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(328282,317480,317539,313737,312276,309391,302950,300316,304035,333476,337698,335932,323931,313927,314485,313218,309664,302963,298989,298423,301631,329765,335083,327616,309119,295916,291413,291542,284678,276475,272566,264981,263290,296806,303598,286994,276427,266424,267153,268381,262522,255542,253158,243803,250741,280445,285257,270976,261076,255603,260376,263903,264291,263276,262572,256167,264221,293860,300713,287224)
> x <- c(283042,276687,277915,277128,277103,275037,270150,267140,264993,287259,291186,292300,288186,281477,282656,280190,280408,276836,275216,274352,271311,289802,290726,292300,278506,269826,265861,269034,264176,255198,253353,246057,235372,258556,260993,254663,250643,243422,247105,248541,245039,237080,237085,225554,226839,247934,248333,246969,245098,246263,255765,264319,268347,273046,273963,267430,271993,292710,295881,293299)
> #'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] 0.7985612 0.7986104 0.7986595 0.7987066 0.7987563 0.7988064 0.7988550
  [8] 0.7989032 0.7989523 0.7989997 0.7990496 0.7990975 0.7991453 0.7991925
 [15] 0.7992408 0.7992872 0.7993355 0.7993822 0.7994292 0.7994762 0.7995233
 [22] 0.7995704 0.7996170 0.7996634 0.7997098 0.7997561 0.7998025 0.7998488
 [29] 0.7998945 0.7999405 0.7999862 0.8000318 0.8000773 0.8001227 0.8001679
 [36] 0.8002131 0.8002581 0.8003030 0.8003478 0.8003925 0.8004370 0.8004814
 [43] 0.8005257 0.8005699 0.8006140 0.8006579 0.8007017 0.8007454 0.8007890
 [50] 0.8008325 0.8008759 0.8009191 0.8009622 0.8010052 0.8010481 0.8010908
 [57] 0.8011334 0.8011759 0.8012183 0.8012606 0.8013028 0.8013448 0.8013867
 [64] 0.8014285 0.8014702 0.8015117 0.8015532 0.8015945 0.8016357 0.8016768
 [71] 0.8017177 0.8017586 0.8017993 0.8018399 0.8018803 0.8019207 0.8019609
 [78] 0.8020011 0.8020411 0.8020810 0.8021207 0.8021604 0.8021999 0.8022393
 [85] 0.8022786 0.8023177 0.8023568 0.8023957 0.8024345 0.8024732 0.8025118
 [92] 0.8025502 0.8025885 0.8026267 0.8026648 0.8027028 0.8027407 0.8027784
 [99] 0.8028160 0.8028535 0.8028909 0.8029281 0.8029652 0.8030023 0.8030392
[106] 0.8030759 0.8031126 0.8031491 0.8031855 0.8032218 0.8032580 0.8032941
[113] 0.8033300 0.8033658 0.8034015 0.8034371 0.8034726 0.8035079 0.8035432
[120] 0.8035783 0.8036133 0.8036481 0.8036829 0.8037175 0.8037520 0.8037864
[127] 0.8038207 0.8038548 0.8038889 0.8039228 0.8039566 0.8039902 0.8040238
[134] 0.8040572 0.8040906 0.8041238 0.8041568 0.8041898 0.8042226 0.8042554
[141] 0.8042880 0.8043204 0.8043528 0.8043851 0.8044172 0.8044492 0.8044811
[148] 0.8045129 0.8045445 0.8045760 0.8046075 0.8046388 0.8046699 0.8047010
[155] 0.8047319 0.8047627 0.8047934 0.8048240 0.8048545 0.8048848 0.8049151
[162] 0.8049452 0.8049752 0.8050050 0.8050348 0.8050644 0.8050939 0.8051233
[169] 0.8051526 0.8051818 0.8052108 0.8052397 0.8052685 0.8052972 0.8053258
[176] 0.8053542 0.8053826 0.8054108 0.8054389 0.8054668 0.8054947 0.8055224
[183] 0.8055500 0.8055775 0.8056049 0.8056322 0.8056593 0.8056863 0.8057133
[190] 0.8057400 0.8057667 0.8057933 0.8058197 0.8058460 0.8058722 0.8058983
[197] 0.8059243 0.8059501 0.8059758 0.8060014 0.8060269 0.8060523 0.8060776
[204] 0.8061027 0.8061277 0.8061526 0.8061774 0.8062021 0.8062266 0.8062510
[211] 0.8062753 0.8062995 0.8063236 0.8063476 0.8063714 0.8063951 0.8064187
[218] 0.8064422 0.8064656 0.8064888 0.8065120 0.8065350 0.8065579 0.8065807
[225] 0.8066033 0.8066259 0.8066483 0.8066706 0.8066928 0.8067149 0.8067369
[232] 0.8067587 0.8067804 0.8068020 0.8068235 0.8068449 0.8068661 0.8068873
[239] 0.8069083 0.8069292 0.8069500 0.8069707 0.8069912 0.8070116 0.8070320
[246] 0.8070522 0.8070722 0.8070922 0.8071121 0.8071318 0.8071514 0.8071709
[253] 0.8071903 0.8072096 0.8072287 0.8072477 0.8072667 0.8072855 0.8073041
[260] 0.8073227 0.8073412 0.8073595 0.8073777 0.8073958 0.8074138 0.8074316
[267] 0.8074494 0.8074670 0.8074845 0.8075019 0.8075192 0.8075364 0.8075535
[274] 0.8075704 0.8075872 0.8076039 0.8076205 0.8076370 0.8076533 0.8076696
[281] 0.8076857 0.8077017 0.8077176 0.8077333 0.8077490 0.8077646 0.8077800
[288] 0.8077953 0.8078105 0.8078256 0.8078405 0.8078554 0.8078701 0.8078847
[295] 0.8078992 0.8079136 0.8079279 0.8079420 0.8079561 0.8079700 0.8079838
[302] 0.8079975 0.8080111 0.8080245 0.8080379 0.8080511 0.8080642 0.8080772
[309] 0.8080901 0.8081029 0.8081155 0.8081281 0.8081405 0.8081528 0.8081650
[316] 0.8081771 0.8081891 0.8082009 0.8082126 0.8082243 0.8082358 0.8082472
[323] 0.8082584 0.8082696 0.8082806 0.8082916 0.8083024 0.8083131 0.8083237
[330] 0.8083342 0.8083445 0.8083548 0.8083649 0.8083749 0.8083848 0.8083946
[337] 0.8084043 0.8084138 0.8084233 0.8084326 0.8084418 0.8084509 0.8084599
[344] 0.8084688 0.8084776 0.8084862 0.8084947 0.8085032 0.8085115 0.8085197
[351] 0.8085277 0.8085357 0.8085436 0.8085513 0.8085589 0.8085664 0.8085738
[358] 0.8085811 0.8085883 0.8085953 0.8086023 0.8086091 0.8086158 0.8086224
[365] 0.8086289 0.8086353 0.8086416 0.8086477 0.8086538 0.8086597 0.8086655
[372] 0.8086712 0.8086768 0.8086823 0.8086876 0.8086929 0.8086980 0.8087030
[379] 0.8087080 0.8087128 0.8087174 0.8087220 0.8087265 0.8087308 0.8087351
[386] 0.8087392 0.8087432 0.8087471 0.8087509 0.8087546 0.8087581 0.8087616
[393] 0.8087649 0.8087681 0.8087712 0.8087743 0.8087771 0.8087799 0.8087826
[400] 0.8087851 0.8087876
> mx
[1] 0.8087876
> 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/19nl71257931937.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/24v231257931937.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/3n1s21257931937.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/4stws1257931938.tab") 
> 
> system("convert tmp/19nl71257931937.ps tmp/19nl71257931937.png")
> system("convert tmp/24v231257931937.ps tmp/24v231257931937.png")
> system("convert tmp/3n1s21257931937.ps tmp/3n1s21257931937.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.767   0.492   0.956