R version 3.3.3 (2017-03-06) -- "Another Canoe"
Copyright (C) 2017 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> 
> RC.capture <- function (expression, collapse = NULL) {
+     resultConn <- textConnection('RC.resultText', open = 'w', local=TRUE)
+     sink(resultConn)
+     on.exit(function() {
+         sink()
+         close(resultConn)
+     })
+     expression
+     on.exit(NULL)
+     sink()
+     close(resultConn)
+     return(paste(c(RC.resultText, ''), collapse = collapse, sep = ''))
+ }
> RC.texteval <- function (sourceText, collapse = NULL, echo = TRUE) {
+     sourceConn <- textConnection(sourceText, open = 'r')
+     on.exit(close(sourceConn))
+     result <- RC.capture(source(file = sourceConn, local = FALSE, echo = echo, print.eval = TRUE), collapse = collapse)
+     on.exit(NULL)
+     close(sourceConn)
+     res <- ''
+     for(i in 1:length(result)) {
+       if (result[i]!='') res <- paste(res,result[i],'
+ ',sep='')
+     }
+     return(res)
+ }
> x <- c(0.79,1.08,1.09,1.00,1.12,1.19,0.90,1.05,1.14,1.17,1.09,1.20,0.79,1.14,1.13,0.74,1.11,1.05,0.95,1.09,1.09,0.74,1.15,1.11)
> par5 = 'No'
> par4 = '0'
> par3 = '2'
> par2 = '-2'
> par1 = 'Full Box-Cox transform'
> par5 <- 'No'
> par4 <- '0'
> par3 <- '2'
> par2 <- '-2'
> par1 <- 'Full Box-Cox transform'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 (Mon, 14 Sep 2015 12:57:53 +0100)
> #Author: root
> #To cite this work: Wessa P., (2015), Box-Cox Normality Plot (v1.1.11) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_boxcoxnorm.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #
> library(car)
> par2 <- abs(as.numeric(par2)*100)
> par3 <- as.numeric(par3)*100
> if(par4=='') par4 <- 0
> par4 <- as.numeric(par4)
> numlam <- par2 + par3 + 1
> x <- x + par4
> n <- length(x)
> c <- array(NA,dim=c(numlam))
> l <- array(NA,dim=c(numlam))
> mx <- -1
> mxli <- -999
> for (i in 1:numlam)
+ {
+ l[i] <- (i-par2-1)/100
+ if (l[i] != 0)
+ {
+ if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
+ if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
+ } else {
+ x1 <- log(x)
+ }
+ c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),sort(x1))
+ if (mx < c[i])
+ {
+ mx <- c[i]
+ mxli <- l[i]
+ x1.best <- x1
+ }
+ }
> c
  [1] 0.8546087 0.8548150 0.8550214 0.8552278 0.8554341 0.8556405 0.8558469
  [8] 0.8560534 0.8562598 0.8564662 0.8566727 0.8568792 0.8570857 0.8572922
 [15] 0.8574986 0.8577052 0.8579117 0.8581182 0.8583247 0.8585313 0.8587378
 [22] 0.8589443 0.8591509 0.8593574 0.8595640 0.8597706 0.8599771 0.8601837
 [29] 0.8603902 0.8605968 0.8608034 0.8610099 0.8612165 0.8614230 0.8616296
 [36] 0.8618361 0.8620427 0.8622492 0.8624557 0.8626623 0.8628688 0.8630753
 [43] 0.8632818 0.8634883 0.8636948 0.8639013 0.8641077 0.8643142 0.8645206
 [50] 0.8647270 0.8649335 0.8651399 0.8653462 0.8655526 0.8657590 0.8659653
 [57] 0.8661716 0.8663779 0.8665842 0.8667905 0.8669968 0.8672030 0.8674092
 [64] 0.8676154 0.8678215 0.8680277 0.8682338 0.8684399 0.8686460 0.8688520
 [71] 0.8690580 0.8692640 0.8694700 0.8696759 0.8698818 0.8700877 0.8702936
 [78] 0.8704994 0.8707052 0.8709110 0.8711167 0.8713224 0.8715280 0.8717337
 [85] 0.8719392 0.8721448 0.8723503 0.8725558 0.8727612 0.8729666 0.8731720
 [92] 0.8733773 0.8735826 0.8737879 0.8739931 0.8741982 0.8744034 0.8746084
 [99] 0.8748135 0.8750185 0.8752234 0.8754283 0.8756332 0.8758380 0.8760427
[106] 0.8762474 0.8764521 0.8766567 0.8768612 0.8770658 0.8772702 0.8774746
[113] 0.8776790 0.8778832 0.8780875 0.8782917 0.8784958 0.8786999 0.8789039
[120] 0.8791078 0.8793117 0.8795156 0.8797194 0.8799231 0.8801267 0.8803303
[127] 0.8805339 0.8807373 0.8809407 0.8811441 0.8813473 0.8815506 0.8817537
[134] 0.8819568 0.8821598 0.8823627 0.8825656 0.8827684 0.8829711 0.8831738
[141] 0.8833764 0.8835789 0.8837813 0.8839837 0.8841860 0.8843882 0.8845903
[148] 0.8847924 0.8849944 0.8851963 0.8853981 0.8855999 0.8858016 0.8860031
[155] 0.8862047 0.8864061 0.8866074 0.8868087 0.8870099 0.8872110 0.8874120
[162] 0.8876129 0.8878137 0.8880145 0.8882151 0.8884157 0.8886162 0.8888166
[169] 0.8890169 0.8892171 0.8894172 0.8896172 0.8898172 0.8900170 0.8902168
[176] 0.8904164 0.8906160 0.8908154 0.8910148 0.8912140 0.8914132 0.8916123
[183] 0.8918112 0.8920101 0.8922088 0.8924075 0.8926061 0.8928045 0.8930029
[190] 0.8932011 0.8933992 0.8935973 0.8937952 0.8939930 0.8941907 0.8943883
[197] 0.8945858 0.8947832 0.8949805 0.8951777 0.8953747 0.8955716 0.8957685
[204] 0.8959652 0.8961618 0.8963583 0.8965546 0.8967509 0.8969470 0.8971430
[211] 0.8973389 0.8975347 0.8977303 0.8979259 0.8981213 0.8983166 0.8985118
[218] 0.8987068 0.8989017 0.8990965 0.8992912 0.8994858 0.8996802 0.8998745
[225] 0.9000686 0.9002627 0.9004566 0.9006504 0.9008440 0.9010375 0.9012309
[232] 0.9014242 0.9016173 0.9018103 0.9020031 0.9021959 0.9023884 0.9025809
[239] 0.9027732 0.9029654 0.9031574 0.9033493 0.9035411 0.9037327 0.9039242
[246] 0.9041155 0.9043067 0.9044978 0.9046887 0.9048794 0.9050701 0.9052605
[253] 0.9054509 0.9056410 0.9058311 0.9060210 0.9062107 0.9064003 0.9065898
[260] 0.9067790 0.9069682 0.9071572 0.9073460 0.9075347 0.9077232 0.9079116
[267] 0.9080998 0.9082879 0.9084758 0.9086636 0.9088512 0.9090386 0.9092259
[274] 0.9094131 0.9096000 0.9097868 0.9099735 0.9101600 0.9103463 0.9105324
[281] 0.9107184 0.9109043 0.9110899 0.9112755 0.9114608 0.9116460 0.9118310
[288] 0.9120158 0.9122005 0.9123850 0.9125693 0.9127535 0.9129375 0.9131213
[295] 0.9133050 0.9134884 0.9136717 0.9138549 0.9140378 0.9142206 0.9144032
[302] 0.9145857 0.9147679 0.9149500 0.9151319 0.9153136 0.9154952 0.9156765
[309] 0.9158577 0.9160387 0.9162196 0.9164002 0.9165807 0.9167610 0.9169411
[316] 0.9171210 0.9173007 0.9174802 0.9176596 0.9178388 0.9180178 0.9181966
[323] 0.9183752 0.9185536 0.9187318 0.9189099 0.9190877 0.9192654 0.9194429
[330] 0.9196201 0.9197972 0.9199741 0.9201508 0.9203273 0.9205036 0.9206798
[337] 0.9208557 0.9210314 0.9212069 0.9213823 0.9215574 0.9217323 0.9219071
[344] 0.9220816 0.9222560 0.9224301 0.9226040 0.9227778 0.9229513 0.9231246
[351] 0.9232978 0.9234707 0.9236434 0.9238159 0.9239882 0.9241603 0.9243322
[358] 0.9245039 0.9246754 0.9248467 0.9250177 0.9251886 0.9253592 0.9255297
[365] 0.9256999 0.9258699 0.9260397 0.9262093 0.9263787 0.9265479 0.9267168
[372] 0.9268856 0.9270541 0.9272224 0.9273905 0.9275584 0.9277260 0.9278935
[379] 0.9280607 0.9282277 0.9283945 0.9285611 0.9287274 0.9288936 0.9290595
[386] 0.9292252 0.9293906 0.9295559 0.9297209 0.9298857 0.9300503 0.9302147
[393] 0.9303788 0.9305427 0.9307064 0.9308698 0.9310331 0.9311961 0.9313589
[400] 0.9315214 0.9316837
> mx
[1] 0.9316837
> mxli
[1] 2
> x1.best
 [1] -0.18795  0.08320  0.09405  0.00000  0.12720  0.20805 -0.09500  0.05125
 [9]  0.14980  0.18445  0.09405  0.22000 -0.18795  0.14980  0.13845 -0.22620
[17]  0.11605  0.05125 -0.04875  0.09405  0.09405 -0.22620  0.16125  0.11605
> if (mxli != 0)
+ {
+ if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
+ if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
+ } else {
+ x1 <- log(x)
+ }
> mypT <- powerTransform(x)
> summary(mypT)
bcPower Transformation to Normality 

  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    5.4641   1.7344           2.0646           8.8636

Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 11.298744  1 0.0007755954
LR test, lambda = (1)  7.412399  1 0.0064775897
> postscript(file="/var/wessaorg/rcomp/tmp/1qchv1495043043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
> mtext(paste('Optimal Lambda =',mxli))
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/28msk1495043043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/323r21495043043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/462hk1495043043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqPlot(x)
> grid()
> mtext('Original Data')
> dev.off()
null device 
          1 
> postscript(file="/var/wessaorg/rcomp/tmp/5fjk61495043043.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqPlot(x1)
> grid()
> mtext('Transformed Data')
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Box-Cox Normality 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',header=TRUE)
> a<-table.element(a,mxli)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'transformation formula',header=TRUE)
> if (par1 == 'Full Box-Cox transform') {
+ a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
+ } else {
+ a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
+ }
> a<-table.row.end(a)
> if(mx<0) {
+ a<-table.row.start(a)
+ a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/6k3nz1495043043.tab") 
> if(par5=='Yes') {
+ a<-table.start()
+ a<-table.row.start(a)
+ a<-table.element(a,'Obs.',header=T)
+ a<-table.element(a,'Original',header=T)
+ a<-table.element(a,'Transformed',header=T)
+ a<-table.row.end(a)
+ for (i in 1:n) {
+ a<-table.row.start(a)
+ a<-table.element(a,i)
+ a<-table.element(a,x[i])
+ a<-table.element(a,x1.best[i])
+ a<-table.row.end(a)
+ }
+ a<-table.end(a)
+ table.save(a,file="/var/wessaorg/rcomp/tmp/7kq0m1495043043.tab") 
+ }
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Maximum Likelihood Estimation of Lambda',1,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,paste('<pre>',RC.texteval('summary(mypT)'),'</pre>',sep=''))
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/8mmtf1495043043.tab") 
> 
> try(system("convert tmp/1qchv1495043043.ps tmp/1qchv1495043043.png",intern=TRUE))
character(0)
> try(system("convert tmp/28msk1495043043.ps tmp/28msk1495043043.png",intern=TRUE))
character(0)
> try(system("convert tmp/323r21495043043.ps tmp/323r21495043043.png",intern=TRUE))
character(0)
> try(system("convert tmp/462hk1495043043.ps tmp/462hk1495043043.png",intern=TRUE))
character(0)
> try(system("convert tmp/5fjk61495043043.ps tmp/5fjk61495043043.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  9.769   0.542  10.609