.7,104.4,124.7,89.1,97,121.6,118.8,114,111.5,97.2,102.5,113.4,109.8,104.9,126.1,80,96.8,117.2,112.3,117.3,111.1,102.2,104.3,122.9,107.6,121.3,131.5,89,104.4,128.9,135.9,133.3,121.3,120.5,120.4,137.9,126.1,133.2,151.1,105,119,140.4,156.6,137.1,122.7)
> #'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(x1,y)
+ if (mx < abs(c[i]))
+ {
+ mx <- abs(c[i])
+ mxli <- l[i]
+ }
+ }
> c
  [1] 0.7608015 0.7610957 0.7613892 0.7616822 0.7619745 0.7622662 0.7625572
  [8] 0.7628476 0.7631374 0.7634266 0.7637151 0.7640030 0.7642902 0.7645768
 [15] 0.7648628 0.7651481 0.7654328 0.7657168 0.7660002 0.7662829 0.7665650
 [22] 0.7668465 0.7671273 0.7674074 0.7676869 0.7679658 0.7682440 0.7685215
 [29] 0.7687984 0.7690746 0.7693502 0.7696251 0.7698993 0.7701729 0.7704458
 [36] 0.7707180 0.7709896 0.7712605 0.7715308 0.7718004 0.7720693 0.7723375
 [43] 0.7726051 0.7728720 0.7731382 0.7734037 0.7736686 0.7739328 0.7741963
 [50] 0.7744591 0.7747212 0.7749827 0.7752435 0.7755036 0.7757630 0.7760217
 [57] 0.7762797 0.7765371 0.7767937 0.7770497 0.7773049 0.7775595 0.7778134
 [64] 0.7780666 0.7783191 0.7785709 0.7788219 0.7790723 0.7793220 0.7795710
 [71] 0.7798193 0.7800669 0.7803137 0.7805599 0.7808054 0.7810501 0.7812942
 [78] 0.7815375 0.7817801 0.7820220 0.7822632 0.7825037 0.7827435 0.7829825
 [85] 0.7832209 0.7834585 0.7836954 0.7839316 0.7841670 0.7844018 0.7846358
 [92] 0.7848690 0.7851016 0.7853334 0.7855645 0.7857949 0.7860246 0.7862535
 [99] 0.7864817 0.7867091 0.7869359 0.7871619 0.7873871 0.7876116 0.7878354
[106] 0.7880585 0.7882808 0.7885023 0.7887232 0.7889433 0.7891626 0.7893812
[113] 0.7895991 0.7898162 0.7900326 0.7902482 0.7904631 0.7906772 0.7908906
[120] 0.7911032 0.7913151 0.7915262 0.7917366 0.7919462 0.7921550 0.7923631
[127] 0.7925705 0.7927771 0.7929829 0.7931880 0.7933923 0.7935959 0.7937987
[134] 0.7940007 0.7942020 0.7944025 0.7946023 0.7948012 0.7949995 0.7951969
[141] 0.7953936 0.7955895 0.7957846 0.7959790 0.7961726 0.7963654 0.7965575
[148] 0.7967488 0.7969393 0.7971290 0.7973180 0.7975062 0.7976936 0.7978802
[155] 0.7980661 0.7982511 0.7984354 0.7986189 0.7988017 0.7989836 0.7991648
[162] 0.7993452 0.7995248 0.7997036 0.7998816 0.8000589 0.8002353 0.8004110
[169] 0.8005858 0.8007599 0.8009332 0.8011057 0.8012775 0.8014484 0.8016185
[176] 0.8017879 0.8019564 0.8021242 0.8022911 0.8024573 0.8026226 0.8027872
[183] 0.8029510 0.8031139 0.8032761 0.8034375 0.8035980 0.8037578 0.8039168
[190] 0.8040750 0.8042323 0.8043889 0.8045446 0.8046996 0.8048537 0.8050071
[197] 0.8051596 0.8053113 0.8054623 0.8056124 0.8057617 0.8059102 0.8060579
[204] 0.8062047 0.8063508 0.8064961 0.8066405 0.8067841 0.8069270 0.8070690
[211] 0.8072102 0.8073505 0.8074901 0.8076288 0.8077668 0.8079039 0.8080402
[218] 0.8081757 0.8083103 0.8084442 0.8085772 0.8087094 0.8088408 0.8089714
[225] 0.8091011 0.8092300 0.8093581 0.8094854 0.8096119 0.8097375 0.8098623
[232] 0.8099863 0.8101095 0.8102318 0.8103533 0.8104740 0.8105939 0.8107129
[239] 0.8108311 0.8109485 0.8110651 0.8111808 0.8112957 0.8114098 0.8115230
[246] 0.8116355 0.8117470 0.8118578 0.8119677 0.8120768 0.8121851 0.8122925
[253] 0.8123991 0.8125049 0.8126098 0.8127139 0.8128172 0.8129196 0.8130212
[260] 0.8131220 0.8132220 0.8133211 0.8134193 0.8135168 0.8136134 0.8137091
[267] 0.8138041 0.8138981 0.8139914 0.8140838 0.8141754 0.8142661 0.8143561
[274] 0.8144451 0.8145334 0.8146208 0.8147073 0.8147930 0.8148779 0.8149619
[281] 0.8150452 0.8151275 0.8152090 0.8152897 0.8153696 0.8154486 0.8155267
[288] 0.8156041 0.8156805 0.8157562 0.8158310 0.8159050 0.8159781 0.8160504
[295] 0.8161218 0.8161924 0.8162622 0.8163311 0.8163991 0.8164664 0.8165328
[302] 0.8165983 0.8166630 0.8167269 0.8167899 0.8168521 0.8169134 0.8169739
[309] 0.8170336 0.8170924 0.8171503 0.8172074 0.8172637 0.8173192 0.8173738
[316] 0.8174275 0.8174804 0.8175325 0.8175837 0.8176341 0.8176836 0.8177323
[323] 0.8177802 0.8178272 0.8178733 0.8179187 0.8179631 0.8180068 0.8180496
[330] 0.8180915 0.8181326 0.8181729 0.8182123 0.8182509 0.8182886 0.8183255
[337] 0.8183616 0.8183968 0.8184312 0.8184647 0.8184974 0.8185292 0.8185602
[344] 0.8185904 0.8186197 0.8186482 0.8186758 0.8187026 0.8187285 0.8187536
[351] 0.8187779 0.8188013 0.8188239 0.8188457 0.8188666 0.8188866 0.8189059
[358] 0.8189243 0.8189418 0.8189585 0.8189744 0.8189894 0.8190036 0.8190170
[365] 0.8190295 0.8190412 0.8190520 0.8190620 0.8190712 0.8190795 0.8190870
[372] 0.8190936 0.8190995 0.8191044 0.8191086 0.8191119 0.8191144 0.8191160
[379] 0.8191168 0.8191168 0.8191159 0.8191142 0.8191117 0.8191083 0.8191041
[386] 0.8190991 0.8190932 0.8190865 0.8190790 0.8190707 0.8190615 0.8190514
[393] 0.8190406 0.8190289 0.8190164 0.8190031 0.8189889 0.8189739 0.8189581
[400] 0.8189414 0.8189240
> mx
[1] 0.8191168
> mxli
[1] 1.78
> 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/1t8n01226414379.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/2adf71226414379.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/3l0gf1226414379.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/4hn0n1226414379.tab") 
> 
> system("convert tmp/1t8n01226414379.ps tmp/1t8n01226414379.png")
> system("convert tmp/2adf71226414379.ps tmp/2adf71226414379.png")
> system("convert tmp/3l0gf1226414379.ps tmp/3l0gf1226414379.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.233   0.823   1.794