R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(420,418,410,418,426,428,430,424,423,427,441,449,452,462,455,461,461,463,462,456,455,456,472,472,471,465,459,465,468,467,463,460,462,461,476,476,471,453,443,442,444,438,427,424,416,406,431,434,418,412,404,409,412,406,398,397,385,390,413,413,401,397,397,409,419,424,428,430,424,433,456,459,446)
> x <- c(8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8.00,8.2,8.1,8.1,8.00,7.9,7.9,8.00,8.00,7.9,8.00,7.7,7.2,7.5,7.3,7.00,7.00,7.00,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9,6.6,6.9,7.7,8.00,8.00,7.7,7.3,7.4,8.1,8.3,8.2)
> #'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] 0.7567865 0.7567910 0.7567951 0.7567989 0.7568024 0.7568056 0.7568085
  [8] 0.7568110 0.7568132 0.7568151 0.7568167 0.7568179 0.7568188 0.7568195
 [15] 0.7568197 0.7568197 0.7568194 0.7568187 0.7568177 0.7568164 0.7568147
 [22] 0.7568128 0.7568105 0.7568079 0.7568050 0.7568018 0.7567982 0.7567943
 [29] 0.7567901 0.7567856 0.7567808 0.7567757 0.7567702 0.7567644 0.7567583
 [36] 0.7567518 0.7567451 0.7567380 0.7567306 0.7567229 0.7567149 0.7567066
 [43] 0.7566979 0.7566889 0.7566796 0.7566700 0.7566601 0.7566498 0.7566392
 [50] 0.7566283 0.7566171 0.7566056 0.7565937 0.7565816 0.7565691 0.7565563
 [57] 0.7565432 0.7565297 0.7565160 0.7565019 0.7564875 0.7564728 0.7564578
 [64] 0.7564425 0.7564268 0.7564108 0.7563945 0.7563779 0.7563610 0.7563438
 [71] 0.7563262 0.7563083 0.7562901 0.7562716 0.7562528 0.7562337 0.7562142
 [78] 0.7561944 0.7561743 0.7561539 0.7561332 0.7561122 0.7560908 0.7560692
 [85] 0.7560472 0.7560249 0.7560023 0.7559794 0.7559561 0.7559326 0.7559087
 [92] 0.7558845 0.7558600 0.7558352 0.7558101 0.7557846 0.7557589 0.7557328
 [99] 0.7557064 0.7556797 0.7556527 0.7556254 0.7555978 0.7555698 0.7555416
[106] 0.7555130 0.7554841 0.7554549 0.7554254 0.7553956 0.7553654 0.7553350
[113] 0.7553042 0.7552731 0.7552417 0.7552101 0.7551780 0.7551457 0.7551131
[120] 0.7550801 0.7550469 0.7550133 0.7549795 0.7549453 0.7549108 0.7548760
[127] 0.7548408 0.7548054 0.7547697 0.7547336 0.7546973 0.7546606 0.7546236
[134] 0.7545863 0.7545487 0.7545108 0.7544726 0.7544341 0.7543953 0.7543561
[141] 0.7543167 0.7542769 0.7542369 0.7541965 0.7541558 0.7541148 0.7540735
[148] 0.7540319 0.7539900 0.7539478 0.7539053 0.7538624 0.7538193 0.7537758
[155] 0.7537321 0.7536880 0.7536437 0.7535990 0.7535540 0.7535087 0.7534631
[162] 0.7534172 0.7533710 0.7533245 0.7532777 0.7532306 0.7531832 0.7531355
[169] 0.7530874 0.7530391 0.7529905 0.7529415 0.7528923 0.7528427 0.7527929
[176] 0.7527427 0.7526923 0.7526415 0.7525905 0.7525391 0.7524874 0.7524355
[183] 0.7523832 0.7523306 0.7522777 0.7522245 0.7521711 0.7521173 0.7520632
[190] 0.7520088 0.7519541 0.7518991 0.7518439 0.7517883 0.7517324 0.7516762
[197] 0.7516197 0.7515629 0.7515058 0.7514484 0.7513908 0.7513328 0.7512745
[204] 0.7512159 0.7511570 0.7510979 0.7510384 0.7509786 0.7509185 0.7508582
[211] 0.7507975 0.7507365 0.7506753 0.7506137 0.7505518 0.7504897 0.7504272
[218] 0.7503645 0.7503015 0.7502381 0.7501745 0.7501106 0.7500463 0.7499818
[225] 0.7499170 0.7498519 0.7497865 0.7497208 0.7496548 0.7495885 0.7495219
[232] 0.7494550 0.7493879 0.7493204 0.7492527 0.7491846 0.7491163 0.7490476
[239] 0.7489787 0.7489095 0.7488400 0.7487702 0.7487001 0.7486297 0.7485590
[246] 0.7484881 0.7484168 0.7483453 0.7482734 0.7482013 0.7481289 0.7480562
[253] 0.7479832 0.7479099 0.7478363 0.7477624 0.7476883 0.7476138 0.7475391
[260] 0.7474641 0.7473888 0.7473132 0.7472373 0.7471611 0.7470846 0.7470079
[267] 0.7469308 0.7468535 0.7467759 0.7466980 0.7466198 0.7465414 0.7464626
[274] 0.7463836 0.7463043 0.7462246 0.7461448 0.7460646 0.7459841 0.7459034
[281] 0.7458223 0.7457410 0.7456594 0.7455775 0.7454954 0.7454129 0.7453302
[288] 0.7452472 0.7451639 0.7450803 0.7449964 0.7449123 0.7448279 0.7447432
[295] 0.7446582 0.7445729 0.7444873 0.7444015 0.7443154 0.7442290 0.7441423
[302] 0.7440554 0.7439682 0.7438807 0.7437929 0.7437048 0.7436165 0.7435278
[309] 0.7434389 0.7433497 0.7432603 0.7431706 0.7430805 0.7429902 0.7428997
[316] 0.7428088 0.7427177 0.7426263 0.7425346 0.7424427 0.7423505 0.7422580
[323] 0.7421652 0.7420721 0.7419788 0.7418852 0.7417913 0.7416972 0.7416028
[330] 0.7415081 0.7414131 0.7413179 0.7412224 0.7411266 0.7410305 0.7409342
[337] 0.7408376 0.7407407 0.7406436 0.7405461 0.7404484 0.7403505 0.7402522
[344] 0.7401537 0.7400550 0.7399559 0.7398566 0.7397570 0.7396572 0.7395571
[351] 0.7394567 0.7393560 0.7392551 0.7391539 0.7390524 0.7389507 0.7388487
[358] 0.7387464 0.7386439 0.7385411 0.7384381 0.7383347 0.7382311 0.7381273
[365] 0.7380231 0.7379187 0.7378141 0.7377092 0.7376040 0.7374985 0.7373928
[372] 0.7372868 0.7371806 0.7370741 0.7369673 0.7368603 0.7367530 0.7366454
[379] 0.7365376 0.7364295 0.7363212 0.7362125 0.7361037 0.7359945 0.7358852
[386] 0.7357755 0.7356656 0.7355554 0.7354450 0.7353343 0.7352233 0.7351121
[393] 0.7350007 0.7348889 0.7347769 0.7346647 0.7345522 0.7344394 0.7343264
[400] 0.7342131 0.7340996
> mx
[1] 0.7568197
> mxli
[1] -1.86
> 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/rcomp/tmp/1m6vl1258034059.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/rcomp/tmp/217fq1258034059.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/rcomp/tmp/3bubj1258034059.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/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 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/rcomp/tmp/41vc91258034059.tab") 
> 
> system("convert tmp/1m6vl1258034059.ps tmp/1m6vl1258034059.png")
> system("convert tmp/217fq1258034059.ps tmp/217fq1258034059.png")
> system("convert tmp/3bubj1258034059.ps tmp/3bubj1258034059.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.755   0.485   1.933