R version 2.13.0 (2011-04-13) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i486-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > x <- c(159 + ,150 + ,128 + ,125 + ,122 + ,109 + ,109 + ,107 + ,107 + ,106 + ,106 + ,104 + ,103 + ,102 + ,100 + ,100 + ,99 + ,97 + ,95 + ,94 + ,93 + ,93 + ,90 + ,88 + ,88 + ,87 + ,87 + ,85 + ,85 + ,85 + ,85 + ,84 + ,84 + ,82 + ,82 + ,82 + ,82 + ,82 + ,81 + ,81 + ,80 + ,80 + ,80 + ,80 + ,80 + ,80 + ,80 + ,79 + ,79 + ,79 + ,79 + ,79 + ,79 + ,79 + ,78 + ,78 + ,78 + ,78 + ,78 + ,77 + ,77 + ,76 + ,76 + ,76 + ,75 + ,75 + ,75 + ,75 + ,74 + ,74 + ,74 + ,74 + ,74 + ,73 + ,73 + ,73 + ,73 + ,72 + ,72 + ,72 + ,71 + ,71 + ,71 + ,71 + ,70 + ,70 + ,70 + ,70 + ,70 + ,70 + ,70 + ,70 + ,70 + ,70 + ,69 + ,69 + ,69 + ,69 + ,69 + ,68 + ,68 + ,68 + ,68 + ,68 + ,67 + ,67 + ,66 + ,66 + ,66 + ,66 + ,66 + ,66 + ,66 + ,65 + ,65 + ,65 + ,65 + ,65 + ,65 + ,64 + ,64 + ,64 + ,64 + ,64 + ,64 + ,64 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,63 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,62 + ,61 + ,61 + ,61 + ,61 + ,61 + ,61 + ,61 + 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+ ,26 + ,26 + ,26 + ,26 + ,25 + ,25 + ,25 + ,25 + ,25 + ,25 + ,24 + ,24 + ,24 + ,24 + ,24 + ,24 + ,24 + ,24 + ,23 + ,23 + ,23 + ,23 + ,23 + ,22 + ,21 + ,21 + ,20 + ,20) > n <- length(x) > c <- array(NA,dim=c(3201)) > l <- array(NA,dim=c(3201)) > mx <- -1.0 > mxli <- -999 > for (i in 1:1601) + { + l[i] <- (i-201)/100 + if (l[i] != 0) + { + x1 <- (x^l[i] - 1) / l[i] + } else { + x1 <- log(x) + } + c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),x1) + if (mx < c[i]) + { + mx <- c[i] + mxli <- l[i] + } + } > c [1] -0.9545053 -0.9550496 -0.9555912 -0.9561301 -0.9566663 -0.9571997 [7] -0.9577304 -0.9582583 -0.9587834 -0.9593058 -0.9598253 -0.9603420 [13] -0.9608559 -0.9613670 -0.9618752 -0.9623805 -0.9628830 -0.9633826 [19] -0.9638793 -0.9643731 -0.9648640 -0.9653519 -0.9658369 -0.9663190 [25] -0.9667980 -0.9672741 -0.9677473 -0.9682174 -0.9686845 -0.9691486 [31] -0.9696096 -0.9700676 -0.9705226 -0.9709744 -0.9714232 -0.9718689 [37] -0.9723115 -0.9727510 -0.9731874 -0.9736206 -0.9740506 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NA NA NA NA [2839] NA NA NA NA NA NA [2845] NA NA NA NA NA NA [2851] NA NA NA NA NA NA [2857] NA NA NA NA NA NA [2863] NA NA NA NA NA NA [2869] NA NA NA NA NA NA [2875] NA NA NA NA NA NA [2881] NA NA NA NA NA NA [2887] NA NA NA NA NA NA [2893] NA NA NA NA NA NA [2899] NA NA NA NA NA NA [2905] NA NA NA NA NA NA [2911] NA NA NA NA NA NA [2917] NA NA NA NA NA NA [2923] NA NA NA NA NA NA [2929] NA NA NA NA NA NA [2935] NA NA NA NA NA NA [2941] NA NA NA NA NA NA [2947] NA NA NA NA NA NA [2953] NA NA NA NA NA NA [2959] NA NA NA NA NA NA [2965] NA NA NA NA NA NA [2971] NA NA NA NA NA NA [2977] NA NA NA NA NA NA [2983] NA NA NA NA NA NA [2989] NA NA NA NA NA NA [2995] NA NA NA NA NA NA [3001] NA NA NA NA NA NA [3007] NA NA NA NA NA NA [3013] NA NA NA NA NA NA [3019] NA NA NA NA NA NA [3025] NA NA NA NA NA NA [3031] NA NA NA NA NA NA [3037] NA NA NA NA NA NA [3043] NA NA NA NA NA NA [3049] NA NA NA NA NA NA [3055] NA NA NA NA NA NA [3061] NA NA NA NA NA NA [3067] NA NA NA NA NA NA [3073] NA NA NA NA NA NA [3079] NA NA NA NA NA NA [3085] NA NA NA NA NA NA [3091] NA NA NA NA NA NA [3097] NA NA NA NA NA NA [3103] NA NA NA NA NA NA [3109] NA NA NA NA NA NA [3115] NA NA NA NA NA NA [3121] NA NA NA NA NA NA [3127] NA NA NA NA NA NA [3133] NA NA NA NA NA NA [3139] NA NA NA NA NA NA [3145] NA NA NA NA NA NA [3151] NA NA NA NA NA NA [3157] NA NA NA NA NA NA [3163] NA NA NA NA NA NA [3169] NA NA NA NA NA NA [3175] NA NA NA NA NA NA [3181] NA NA NA NA NA NA [3187] NA NA NA NA NA NA [3193] NA NA NA NA NA NA [3199] NA NA NA > mx [1] -0.1433055 > mxli [1] 14 > if (mxli != 0) + { + x1 <- (x^mxli - 1) / mxli + } else { + x1 <- log(x) + } > postscript(file="/var/wessaorg/rcomp/tmp/1y2wj1342168333.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/2bdxe1342168333.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/3uka31342168333.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/4h6x41342168333.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(x) > qqline(x) > grid() > mtext('Original Data') > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/5cgig1342168333.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(x1) > qqline(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.end(a) > table.save(a,file="/var/wessaorg/rcomp/tmp/66e1a1342168334.tab") > > try(system("convert tmp/1y2wj1342168333.ps tmp/1y2wj1342168333.png",intern=TRUE)) character(0) > try(system("convert tmp/2bdxe1342168333.ps tmp/2bdxe1342168333.png",intern=TRUE)) character(0) > try(system("convert tmp/3uka31342168333.ps tmp/3uka31342168333.png",intern=TRUE)) character(0) > try(system("convert tmp/4h6x41342168333.ps tmp/4h6x41342168333.png",intern=TRUE)) character(0) > try(system("convert tmp/5cgig1342168333.ps tmp/5cgig1342168333.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 3.385 0.376 3.760