R version 2.8.1 (2008-12-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(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)
> x <- c(162,161,149,139,135,130,127,122,117,112,113,149,157,157,147,137,132,125,123,117,114,111,112,144,150,149,134,123,116,117,111,105,102,95,93,124,130,124,115,106,105,105,101,95,93,84,87,116,120,117,109,105,107,109,109,108,107,99,103,131,137)
> #'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] 0.7888035 0.7888171 0.7888298 0.7888416 0.7888526 0.7888627 0.7888719
  [8] 0.7888803 0.7888879 0.7888945 0.7889003 0.7889053 0.7889094 0.7889126
 [15] 0.7889150 0.7889165 0.7889172 0.7889170 0.7889159 0.7889140 0.7889112
 [22] 0.7889075 0.7889030 0.7888976 0.7888914 0.7888843 0.7888764 0.7888675
 [29] 0.7888579 0.7888473 0.7888359 0.7888237 0.7888106 0.7887966 0.7887817
 [36] 0.7887661 0.7887495 0.7887321 0.7887138 0.7886947 0.7886747 0.7886538
 [43] 0.7886321 0.7886095 0.7885861 0.7885618 0.7885366 0.7885106 0.7884838
 [50] 0.7884561 0.7884275 0.7883980 0.7883677 0.7883366 0.7883046 0.7882717
 [57] 0.7882380 0.7882034 0.7881680 0.7881317 0.7880946 0.7880566 0.7880177
 [64] 0.7879780 0.7879375 0.7878960 0.7878538 0.7878107 0.7877667 0.7877219
 [71] 0.7876762 0.7876297 0.7875823 0.7875341 0.7874850 0.7874351 0.7873844
 [78] 0.7873327 0.7872803 0.7872270 0.7871728 0.7871178 0.7870620 0.7870053
 [85] 0.7869477 0.7868894 0.7868301 0.7867701 0.7867092 0.7866474 0.7865848
 [92] 0.7865214 0.7864571 0.7863920 0.7863261 0.7862593 0.7861916 0.7861232
 [99] 0.7860539 0.7859837 0.7859128 0.7858410 0.7857683 0.7856949 0.7856206
[106] 0.7855454 0.7854694 0.7853927 0.7853150 0.7852366 0.7851573 0.7850772
[113] 0.7849962 0.7849145 0.7848319 0.7847485 0.7846642 0.7845792 0.7844933
[120] 0.7844066 0.7843191 0.7842307 0.7841416 0.7840516 0.7839608 0.7838692
[127] 0.7837767 0.7836835 0.7835894 0.7834946 0.7833989 0.7833024 0.7832051
[134] 0.7831070 0.7830081 0.7829083 0.7828078 0.7827065 0.7826043 0.7825014
[141] 0.7823976 0.7822931 0.7821877 0.7820815 0.7819746 0.7818668 0.7817583
[148] 0.7816489 0.7815388 0.7814279 0.7813161 0.7812036 0.7810903 0.7809762
[155] 0.7808613 0.7807457 0.7806292 0.7805119 0.7803939 0.7802751 0.7801555
[162] 0.7800351 0.7799140 0.7797920 0.7796693 0.7795458 0.7794215 0.7792965
[169] 0.7791707 0.7790441 0.7789167 0.7787886 0.7786597 0.7785300 0.7783996
[176] 0.7782684 0.7781364 0.7780037 0.7778702 0.7777360 0.7776009 0.7774652
[183] 0.7773287 0.7771914 0.7770533 0.7769145 0.7767750 0.7766347 0.7764937
[190] 0.7763519 0.7762094 0.7760661 0.7759220 0.7757773 0.7756318 0.7754855
[197] 0.7753385 0.7751908 0.7750423 0.7748931 0.7747432 0.7745925 0.7744411
[204] 0.7742890 0.7741361 0.7739825 0.7738282 0.7736732 0.7735174 0.7733609
[211] 0.7732037 0.7730458 0.7728872 0.7727278 0.7725677 0.7724069 0.7722454
[218] 0.7720832 0.7719203 0.7717567 0.7715924 0.7714273 0.7712616 0.7710951
[225] 0.7709280 0.7707601 0.7705916 0.7704223 0.7702524 0.7700818 0.7699104
[232] 0.7697384 0.7695657 0.7693923 0.7692183 0.7690435 0.7688680 0.7686919
[239] 0.7685151 0.7683376 0.7681594 0.7679806 0.7678011 0.7676209 0.7674400
[246] 0.7672585 0.7670763 0.7668934 0.7667099 0.7665257 0.7663408 0.7661553
[253] 0.7659691 0.7657823 0.7655948 0.7654066 0.7652178 0.7650284 0.7648383
[260] 0.7646475 0.7644561 0.7642641 0.7640714 0.7638781 0.7636841 0.7634895
[267] 0.7632942 0.7630983 0.7629018 0.7627047 0.7625069 0.7623085 0.7621094
[274] 0.7619098 0.7617095 0.7615086 0.7613070 0.7611049 0.7609021 0.7606987
[281] 0.7604947 0.7602901 0.7600849 0.7598790 0.7596726 0.7594655 0.7592579
[288] 0.7590496 0.7588407 0.7586313 0.7584212 0.7582106 0.7579993 0.7577874
[295] 0.7575750 0.7573620 0.7571483 0.7569341 0.7567193 0.7565040 0.7562880
[302] 0.7560715 0.7558544 0.7556367 0.7554184 0.7551995 0.7549801 0.7547601
[309] 0.7545396 0.7543185 0.7540968 0.7538745 0.7536517 0.7534284 0.7532044
[316] 0.7529799 0.7527549 0.7525293 0.7523032 0.7520765 0.7518492 0.7516214
[323] 0.7513931 0.7511642 0.7509348 0.7507048 0.7504743 0.7502433 0.7500117
[330] 0.7497796 0.7495470 0.7493138 0.7490801 0.7488459 0.7486112 0.7483759
[337] 0.7481401 0.7479038 0.7476670 0.7474297 0.7471918 0.7469534 0.7467146
[344] 0.7464752 0.7462353 0.7459949 0.7457540 0.7455126 0.7452707 0.7450283
[351] 0.7447854 0.7445420 0.7442981 0.7440538 0.7438089 0.7435635 0.7433177
[358] 0.7430714 0.7428246 0.7425773 0.7423295 0.7420813 0.7418325 0.7415833
[365] 0.7413337 0.7410835 0.7408329 0.7405818 0.7403303 0.7400783 0.7398258
[372] 0.7395729 0.7393195 0.7390656 0.7388113 0.7385566 0.7383014 0.7380457
[379] 0.7377896 0.7375331 0.7372761 0.7370186 0.7367607 0.7365024 0.7362437
[386] 0.7359845 0.7357248 0.7354648 0.7352043 0.7349434 0.7346820 0.7344202
[393] 0.7341580 0.7338954 0.7336324 0.7333689 0.7331050 0.7328407 0.7325760
[400] 0.7323109 0.7320453
> mx
[1] 0.7889172
> mxli
[1] -1.84
> 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/1nkt81257759174.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/rcomp/tmp/2euth1257759174.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/rcomp/tmp/3ah6x1257759174.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/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/45u371257759174.tab") 
> 
> system("convert tmp/1nkt81257759174.ps tmp/1nkt81257759174.png")
> system("convert tmp/2euth1257759174.ps tmp/2euth1257759174.png")
> system("convert tmp/3ah6x1257759174.ps tmp/3ah6x1257759174.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.840   0.620   1.562