R version 2.7.0 (2008-04-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> y <- c(22780,17351,21382,24561,17409,11514,31514,27071,29462,26105,22397,23843,21705,18089,20764,25316,17704,15548,28029,29383,36438,32034,22679,24319,18004,17537,20366,22782,19169,13807,29743,25591,29096,26482,22405,27044,17970,18730,19684,19785,18479,10698,31956,29506,34506,27165,26736,23691,18157,17328,18205,20995,17382,9367,31124,26551,30651,25859,25100,25778,20418,18688,20424,24776,19814,12738,31566,30111,30019,31934,25826,26835)
> x <- c(517,525,523,519,509,512,519,517,510,509,501,507,569,580,578,565,547,555,562,561,555,544,537,543,594,611,613,611,594,595,591,589,584,573,567,569,621,629,628,612,595,597,593,590,580,574,573,573,620,626,620,588,566,557,561,549,532,526,511,499,555,565,542,527,510,514,517,508,493,490,469,478)
> #'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] -0.2710794 -0.2711246 -0.2711697 -0.2712149 -0.2712600 -0.2713052
  [7] -0.2713503 -0.2713955 -0.2714406 -0.2714857 -0.2715308 -0.2715760
 [13] -0.2716211 -0.2716662 -0.2717113 -0.2717564 -0.2718015 -0.2718466
 [19] -0.2718917 -0.2719367 -0.2719818 -0.2720269 -0.2720720 -0.2721170
 [25] -0.2721621 -0.2722072 -0.2722522 -0.2722973 -0.2723423 -0.2723873
 [31] -0.2724324 -0.2724774 -0.2725224 -0.2725674 -0.2726125 -0.2726575
 [37] -0.2727025 -0.2727475 -0.2727925 -0.2728375 -0.2728824 -0.2729274
 [43] -0.2729724 -0.2730174 -0.2730623 -0.2731073 -0.2731523 -0.2731972
 [49] -0.2732422 -0.2732871 -0.2733320 -0.2733770 -0.2734219 -0.2734668
 [55] -0.2735117 -0.2735566 -0.2736015 -0.2736464 -0.2736913 -0.2737362
 [61] -0.2737811 -0.2738260 -0.2738709 -0.2739157 -0.2739606 -0.2740055
 [67] -0.2740503 -0.2740952 -0.2741400 -0.2741848 -0.2742297 -0.2742745
 [73] -0.2743193 -0.2743641 -0.2744089 -0.2744537 -0.2744985 -0.2745433
 [79] -0.2745881 -0.2746329 -0.2746777 -0.2747224 -0.2747672 -0.2748119
 [85] -0.2748567 -0.2749014 -0.2749462 -0.2749909 -0.2750356 -0.2750803
 [91] -0.2751251 -0.2751698 -0.2752145 -0.2752592 -0.2753039 -0.2753485
 [97] -0.2753932 -0.2754379 -0.2754826 -0.2755272 -0.2755719 -0.2756165
[103] -0.2756612 -0.2757058 -0.2757504 -0.2757950 -0.2758397 -0.2758843
[109] -0.2759289 -0.2759735 -0.2760181 -0.2760626 -0.2761072 -0.2761518
[115] -0.2761963 -0.2762409 -0.2762855 -0.2763300 -0.2763745 -0.2764191
[121] -0.2764636 -0.2765081 -0.2765526 -0.2765971 -0.2766416 -0.2766861
[127] -0.2767306 -0.2767751 -0.2768195 -0.2768640 -0.2769085 -0.2769529
[133] -0.2769973 -0.2770418 -0.2770862 -0.2771306 -0.2771750 -0.2772194
[139] -0.2772638 -0.2773082 -0.2773526 -0.2773970 -0.2774414 -0.2774857
[145] -0.2775301 -0.2775744 -0.2776188 -0.2776631 -0.2777074 -0.2777517
[151] -0.2777961 -0.2778404 -0.2778847 -0.2779289 -0.2779732 -0.2780175
[157] -0.2780618 -0.2781060 -0.2781503 -0.2781945 -0.2782388 -0.2782830
[163] -0.2783272 -0.2783714 -0.2784156 -0.2784598 -0.2785040 -0.2785482
[169] -0.2785924 -0.2786365 -0.2786807 -0.2787248 -0.2787690 -0.2788131
[175] -0.2788572 -0.2789013 -0.2789454 -0.2789896 -0.2790336 -0.2790777
[181] -0.2791218 -0.2791659 -0.2792099 -0.2792540 -0.2792980 -0.2793421
[187] -0.2793861 -0.2794301 -0.2794741 -0.2795181 -0.2795621 -0.2796061
[193] -0.2796501 -0.2796940 -0.2797380 -0.2797819 -0.2798259 -0.2798698
[199] -0.2799137 -0.2799577 -0.2800016 -0.2800455 -0.2800894 -0.2801332
[205] -0.2801771 -0.2802210 -0.2802648 -0.2803087 -0.2803525 -0.2803963
[211] -0.2804401 -0.2804840 -0.2805278 -0.2805715 -0.2806153 -0.2806591
[217] -0.2807029 -0.2807466 -0.2807904 -0.2808341 -0.2808778 -0.2809215
[223] -0.2809653 -0.2810090 -0.2810526 -0.2810963 -0.2811400 -0.2811837
[229] -0.2812273 -0.2812710 -0.2813146 -0.2813582 -0.2814018 -0.2814454
[235] -0.2814890 -0.2815326 -0.2815762 -0.2816198 -0.2816633 -0.2817069
[241] -0.2817504 -0.2817939 -0.2818374 -0.2818809 -0.2819244 -0.2819679
[247] -0.2820114 -0.2820549 -0.2820983 -0.2821418 -0.2821852 -0.2822287
[253] -0.2822721 -0.2823155 -0.2823589 -0.2824023 -0.2824456 -0.2824890
[259] -0.2825324 -0.2825757 -0.2826190 -0.2826624 -0.2827057 -0.2827490
[265] -0.2827923 -0.2828356 -0.2828788 -0.2829221 -0.2829654 -0.2830086
[271] -0.2830518 -0.2830951 -0.2831383 -0.2831815 -0.2832247 -0.2832678
[277] -0.2833110 -0.2833542 -0.2833973 -0.2834404 -0.2834836 -0.2835267
[283] -0.2835698 -0.2836129 -0.2836560 -0.2836990 -0.2837421 -0.2837851
[289] -0.2838282 -0.2838712 -0.2839142 -0.2839572 -0.2840002 -0.2840432
[295] -0.2840862 -0.2841291 -0.2841721 -0.2842150 -0.2842579 -0.2843009
[301] -0.2843438 -0.2843867 -0.2844295 -0.2844724 -0.2845153 -0.2845581
[307] -0.2846009 -0.2846438 -0.2846866 -0.2847294 -0.2847722 -0.2848149
[313] -0.2848577 -0.2849005 -0.2849432 -0.2849859 -0.2850286 -0.2850713
[319] -0.2851140 -0.2851567 -0.2851994 -0.2852421 -0.2852847 -0.2853273
[325] -0.2853700 -0.2854126 -0.2854552 -0.2854977 -0.2855403 -0.2855829
[331] -0.2856254 -0.2856680 -0.2857105 -0.2857530 -0.2857955 -0.2858380
[337] -0.2858805 -0.2859229 -0.2859654 -0.2860078 -0.2860503 -0.2860927
[343] -0.2861351 -0.2861775 -0.2862198 -0.2862622 -0.2863045 -0.2863469
[349] -0.2863892 -0.2864315 -0.2864738 -0.2865161 -0.2865584 -0.2866006
[355] -0.2866429 -0.2866851 -0.2867274 -0.2867696 -0.2868118 -0.2868539
[361] -0.2868961 -0.2869383 -0.2869804 -0.2870226 -0.2870647 -0.2871068
[367] -0.2871489 -0.2871910 -0.2872330 -0.2872751 -0.2873171 -0.2873591
[373] -0.2874012 -0.2874432 -0.2874851 -0.2875271 -0.2875691 -0.2876110
[379] -0.2876529 -0.2876949 -0.2877368 -0.2877787 -0.2878205 -0.2878624
[385] -0.2879043 -0.2879461 -0.2879879 -0.2880297 -0.2880715 -0.2881133
[391] -0.2881551 -0.2881968 -0.2882386 -0.2882803 -0.2883220 -0.2883637
[397] -0.2884054 -0.2884471 -0.2884887 -0.2885304 -0.2885720
> mx
[1] 0.288572
> 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/rcomp/tmp/194qo1226399004.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/2mhub1226399004.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/32jou1226399004.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/4ge551226399004.tab") 
> 
> system("convert tmp/194qo1226399004.ps tmp/194qo1226399004.png")
> system("convert tmp/2mhub1226399004.ps tmp/2mhub1226399004.png")
> system("convert tmp/32jou1226399004.ps tmp/32jou1226399004.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.852   0.820   1.987